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Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nystr\"om approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices. [ABSTRACT FROM AUTHOR]

High-fidelity computer simulations of childbirth remain prohibitively expensive and time consuming, making them impractical for guiding decision-making during obstetric emergencies. Cheap computer simulations that preserve the accuracy of high-fidelity models can be developed using surrogate modeling. Two common approaches to surrogate modeling are physics-based reduced order modeling (ROM) and machine learning (ML), with the latter gaining popularity as the scientific computing community seeks to leverage advances from other, mostly non-physics-based, computational strategies. Although ROM and ML have been compared for various problems, to our knowledge, such a comparison for simulations of vaginal deformations is currently missing. This study provides a baseline numerical comparison between methods from these two fundamentally different approaches. Since there are many methods falling into each modeling approach, to provide a fair and natural comparison, we select a basic model from each category, with each allowing (i) a straightforward implementation in commercial software packages, and (ii) use by practitioners with limited experience in the field. As a benchmark for the numerical comparison of the ROM and ML approaches, we use the finite element (FE) modeling of the ex vivo deformations of rat vaginal tissue subjected to inflation testing to study the effect of a pre-imposed tear. From the ROM strategies, we consider a simplified Galerkin ROM (G-ROM) that is based on the linearization of the underlying nonlinear equations. From the ML strategies, we select a feed-forward neural network to create mappings from constitutive model parameters and luminal pressure values to either the FE displacement history (in which case we denote the resulting model ML) or the proper orthogonal decomposition (POD) coefficients of the displacement history (in which case we denote the resulting model POD-ML). The numerical investigation of G-ROM, ML, and POD-ML takes place in the reconstructive regime. The numerical results show that the G-ROM outperforms the ML model in terms of offline central processing unit (CPU) time for model training, online CPU time required to generate approximations, and relative error with respect to the FE models. The G-ROM achieves superior error performance to the best ML model with 11 POD basis functions. With higher-dimensional POD bases, the G-ROM achieves a relative error 3 orders of magnitude lower than that of the best ML model with an online CPU time still on the same order of magnitude as the best ML model. The POD-ML model improves on the speed performance of the ML, having online CPU times comparable to those of the G-ROM given the same size of POD bases. However, the POD-ML model does not improve on the error performance of the ML and is still outperformed by the G-ROM for POD bases of size greater than 11. This baseline numerical investigation serves as a starting point for future computer simulations that consider state-of-the-art G-ROM and ML strategies, and the in vivo geometry, boundary conditions, and material properties of the human vagina, as well as their changes during labor. [ABSTRACT FROM AUTHOR]

Recent experiments show that the diffusivities of C8 and C10 n‐alkanes in ZIF‐8 are higher than those of C7 and C9, respectively. We investigated this unusual 'odd‐even' effect by simulating the adsorption of C7‐C14 n‐alkanes in ZIF‐8 using hybrid Monte Carlo molecular simulations. The resultant adsorption isotherms, guest‐host energies, isosteric heats, and chain length distributions are analyzed for trends among the n‐alkanes. ZIF‐8 cages filled with n‐alkanes are characterized using a combination of image processing and data science to quantify the differences in packing that occur with chain length. Results indicate that packing changes drastically from C7 to C8 and from C9 to C10, which is consistent with the diffusion trends previously reported in experiments. [ABSTRACT FROM AUTHOR]

Complex systems, as interwoven miscellaneous interacting entities that emerge and evolve through self-organization in a myriad of spiraling contexts, exhibit subtleties on global scale besides steering the way to understand complexity which has been under evolutionary processes with unfolding cumulative nature wherein order is viewed as the unifying framework. Indicating the striking feature of non-separability in components, a complex system cannot be understood in terms of the individual isolated constituents' properties per se, it can rather be comprehended as a way to multilevel approach systems behavior with systems whose emergent behavior and pattern transcend the characteristics of ubiquitous units composing the system itself. This observation specifies a change of scientific paradigm, presenting that a reductionist perspective does not by any means imply a constructionist view; and in that vein, complex systems science, associated with multiscale problems, is regarded as ascendancy of emergence over reductionism and level of mechanistic insight evolving into complex system. While evolvability being related to the species and humans owing their existence to their ancestors' capability with regards to adapting, emerging and evolving besides the relation between complexity of models, designs, visualization and optimality, a horizon that can take into account the subtleties making their own means of solutions applicable is to be entailed by complexity. Such views attach their germane importance to the future science of complexity which may probably be best regarded as a minimal history congruent with observable variations, namely the most parallelizable or symmetric process which can turn random inputs into regular outputs. Interestingly enough, chaos and nonlinear systems come into this picture as cousins of complexity which with tons of its components are involved in a hectic interaction with one another in a nonlinear fashion amongst the other related systems and fields. Relation, in mathematics, is a way of connecting two or more things, which is to say numbers, sets or other mathematical objects, and it is a relation that describes the way the things are interrelated to facilitate making sense of complex mathematical systems. Accordingly, mathematical modeling and scientific computing are proven principal tools toward the solution of problems arising in complex systems' exploration with sound, stimulating and innovative aspects attributed to data science as a tailored-made discipline to enable making sense out of voluminous (-big) data. Regarding the computation of the complexity of any mathematical model, conducting the analyses over the run time is related to the sort of data determined and employed along with the methods. This enables the possibility of examining the data applied in the study, which is dependent on the capacity of the computer at work. Besides these, varying capacities of the computers have impact on the results; nevertheless, the application of the method on the code step by step must be taken into consideration. In this sense, the definition of complexity evaluated over different data lends a broader applicability range with more realism and convenience since the process is dependent on concrete mathematical foundations. All of these indicate that the methods need to be investigated based on their mathematical foundation together with the methods. In that way, it can become foreseeable what level of complexity will emerge for any data desired to be employed. With relation to fractals, fractal theory and analysis are geared toward assessing the fractal characteristics of data, several methods being at stake to assign fractal dimensions to the datasets, and within that perspective, fractal analysis provides expansion of knowledge regarding the functions and structures of complex systems while acting as a potential means to evaluate the novel areas of research and to capture the roughness of objects, their nonlinearity, randomness, and so on. The idea of fractional-order integration and differentiation as well as the inverse relationship between them lends fractional calculus applications in various fields spanning across science, medicine and engineering, amongst the others. The approach of fractional calculus, within mathematics-informed frameworks employed to enable reliable comprehension into complex processes which encompass an array of temporal and spatial scales notably provides the novel applicable models through fractional-order calculus to optimization methods. Computational science and modeling, notwithstanding, are oriented toward the simulation and investigation of complex systems through the use of computers by making use of domains ranging from mathematics to physics as well as computer science. A computational model consisting of numerous variables that characterize the system under consideration allows the performing of many simulated experiments via computerized means. Furthermore, Artificial Intelligence (AI) techniques whether combined or not with fractal, fractional analysis as well as mathematical models have enabled various applications including the prediction of mechanisms ranging extensively from living organisms to other interactions across incredible spectra besides providing solutions to real-world complex problems both on local and global scale. While enabling model accuracy maximization, AI can also ensure the minimization of functions such as computational burden. Relatedly, level of complexity, often employed in computer science for decision-making and problem-solving processes, aims to evaluate the difficulty of algorithms, and by so doing, it helps to determine the number of required resources and time for task completion. Computational (-algorithmic) complexity, referring to the measure of the amount of computing resources (memory and storage) which a specific algorithm consumes when it is run, essentially signifies the complexity of an algorithm, yielding an approximate sense of the volume of computing resources and seeking to prove the input data with different values and sizes. Computational complexity, with search algorithms and solution landscapes, eventually points toward reductions vis à vis universality to explore varying degrees of problems with different ranges of predictability. Taken together, this line of sophisticated and computer-assisted proof approach can fulfill the requirements of accuracy, interpretability, predictability and reliance on mathematical sciences with the assistance of AI and machine learning being at the plinth of and at the intersection with different domains among many other related points in line with the concurrent technical analyses, computing processes, computational foundations and mathematical modeling. Consequently, as distinctive from the other ones, our special issue series provides a novel direction for stimulating, refreshing and innovative interdisciplinary, multidisciplinary and transdisciplinary understanding and research in model-based, data-driven modes to be able to obtain feasible accurate solutions, designed simulations, optimization processes, among many more. Hence, we address the theoretical reflections on how all these processes are modeled, merging all together the advanced methods, mathematical analyses, computational technologies, quantum means elaborating and exhibiting the implications of applicable approaches in real-world systems and other related domains. [ABSTRACT FROM AUTHOR]

Population declines and range contractions due to habitat loss are pervasive among nonhuman primates, with 60% of species threatened with extinction. However, the extensive vocal activity displayed by many primates makes them excellent candidates for passive acoustic surveys. Passive acoustic survey data is increasingly being used to support occupancy models, which have proven to be an efficient means of estimating both population trends and distributions. Passive acoustic surveys can be conducted relatively quickly and at broad scales, but efficient audio data processing has long proven elusive. The machine learning algorithm BirdNET was originally developed for birds but was recently expanded to include nonavian taxa. We demonstrate that BirdNET can accurately and efficiently identify an endangered primate, the Yucatán black howler monkey (Alouatta pigra), by sound in passive acoustic survey data (collected in southeastern Chiapas, Mexico), enabling us to use a single‐season occupancy model to inform further survey efforts. Importantly, we also generated data on up to 286 co‐occurring bird species, demonstrating the value of integrated animal sound classification tools for biodiversity surveys. BirdNET is freely available, requires no computer science expertise to use, and can readily be expanded to include more species (e.g., its species list recently tripled to >3000), suggesting that passive acoustic surveys, and thus occupancy modeling, for primate conservation could rapidly become much more accessible. Importantly, the long history of bioacoustics in primate research has yielded a wealth of information about their vocal behavior, which can facilitate appropriate survey design and data interpretation. Highlights: The BirdNET algorithm was developed to identify birds by sound but was recently expanded to include non‐avian taxa; we demonstrate that it can identify an endangered primate, the Yucatán black howler monkey (Alouatta pigra).BirdNET‐based howler monkey detections enabled us to use an occupancy model to inform further survey efforts—and to generate data on up to 286 co‐occurring bird species, illustrating the value of multispecies classifiers for biodiversity surveys.Combining free and easy‐to‐use tools like BirdNET, passive acoustic surveys, and occupancy modeling can facilitate rapid, broad‐scale assessments of primate population trends and distributions. [ABSTRACT FROM AUTHOR]

The dynamic formulation of optimal transport has attracted growing interest in scientific computing and machine learning, and its computation requires solving a PDE-constrained optimization problem. The classical Eulerian discretization based approaches suffer from the curse of dimensionality, which arises from the approximation of a high-dimensional velocity field. In this work, we propose a deep learning based method for solving the dynamic optimal transport in highdimensional space. Our method contains three main ingredients: a carefully designed representation of the velocity field, the discretization of the PDE constraint along the characteristics, and the computation of a high-dimensional integral by the Monte Carlo method in each time step. Specifically, in the representation of the velocity field, we apply the classical nodal basis function in time and the deep neural networks in the space domain with the H1-norm regularization. This technique promotes the regularity of the velocity field in both time and space such that the discretization along the characteristic remains stable during the training process. Extensive numerical examples have been conducted to test the proposed method. Compared to other solvers of optimal transport, our method could give more accurate results in high-dimensional cases and has very good scalability with respect to dimension. Finally, we extend our method to more complicated cases such as the crowd motion problem. [ABSTRACT FROM AUTHOR]

There is a wide variety of techniques and models for forecasting electrical energy consumption, depending on both the type of user, the forecast horizon, and the resolution of the available data. Likewise, there are different metrics to evaluate the performance of these models. So, in this research an integrated multi-criteria methodology is proposed to select the best forecast model for residential electricity consumption, using the Analytical Hierarchical Process (AHP) to establish the weights of relative importance of the decision criteria, and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to make the selection of the optimal model. The methodology is in turn framed within a data science process, through which the data is extracted, processed, and analyzed, prior to the application of the machine learning algorithms to obtain the forecast models, which will correspond to decision alternatives. The performance metrics in the evaluation phase of the models, and the performance metrics obtained from the forecast phase, are considered as the decision criteria. From the pairwise comparisons technique, it was obtained that the mean absolute percentage error (MAPE) of the prognosis phase was the criterion with the greatest weight of importance, followed by the coefficient of determination R2 and the MAPE of the evaluation phase. From the TOPSIS method, the Multiple Linear Regression model was selected as the optimal forecast model. [ABSTRACT FROM AUTHOR]

Scientific computing heavily relies on data shared by the community, especially in distributed data-intensive applications. This research focuses on predicting slow connections that create bottlenecks in distributed workflows. In this study, we analyze network traffic logs collected between January 2021 and August 2022 at the National Energy Research Scientific Computing Center (NERSC). Based on the observed patterns, we define a set of features primarily based on history for identifying low-performing data transfers. Typically, there are far fewer slow connections on well-maintained networks, which creates difficulty in learning to identify these abnormally slow connections from the normal ones. We devise several stratified sampling techniques to address the class-imbalance challenge and study how they affect the machine learning approaches. Our tests show that a relatively simple technique that undersamples the normal cases to balance the number of samples in two classes (normal and slow) is very effective for model training. This model predicts slow connections with an F1 score of 0.926. [ABSTRACT FROM AUTHOR]

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data. [ABSTRACT FROM AUTHOR]

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning. [ABSTRACT FROM AUTHOR]

Researchers across cognitive, neuro- and computer sciences increasingly reference 'human-like' artificial intelligence and 'neuroAI'. However, the scope and use of the terms are often inconsistent. Contributed research ranges widely from mimicking behaviour, to testing machine learning methods as neurally plausible hypotheses at the cellular or functional levels, or solving engineering problems. However, it cannot be assumed nor expected that progress on one of these three goals will automatically translate to progress in others. Here, a simple rubric is proposed to clarify the scope of individual contributions, grounded in their commitments to human-like behaviour, neural plausibility or benchmark/engineering/computer science goals. This is clarified using examples of weak and strong neuroAI and human-like agents, and discussing the generative, corroborate and corrective ways in which the three dimensions interact with one another. The author maintains that future progress in artificial intelligence will need strong interactions across the disciplines, with iterative feedback loops and meticulous validity tests—leading to both known and yet-unknown advances that may span decades to come. This article is part of a discussion meeting issue 'New approaches to 3D vision'. [ABSTRACT FROM AUTHOR]

Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning. To solve PDEs with Dirichlet boundary condition, our "Q-PDE" algorithm is mesh-free and therefore has the potential to overcome the curse of dimensionality. Using a neural tangent kernel (NTK) approach, we prove that the neural network approximator for the PDE solution, trained with the QPDE algorithm, converges to the trajectory of an infinite-dimensional ordinary differential equation (ODE) as the number of hidden units → ∞. For monotone PDEs (i.e. those given by monotone operators, which may be nonlinear), despite the lack of a spectral gap in the NTK, we then prove that the limit neural network, which satisfies the infinite-dimensional ODE, strongly converges in L² to the PDE solution as the training time → ∞. More generally, we can prove that any fixed point of the wide-network limit for the Q-PDE algorithm is a solution of the PDE (not necessarily under the monotone condition). The numerical performance of the Q-PDE algorithm is studied for several elliptic PDEs. [ABSTRACT FROM AUTHOR]

Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein “hyperedges” may connect any number of nodes. As a result, hypergraph partitioning is an NP-Hard problem to both solve or approximate. State-of-the-art algorithms that solve this problem follow the multilevel paradigm, which begins by iteratively “coarsening” the input hypergraph to smaller problem instances that share key structural features. Once identifying an approximate problem that is small enough to be solved directly, that solution can be interpolated and refined to the original problem. While this strategy represents an excellent trade off between quality and running time, it is sensitive to coarsening strategy. In this work we propose using graph embeddings of the initial hypergraph in order to ensure that coarsened problem instances retrain key structural features. Our approach prioritizes coarsening within self-similar regions within the input graph, and leads to significantly improved solution quality across a range of considered hypergraphs. Reproducibility: All source code, plots and experimental data are available at https://sybrandt.com/2019/partition. [ABSTRACT FROM AUTHOR]

Fatal diseases like cancer, dementia, and diabetes are very dangerous. This leads to fear of death if these are not diagnosed at early stages. Computer science uses biomedical studies to diagnose cancer, dementia, and diabetes. With the advancement of machine learning, there are various techniques which are accessible to predict and prognosis these diseases based on different datasets. These datasets varied (image datasets and CSV datasets) around the world. So, there is a need for some machine learning classifiers to predict cancer, dementia, and diabetes in a human. In this paper, we used a multifactorial genetic inheritance disorder dataset to predict cancer, dementia, and diabetes. Several studies used different machine learning classifiers to predict cancer, dementia, and diabetes separately with the help of different types of datasets. So, in this paper, multiclass classification proposed methodology used support vector machine (SVM) and K-nearest neighbor (KNN) machine learning techniques to predict three diseases and compared these techniques based on accuracy. Simulation results have shown that the proposed model of SVM and KNN for prediction of dementia, cancer, and diabetes from multifactorial genetic inheritance disorder achieved 92.8% and 92.5%, 92.8% and 91.2% accuracy during training and testing, respectively. So, it is observed that proposed SVM-based dementia, cancer, and diabetes from multifactorial genetic inheritance disorder prediction (MGIDP) give attractive results as compared with the proposed model of KNN. The application of the proposed model helps to prognosis and prediction of cancer, dementia, and diabetes before time and plays a vital role to minimize the death ratio around the world. [ABSTRACT FROM AUTHOR]

The article introduces a new section structure for the SIAM Journal on Scientific Computing (SISC), including a focus on Scientific Machine Learning as a major development in the field of scientific computing. Topics include the development of accurate, efficient, and scalable machine learning algorithms for solving mathematical modeling problems, emphasizing the importance of reproducibility in the review process.

We present an introduction to some of the state of the art in reduced order and surrogate modeling in gravitational-wave (GW) science. Approaches that we cover include principal component analysis, proper orthogonal (singular value) decompositions, the reduced basis approach, the empirical interpolation method, reduced order quadratures, and compressed likelihood evaluations. We divide the review into three parts: representation/compression of known data, predictive models, and data analysis. The targeted audience is practitioners in GW science, a field in which building predictive models and data analysis tools that are both accurate and fast to evaluate, especially when dealing with large amounts of data and intensive computations, are necessary yet can be challenging. As such, practical presentations and, sometimes, heuristic approaches are here preferred over rigor when the latter is not available. This review aims to be self-contained, within reasonable page limits, with little previous knowledge (at the undergraduate level) requirements in mathematics, scientific computing, and related disciplines. Emphasis is placed on optimality, as well as the curse of dimensionality and approaches that might have the promise of beating it. We also review most of the state of the art of GW surrogates. Some numerical algorithms, conditioning details, scalability, parallelization and other practical points are discussed. The approaches presented are to a large extent non-intrusive (in the sense that no differential equations are invoked) and data-driven and can therefore be applicable to other disciplines. We close with open challenges in high dimension surrogates, which are not unique to GW science. [ABSTRACT FROM AUTHOR]

The integration of machine learning (Keplerian paradigm) and more general artificial intelligence technologies with physical modeling based on first principles (Newtonian paradigm) will impact scientific computing in engineering in fundamental ways. Such hybrid models combine first principle-based models with data-based models into a joint architecture. This paper will give some background, explain trends and showcase recent achievements from an applied mathematics and industrial perspective. Examples include characterization of superconducting accelerator magnets by blending data with physics, data-driven magnetostatic field simulation without an explicit model of the constitutive law, and Bayesian free-shape optimization of a trace pair with bend on a printed circuit board. [ABSTRACT FROM AUTHOR]

Microbioreactor (MBR) devices have emerged as powerful cultivation tools for tasks of microbial phenotyping and bioprocess characterization and provide a wealth of online process data in a highly parallelized manner. Such datasets are difficult to interpret in short time by manual workflows. In this study, we present the Python package bletl and show how it enables robust data analyses and the application of machine learning techniques without tedious data parsing and preprocessing. bletl reads raw result files from BioLector I, II and Pro devices to make all the contained information available to Python‐based data analysis workflows. Together with standard tooling from the Python scientific computing ecosystem, interactive visualizations and spline‐based derivative calculations can be performed. Additionally, we present a new method for unbiased quantification of time‐variable specific growth rate μ⃗t$\overrightarrow{\mu }_t$ based on unsupervised switchpoint detection with Student‐t distributed random walks. With an adequate calibration model, this method enables practitioners to quantify time‐variable growth rate with Bayesian uncertainty quantification and automatically detect switch‐points that indicate relevant metabolic changes. Finally, we show how time series feature extraction enables the application of machine learning methods to MBR data, resulting in unsupervised phenotype characterization. As an example, Neighbor Embedding (t‐SNE) is performed to visualize datasets comprising a variety of growth/DO/pH phenotypes. [ABSTRACT FROM AUTHOR]

Nowadays, computer simulations have become a standard tool in essentially all fields of chemistry, condensed matter physics, and materials science. In order to keep up with state-of-the-art experiments and the ever growing complexity of the investigated problems, there is a constantly increasing need for simulations of more realistic, i.e., larger, model systems with improved accuracy. In many cases, the availability of sufficiently efficient interatomic potentials providing reliable energies and forces has become a serious bottleneck for performing these simulations. To address this problem, currently a paradigm change is taking place in the development of interatomic potentials. Since the early days of computer simulations simplified potentials have been derived using physical approximations whenever the direct application of electronic structure methods has been too demanding. Recent advances in machine learning (ML) now offer an alternative approach for the representation of potential-energy surfaces by fitting large data sets from electronic structure calculations. In this perspective, the central ideas underlying these ML potentials, solved problems and remaining challenges are reviewed along with a discussion of their current applicability and limitations. [ABSTRACT FROM AUTHOR]

Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we propose homotopy physics-informed neural networks (HomPINNs), a novel framework that leverages homotopy continuation and neural networks (NNs) to solve inverse problems. The proposed framework begins with the use of NNs to simultaneously approximate unlabeled observations across diverse solutions while adhering to DE constraints. Through homotopy continuation, the proposed method solves the inverse problem by tracing the observations and identifying multiple solutions. The experiments involve testing the performance of the proposed method on one-dimensional DEs and applying it to solve a two-dimensional Gray-Scott simulation. Our findings demonstrate that the proposed method is scalable and adaptable, providing an effective solution for solving DEs with multiple solutions and unknown parameters. Moreover, it has significant potential for various applications in scientific computing, such as modeling complex systems and solving inverse problems in physics, chemistry, biology, etc. • Physics-informed neural networks are used to estimate unknown parameters with physical constraints. • HomPINNs helps to identify multiple solutions and solve inverse problems. • Numerical examples demonstrate its scalability and adaptability. • HomPINNs facilitates the discovery of previously unknown solutions. [ABSTRACT FROM AUTHOR]

Many applications in scientific computing process very large sparse matrices on parallel architectures. The presented work in this paper is a part of a project where our general aim is to develop an auto-tuner system for the selection of the best matrix compression format in the context of high-performance computing. The target smart system can automatically select the best compression format for a given sparse matrix, a numerical method processing this matrix, a parallel programming model and a target architecture. Hence, this paper describes the design and implementation of the proposed concept. We consider a case study consisting of a numerical method reduced to the sparse matrix vector product (SpMV), some compression formats, the data parallel as a programming model and, a distributed multi-core platform as a target architecture. This study allows extracting a set of important novel metrics and parameters which are relative to the considered programming model. Our metrics are used as input to a machine-learning algorithm to predict the best matrix compression format. An experimental study targeting a distributed multi-core platform and processing random and real-world matrices shows that our system can improve in average up to 7% the accuracy of the machine learning. [ABSTRACT FROM AUTHOR]

Data-parallel applications, such as data analytics, machine learning, and scientific computing, are placing an ever-growing demand on floating-point operations per second on emerging systems. With increasing integration density, the quest for energy efficiency becomes the number one design concern. While dedicated accelerators provide high energy efficiency, they are over-specialized and hard to adjust to algorithmic changes. We propose an architectural concept that tackles the issues of achieving extreme energy efficiency while still maintaining high flexibility as a general-purpose compute engine. The key idea is to pair a tiny 10kGE (kilo gate equivalent) control core, called Snitch, with a double-precision floating-point unit (FPU) to adjust the compute to control ratio. While traditionally minimizing non-floating-point unit (FPU) area and achieving high floating-point utilization has been a trade-off, with Snitch, we achieve them both, by enhancing the ISA with two minimally intrusive extensions: stream semantic registers (SSR) and a floating-point repetition instruction (FREP). SSRs allow the core to implicitly encode load/store instructions as register reads/writes, eliding many explicit memory instructions. The FREP extension decouples the floating-point and integer pipeline by sequencing instructions from a micro-loop buffer. These ISA extensions significantly reduce the pressure on the core and free it up for other tasks, making Snitch and FPU effectively dual-issue at a minimal incremental cost of 3.2 percent. The two low overhead ISA extensions make Snitch more flexible than a contemporary vector processor lane, achieving a $2\times$ 2 × energy-efficiency improvement. We have evaluated the proposed core and ISA extensions on an octa-core cluster in 22 nm technology. We achieve more than $6\times$ 6 × multi-core speed-up and a $3.5\times$ 3. 5 × gain in energy efficiency on several parallel microkernels. [ABSTRACT FROM AUTHOR]

It is a fact that technology has made a great contribution to our lives and has a great impact on society. With the development of technology, the amount of data created on the internet has also increased. In particular, social media has turned into an important medium where users can share their beliefs and opinions freely. In this regard, many different sectors have started scrutinizing users’ opinions and emotions with the “opinion mining” method which is one of the fields of Natural Language Processing (NLP). The objective of this paper is to present an approach towards analyzing the community interpreters’ emotions and opinions using “opinion mining” method. In other words, this paper aims at providing a new insight into community interpreting research by introducing opinion mining and sentiment analysis methods, which are mainly used in Computer Science and Management Information Systems. With this aim in mind, the contributions of the opinion mining method to community interpreting research have been discussed with a descriptive approach. [ABSTRACT FROM AUTHOR]

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this work, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems. [ABSTRACT FROM AUTHOR]

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modelled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalisation error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speedup over competing algorithms. [ABSTRACT FROM AUTHOR]

We propose a supervised deep learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly outperforms standard deep learning algorithms that are based on randomly chosen training data for problems in moderately high dimensions. The proposed algorithm provides an efficient method for building inexpensive surrogates for many underlying maps in the context of scientific computing. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) is integral to Industry 4.0 and the evolution of smart factories. To realize this future, material processing industries are embarking on adopting AI technologies into their enterprise and plants; however, like all new technologies, there is always the potential for misuse or the false belief that the outcomes are reliable. The goal of this paper is to provide context for the application of machine learning to materials processing. The general landscapes of data science and materials processing are presented, using the foundry and the metal casting industry as an exemplar. The challenges that exist with typical foundry data are that the data are unbalanced, semi-supervised, heterogeneous, and limited in sample size. Data science methods to address these issues are presented and discussed. The elements of a data science project are outlined and illustrated by a case study using sand cast foundry data. Finally, a prospective view of the application of data science to materials processing and the impact this will have in the field are given. [ABSTRACT FROM AUTHOR]

Machine Learning methods are emerging as faster and efficient alternatives to numerical simulation techniques. The field of Scientific Computing has started adopting these data-driven approaches to faithfully model physical phenomena using scattered, noisy observations from coarse-grained grid-based simulations. In this paper, we investigate data-driven modelling of Bose-Einstein Condensates (BECs). In particular, we use Gaussian Processes (GPs) to model the ground state wave function of BECs as a function of scattering parameters from the dimensionless Gross Pitaveskii Equation (GPE). Experimental results illustrate the ability of GPs to accurately reproduce ground state wave functions using a limited number of data points from simulations. Consistent performance across different configurations of BECs, namely Scalar and Vectorial BECs generated under different potentials, including harmonic, double well and optical lattice potentials pronounces the versatility of our method. Comparison with existing data-driven models indicates that our model achieves similar accuracy with only a small fraction ( 1 50 th) of data points used by existing methods, in addition to modelling uncertainty from data. When used as a simulator post-training, our model generates ground state wave functions 36 × faster than Trotter Suzuki, a numerical approximation technique that uses Imaginary time evolution. Our method is quite general; with minor changes it can be applied to similar quantum many-body problems. [ABSTRACT FROM AUTHOR]

Scientific machine learning (SciML), an area of research where techniques from machine learning and scientific computing are combined, has become of increasing importance and receives growing attention. Here, our focus is on a very specific area within SciML given by the combination of domain decomposition methods (DDMs) with machine learning techniques for the solution of partial differential equations. The aim of the present work is to make an attempt of providing a review of existing and also new approaches within this field as well as to present some known results in a unified framework; no claim of completeness is made. As a concrete example of machine learning enhanced DDMs, an approach is presented which uses neural networks to reduce the computational effort in adaptive DDMs while retaining their robustness. More precisely, deep neural networks are used to predict the geometric location of constraints which are needed to define a robust coarse space. Additionally, two recently published deep domain decomposition approaches are presented in a unified framework. Both approaches use physics‐constrained neural networks to replace the discretization and solution of the subdomain problems of a given decomposition of the computational domain. Finally, a brief overview is given of several further approaches which combine machine learning with ideas from DDMs to either increase the performance of already existing algorithms or to create completely new methods. [ABSTRACT FROM AUTHOR]

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering applications. This work proposes Neural Galerkin schemes based on deep learning that generate training data with active learning for numerically solving high-dimensional partial differential equations. Neural Galerkin schemes build on the Dirac-Frenkel variational principle to train networks by minimizing the residual sequentially over time, which enables adaptively collecting new training data in a self-informed manner that is guided by the dynamics described by the partial differential equations. This is in contrast to other machine learning methods that aim to fit network parameters globally in time without taking into account training data acquisition. Our finding is that the active form of gathering training data of the proposed Neural Galerkin schemes is key for numerically realizing the expressive power of networks in high dimensions. Numerical experiments demonstrate that Neural Galerkin schemes have the potential to enable simulating phenomena and processes with many variables for which traditional and other deep-learning-based solvers fail, especially when features of the solutions evolve locally such as in high-dimensional wave propagation problems and interacting particle systems described by Fokker-Planck and kinetic equations. • Coupling training of deep networks with adaptive data acquisition to solve high-dimensional evolution equations. • Enables predicting local features in high dimensions for which training with classical, uniform data acquisition fails. • Sequentially collects data over time and so avoids requirement of having rich initial data set over the time-space domain. • Suited for transport problems, for which collocation-based deep-network methods with uniform data sampling are inefficient. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) is a fast-growing research area in computer science that aims to mimic cognitive processes through a number of techniques. Supervised machine learning, a subfield of AI, includes methods that can identify patterns in high-dimensional data using labeled 'ground truth' data and apply these learnt patterns to analyze, interpret, or make predictions on new datasets. Supervised machine learning has become a significant area of interest within the medical community. Radiology and neuroradiology in particular are especially well suited for application of machine learning due to the vast amount of data that is generated. One devastating disease for which neuroimaging plays a significant role in the clinical management is stroke. Within this context, AI techniques can play pivotal roles for image-based diagnosis and management of stroke. This overview focuses on the recent advances of artificial intelligence methods – particularly supervised machine learning and deep learning – with respect to workflow, image acquisition and reconstruction, and image interpretation in patients with acute stroke, while also discussing potential pitfalls and future applications. • Artificial Intelligence (AI) is a growing subfield of computer science that aims to mimic cognitive processes through a number of techniques. • Superficial AI, which is comprised of techniques that learn patterns with the use of labels of 'ground truth' data, have become a significant area of interest within the medical community. As images are, in essence, volumes of mineable data, radiology is a field of medicine particularly well suited to supervised AI techniques. • AI techniques could play pivotal roles in neuroradiology, particular in the diagnosis and management of time sensitive diseases such as stroke. • Several AI techniques, comprised of machine and deep learning methods, have shown incredible promise as an adjunct to a neuroradiologist's workflow, particularly within stroke imaging. • Although encouraging, there are data protection and medicolegal implications that must be considered for widespread clinical use of AI techniques. [ABSTRACT FROM AUTHOR]

• Neuroscience is rapidly adopting machine-learning in many forms. • Overfitting of parameters in machine-learning is well-known but also misunderstood. • Over-hyping can occur when analyses are optimized, and despite cross-validation. • Over-hyping threatens the integrity of the machine-learning neuroscience literature. • Alternative methods are provided that allow detection and prevention of over-hyping. Machine learning has enhanced the abilities of neuroscientists to interpret information collected through EEG, fMRI, and MEG data. With these powerful techniques comes the danger of overfitting of hyperparameters which can render results invalid. We refer to this problem as 'overhyping' and show that it is pernicious despite commonly used precautions. Overhyping occurs when analysis decisions are made after observing analysis outcomes and can produce results that are partially or even completely spurious. It is commonly assumed that cross-validation is an effective protection against overfitting or overhyping, but this is not actually true. In this article, we show that spurious results can be obtained on random data by modifying hyperparameters in seemingly innocuous ways, despite the use of cross-validation. We recommend a number of techniques for limiting overhyping, such as lock boxes, blind analyses, pre-registrations, and nested cross-validation. These techniques, are common in other fields that use machine learning, including computer science and physics. Adopting similar safeguards is critical for ensuring the robustness of machine-learning techniques in the neurosciences. [ABSTRACT FROM AUTHOR]

The paper introduces DeepForge, a gateway to deep learning for scientific computing. DeepForge provides an easy to use, yet powerful visual/textual interface to facilitate the rapid development of deep learning models by novices as well as experts. Utilizing a cloud-based infrastructure, built-in version control, and multiuser collaboration support, DeepForge promotes reproducibility and ease of access and enables remote execution of machine learning pipelines. The tool currently supports TensorFlow/Keras, but its extensible architecture enables easy integration of additional platforms. [ABSTRACT FROM AUTHOR]

Recently some scientific computing users have discovered that they can replace 64-bit with 32-bit operations for carefully selected portions of the computation, and still retain acceptable accuracy in the final results. In addition, developers of some emerging applications such as machine learning have discovered that they can achieve acceptable results with only 16-bit precision in certain portions of the code. At the other end of the precision spectrum, some users have explored using 128-bit arithmetic in some particularly demanding applications, while others have done computations using much higher precision—hundreds or even thousands of digits. Such work has underscored the need to develop new mathematical and software frameworks to support a dynamically variable level of precision, and, more generally, to rethink what "reproducibility" means in a variable precision environment. This article summarizes some of the work being done in this arena, and lists research problems that need to be solved. [ABSTRACT FROM AUTHOR]

Advanced approaches to predicting offending are increasingly transpiring without the forensic psychology discipline's involvement – an area that it has piloted and influenced for many decades. Computer science experts have built an impressive decade-long literature base on risk assessment – a technical literature that is not only progressing at a fast pace, but appears to function independently, for the most part, from the forensic risk assessment literature. This paper outlines the potential utility of machine learning approaches and the broader 'algorithmic culture', for forensic risk assessment, and the implications their use (and non-use) may have for the discipline. [ABSTRACT FROM AUTHOR]

Transient simulations of dynamic systems, using physics-based scientific computing tools, are practically limited by availability of computational resources and power. While the promise of machine learning has been explored in a variety of scientific disciplines, its application in creation of a framework for computationally expensive transient models has not been fully explored. Here, we present an ensemble approach where one such computationally expensive tool, discrete element method, is combined with time-series forecasting via auto regressive integrated moving average and machine learning methods to simulate a complex pharmaceutical problem: development of an agitation protocol in an agitated filter dryer to ensure uniform solid bed mixing. This ensemble approach leads to a significant reduction in the computational burden, while retaining model accuracy and performance, practically rendering simulations possible. The developed machine-learning model shows good predictability and agreement with the literature, demonstrating its tremendous potential in scientific computing. [ABSTRACT FROM AUTHOR]

While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn low frequency components first. Novel architectures such as multi-scale deep neural network (MscaleDNN) were proposed to alleviate this problem to some extent. In this paper, we construct a subspace decomposition based DNN (dubbed SD2NN) architecture for a class of multi-scale problems by combining MscaleDNN algorithms with traditional numerical analysis ideas. The proposed architecture includes one low frequency normal DNN submodule, and one (or a few) high frequency MscaleDNN submodule(s), which are designed to capture the smooth part and the oscillatory part of the multi-scale solutions simultaneously. We demonstrate that the SD2NN outperforms existing models such as MscaleDNN, through several benchmark multi-scale problems in regular or perforated domains. • We propose SD2NN, a new architecture, combining subspace decomposition from numerical analysis and multiscale DNN solvers. • SD2NN has low/high frequency submodules, simultaneously capturing smooth/oscillatory parts of multi-scale solutions. • The new method outperforms state-of-the-art DNN solvers for 1D-3D multiscale PDEs on regular and perforated domains. [ABSTRACT FROM AUTHOR]

Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. The effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves. Highlights • We put forth a deep learning framework that enables the synergistic combination of mathematical models and data. • We introduce an effective mechanism for regularizing the training of deep neural networks in small data regimes. • The proposed methods enable scientific prediction and discovery from incomplete models and incomplete data. [ABSTRACT FROM AUTHOR]

Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier-Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression. This new algorithm employs Bayesian inference to tune the hyperparameters automatically. Our approach is effective, robust and able to quantify uncertainties by providing an error bar for each discovered candidate equation. The effectiveness of our algorithm is demonstrated through a collection of classical ODEs and PDEs. Numerical experiments demonstrate the robustness of our algorithm with respect to noisy data and its ability to discover various candidate equations with error bars that represent the quantified uncertainties. Detailed comparisons with the sequential threshold least-squares algorithm and the lasso algorithm are studied from noisy time-series measurements and indicate that the proposed method provides more robust and accurate results. In addition, the datadriven prediction of dynamics with error bars using discovered governing physical laws is more accurate and robust than classical polynomial regressions. [ABSTRACT FROM AUTHOR]

Tight collaboration between manycore system designers and machine-learning experts is necessary to create a data-driven manycore design framework that integrates both learning and expert knowledge. Such a framework will be necessary to address the rising complexity of designing large-scale manycore systems and machine-learning techniques. [ABSTRACT FROM AUTHOR]

Medical decision support systems have been on the rise with technological advances and they have been the subject of many studies. Developing an effective medical decision support system requires a high amount of accuracy, precision, and sensitivity as well as time efficiency that is inversely proportional to the complexity of the model. Hepatitis C virus (HCV) infection is one of the most important causes of chronic liver disease worldwide. In this study, data discovery has been made by applying data science processes, and the HCV has been estimated with machine learning methods. By analyzing and visualizing the values in the data set, features that may be important for HCV was determined, and HCV estimation was made using various machine learning methods, pre-processing and feature extraction. According to the features obtained from this study, the estimation of HCV can be made automatically and can be a decision support system that helps the researchers and clinicians. In this study, HCV was obtained with 99.31% accuracy by adding new features and eliminating imbalances between classes. The model in this study can be used as an alternative method in the prediction of Hepatitis C-related diseases. • In this study, data analysis was performed and HCV was estimated by ML methods. • Thanks to the new features obtained, HCV estimation can be made automatically. • In this study, HCV prediction success was increased with the newly obtained features. [ABSTRACT FROM AUTHOR]

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in adversarial network discriminators, network generators are utilized to learn the uncertainty in solutions of partial differential equations observed from the initial/boundary data. Under mild assumptions, we show that the generalization error of the computed generator converges to the approximation error of the network with high probability, when the number of samples are sufficiently taken. According to our established error bound, we also find that our physics-informed WGANs have higher requirement for the capacity of discriminators than that of generators. Numerical results on synthetic examples of partial differential equations are reported to validate our theoretical results and demonstrate how uncertainty quantification can be obtained for solutions of partial differential equations and the distributions of initial/boundary data. However, the quality or the accuracy of the uncertainty quantification theory in all the points in the interior is still the theoretical vacancy, and required for further research. • Wasserstein generative adversarial networks need little priors for uncertainty quantifications. • Physics-informed regularization term enforces the satisfaction of governing PDEs. • The proposed probabilistic model (WGAN-PINNs) is able to deal with non-Gaussian and spatially dependent noise. • WGAN-PINNs have good convergence and generalization properties. • Theoretically we have higher requirements on discriminators than generators. [ABSTRACT FROM AUTHOR]

Gas-particle flows can be well described by highly resolved simulations (HRS). Limited by the daunting computational cost, HRS at scale remains infeasible. Many methods are proposed to strike tradeoffs between accuracy and computational cost. Here, we design a machine learning (ML) based alternate mode to accelerate HRS without sacrificing accuracy. Spatiotemporal samples (~1.3 × 106) generated from two-fluid model-based HRS of gas-particle flows are trained for developing artificial neural network (ANN) and long short-term memory (LSTM) models. Simple time-series predictions consisting of repeated ANN iterations can accurately predict the flow field in ~10−3 s. Hybrid accelerations combining CFD and the offline trained ML in time scale can approximate to the time-series highly resolved flow fields within 1% error, saving 40% computing time. This work may contribute to a new transformative paradigm that how scientific computing can leverage ML to improve gas-particle simulations without new device requirements. [Display omitted] • Gas-particle flow fields are well predicted via ANN and LSTM. • Simple ML can accurately predict the flow field in ~10−3 s. • Highly resolved simulations are accelerated by combining CFD & ML within 1% error, saving 40% computing time. • Accelerated simulation is deployed on the CPU devices supporting multi-core parallel computation. [ABSTRACT FROM AUTHOR]

Permutation variable importance measure (PVIM) based on random forest and Morris' screening design are two effective techniques for measuring the variable importance in high dimensions. The former technique is developed in the machine learning discipline and widely used in bioinformatics, while the latter technique is popular in scientific computing. We present three main contributions to variable importance analysis (VIA). First, through theoretical derivation, we show that the PVIM converges to double the non-standardized Sobol' total effect index. This observation indicates that the PVIM is especially useful for variable screening as it captures both the individual and interaction effects. Second, three numerical examples with different types of model behavior are presented for comparing the performances of these two techniques. The main conclusions are as follows. For high-dimensional additive or approximately additive models, the PVIM is much more efficient than Morris' screening design when used for both variable importance ranking and variable screening. For high-dimensional models mainly governed by interaction effects, the performance of PVIM degrades, but it is still a competitive technique. Finally, the two techniques are applied to an environmental multi-indicators system for improving the robustness of the partial order structure of this system. [ABSTRACT FROM AUTHOR]