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General matrix multiplication (gemm) is a fundamental kernel in scientific computing and current frameworks for deep learning. Modern realisations of gemm are mostly written in C, on top of a small, highly tuned micro-kernel that is usually encoded in assembly. The high performance realisation of gemm in linear algebra libraries in general include a single micro-kernel per architecture, usually implemented by an expert. In this paper, we explore a couple of paths to automatically generate gemm micro-kernels, either using C++ templates with vector intrinsics or high-level Python scripts that directly produce assembly code. Both solutions can integrate high performance software techniques, such as loop unrolling and software pipelining, accommodate any data type, and easily generate micro-kernels of any requested dimension. The performance of this solution is tested on three ARM-based cores and compared with state-of-the-art libraries for these processors: BLIS, OpenBLAS and ArmPL. The experimental results show that the auto-generation approach is highly competitive, mainly due to the possibility of adapting the micro-kernel to the problem dimensions. [ABSTRACT FROM AUTHOR]

With the continuous progress of technology, the subject of life science plays an increasingly important role, among which the application of artificial intelligence in the medical field has attracted more and more attention. Bell facial palsy, a neurological ailment characterized by facial muscle weakness or paralysis, exerts a profound impact on patients' facial expressions and masticatory abilities, thereby inflicting considerable distress upon their overall quality of life and mental well-being. In this study, we designed a facial attribute recognition model specifically for individuals with Bell's facial palsy. The model utilizes an enhanced SSD network and scientific computing to perform a graded assessment of the patients' condition. By replacing the VGG network with a more efficient backbone, we improved the model's accuracy and significantly reduced its computational burden. The results show that the improved SSD network has an average precision of 87.9% in the classification of light, middle and severe facial palsy, and effectively performs the classification of patients with facial palsy, where scientific calculations also increase the precision of the classification. This is also one of the most significant contributions of this article, which provides intelligent means and objective data for future research on intelligent diagnosis and treatment as well as progressive rehabilitation. [ABSTRACT FROM AUTHOR]

Deep neural networks are extensively used in text mining and Natural Language Processing is to enable computers to understand, analyze, and generate natural language data, such as text or speech, but semantic resources, such as taxonomies and ontologies, are not fully included in deep learning. In this paper, we use Deep Convolutional Neural Network (Deep CNN) to classify research papers using the Computer Science Ontology, an ontology of research areas in the field of computer science. It takes as input the abstract and keywords of a particular research paper and returns the relevant research topic. To evaluate our ontology, we used a gold standard dataset that includes research articles. To further improve text classification results, we propose to design a Deep CNN model. We then used ontology matching to reduce the classes and get better results. Experimental results show that the proposed approach outperforms the one with the highest precision, recall, and F1-score. [ABSTRACT FROM AUTHOR]

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs' predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN's simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases. [ABSTRACT FROM AUTHOR]

General Sparse Matrix-Matrix Multiplication (SpGEMM) has attracted much attention from researchers in graph analyzing, scientific computing, and deep learning. Many optimization techniques have been developed for different applications and computing architectures over the past decades. The objective of this article is to provide a structured and comprehensive overview of the researches on SpGEMM. Existing researches have been grouped into different categories based on target architectures and design choices. Covered topics include typical applications, compression formats, general formulations, key problems and techniques, architecture-oriented optimizations, and programming models. The rationales of different algorithms are analyzed and summarized. This survey sufficiently reveals the latest progress of SpGEMM research to 2021. Moreover, a thorough performance comparison of existing implementations is presented. Based on our findings, we highlight future research directions, which encourage better design and implementations in later studies. [ABSTRACT FROM AUTHOR]

Sparse tensor algorithms are becoming widespread, particularly in the domains of deep learning, graph and data analytics, and scientific computing. Current high-performance broad-domain architectures, such as GPUs, often suffer memory system inefficiencies by moving too much data or moving it too far through the memory hierarchy. To increase performance and efficiency, proposed domain-specific accelerators tailor their architectures to the data needs of a narrow application domain, but as a result cannot be applied to a wide range of algorithms or applications that contain a mix of sparse and dense algorithms. This article proposes Symphony, a hybrid programmable/specialized architecture that focuses on the orchestration of data throughout the memory hierarchy to simultaneously reduce the movement of unnecessary data and data movement distances. Key elements of the Symphony architecture include (1) specialized reconfigurable units aimed not only at roofline floating-point computations but also at supporting data orchestration features, such as address generation, data filtering, and sparse metadata processing; and (2) distribution of computation resources (both programmable and specialized) throughout the on-chip memory hierarchy. We demonstrate that Symphony can match non-programmable ASIC performance on sparse tensor algebra and provide 31× improved runtime and 44× improved energy over a comparably provisioned GPU for these applications. [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]

Especially on the Internet, popular topics in computer sciences which are artificial intelligence, big data, business analytics, data mining, data science, deep learning, and machine learning have been compared or classified using confusing Venn diagrams without any scientific proof. Relationships among the topics have been visualized in this study with the help of Venn diagrams to add scientificity to visualizations. Therefore, this study aims to determine the interactions among the seven popular topics in computer sciences. Five books for each topic (35 books) were included in the analysis. To illustrate the interactions among these topics, the Latent Dirichlet Allocation (LDA) analysis, a topic modeling analysis method, was applied. Further, the pairwise correlation was applied to determine the relationships among the chosen topics. The LDA analysis produced expected results in differentiating the topics, and pairwise correlation results revealed that all the topics are related to each other and that it is challenging to differentiate between them. [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]

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) has acquired tens of millions of low-resolution spectra of stars. This paper investigates the parameter estimation problem for these spectra. To this end, we propose the deep learning model StarGRU network (StarGRUNet). This network is applied to estimate the stellar atmospheric physical parameters and 13 elemental abundances from LAMOST low-resolution spectra. On the spectra with signal-to-noise ratios greater than or equal to 5, the estimation precisions are 94 K and 0.16 dex on |$T_\texttt {eff}$| and log   g respectively, 0.07 to 0.10 dex on [C/H], [Mg/H], [Al/H], [Si/H], [Ca/H], [Ni/H] and [Fe/H], 0.10 to 0.16 dex on [O/H], [S/H], [K/H], [Ti/H] and [Mn/H], and 0.18 and 0.22 dex on [N/H] and [Cr/H]. The model shows advantages over other available models and high consistency with high-resolution surveys. We released the estimated catalogue computed from about 8.21 million low-resolution spectra in LAMOST DR8, code, trained model, and experimental data for astronomical science exploration and data processing algorithm research. [ABSTRACT FROM AUTHOR]

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. However, deep-learning methods find it very challenging to learn stiff dynamics. In this paper, we develop DAE-PINN, the first effective physics-informed deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE). DAEs are used to model complex engineering systems, e.g., power networks, and present a "form" of infinite stiffness, which makes learning their solution trajectories challenging. Our DAE-PINN bases its effectiveness on the synergy between implicit Runge–Kutta time-stepping schemes (designed specifically for solving DAEs) and physics-informed neural networks (PINN) (deep neural networks that we train to satisfy the dynamics of the underlying problem). Furthermore, our framework (i) enforces the neural network to satisfy the DAEs as (approximate) hard constraints using a penalty-based method and (ii) enables simulating DAEs for long-time horizons. We showcase the effectiveness and accuracy of DAE-PINN by learning the solution trajectories of a three-bus power network. [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]

AI provides a new method for massive simulated data calculations in molecular dynamics, materials, and other scientific computing fields. However, the complex structures and large-scale parameters of neural network models make them difficult to develop and train. The automatic parallel technology based on graph algorithms is one of the most promising methods to solve this problem, despite the low efficiency in the design, implementation, and execution of distributed parallel policies for large-scale neural network models. In this paper, we propose an adaptive distributed parallel training method based on the dynamic generation of critical DAG (directed acyclic graph) paths, called FD-DPS, to solve this efficiency problem. Firstly, the proposed model splits operators with the dimension of the tensor, which can expand the space available for model parallelism. Secondly, a dynamic critical path generation method is employed to determine node priority changes in the DAG of the neural network models. Finally, the model implements the optimal scheduling of critical paths based on the priority of the nodes, thereby improving the performance of parallel strategies. Our experiments show that FD-DPS can achieve 12.76% and 11.78% faster training on PnasNet_mobile and ResNet_200 models, respectively, compared with the MP-DPS and Fast methods. [ABSTRACT FROM AUTHOR]

Collaborative filtering (CF) is a classical model for recommender systems. Though neural network-based CF models have been shown to perform well in some cases, they still suffer from the sparsity and cold-start issues. To address these issues, we propose a novel neural network-based CF model, termed the cross-domain explicit–implicit-mixed CF neural network (CEICFNet). The proposed model utilizes deep neural networks to learn latent factors not only from the explicit ratings and the implicit interactions but also in a cross-domain manner. In particular, domain-shared multilayer perception (MLP) networks are designed to learn the user rating latent factors and the user interaction latent factors from the explicit ratings and the implicit interactions, respectively, which act as bridges for transferring knowledge across domains. On the other hand, domain-specific MLP networks are designed to learn the item rating latent factors and the item interaction latent factors from the explicit ratings and the implicit interactions, respectively. Then, in each domain, based on the user rating latent factors and the item rating latent factors, the rating predictive representation for each user–item pair can be learned by an MLP. Similarly, the interaction predictive representation for each user–item pair can be learned. For integrating the explicit ratings and the implicit interactions, in each domain, a fully connected layer is used to automatically assign different weights to the rating predictive representations and the interaction predictive representations, based on which the final interaction probability can be generated. Extensive experiments are conducted on five datasets and the results have confirmed the effectiveness of our model. [ABSTRACT FROM AUTHOR]

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of timescales, making numerical integration expensive. In this work, we develop a hierarchy of deep neural network time-steppers to approximate the dynamical system flow map over a range of time-scales. The model is purely data-driven, enabling accurate and efficient numerical integration and forecasting. Similar ideas can be used to couple neural network-based models with classical numerical time-steppers. Our hierarchical time-stepping scheme provides advantages over current time-stepping algorithms, including (i) capturing a range of timescales, (ii) improved accuracy in comparison with leading neural network architectures, (iii) efficiency in long-time forecasting due to explicit training of slow time-scale dynamics, and (iv) a flexible framework that is parallelizable and may be integrated with standard numerical time-stepping algorithms. The method is demonstrated on numerous nonlinear dynamical systems, including the Van der Pol oscillator, the Lorenz system, the Kuramoto–Sivashinsky equation, and fluid flow pass a cylinder; audio and video signals are also explored. On the sequence generation examples, we benchmark our algorithm against state-of-the-art methods, such as LSTM, reservoir computing and clockwork RNN. This article is part of the theme issue 'Data-driven prediction in dynamical systems'. [ABSTRACT FROM AUTHOR]

Multiscale is a hallmark feature of complex systems, presenting challenges for traditional numerical methods due to their reliance on local Taylor series constraints. Further, multiscale techniques often face limitations in identifying appropriate heuristic closures used to handle unresolved scales or processes within the system being modeled. In this study, we develop an efficient time-stepping strategy for multiscale problems. The proposed method's novelty lies in synergizing the hierarchical deep learning formalism with an adaptive step-size estimation process to approximate dynamical system flow maps across timescales efficiently. The model is purely data-driven and provides improved forecasting accuracy compared to fixed-step neural network time steppers. To demonstrate the effectiveness of the proposed scheme, we provide numerical simulations for several canonical nonlinear systems and source codes for their implementation. We believe the method has the potential to benefit multiscale analysis of complex systems and encourage further investigation in this area. • Identifies potential drawbacks in the current multiscale methods. • Introduces efficient time-stepping algorithm for multiscale problems using hierarchical deep learning. • Demonstrates the application of adaptive time-stepping on canonical ODEs and PDEs with noisy measurements. [ABSTRACT FROM AUTHOR]

Multiscale is a hallmark feature of complex systems, presenting challenges for traditional numerical methods due to their reliance on local Taylor series constraints. Further, multiscale techniques often face limitations in identifying appropriate heuristic closures used to handle unresolved scales or processes within the system being modeled. In this study, we develop an efficient time-stepping strategy for multiscale problems. The proposed method's novelty lies in synergizing the hierarchical deep learning formalism with an adaptive step-size estimation process to approximate dynamical system flow maps across timescales efficiently. The model is purely data-driven and provides improved forecasting accuracy compared to fixed-step neural network time steppers. To demonstrate the effectiveness of the proposed scheme, we provide numerical simulations for several canonical nonlinear systems and source codes for their implementation. We believe the method has the potential to benefit multiscale analysis of complex systems and encourage further investigation in this area. • Identifies potential drawbacks in the current multiscale methods. • Introduces efficient time-stepping algorithm for multiscale problems using hierarchical deep learning. • Demonstrates the application of adaptive time-stepping on canonical ODEs and PDEs with noisy measurements. [ABSTRACT FROM AUTHOR]

"Deep Learning and Scientific Computing with R torch" by Sigrid Keydana is a book that introduces an R interface for PyTorch, a popular deep learning framework. The book is well-written and easy to follow, with plenty of illustrations and examples. It is divided into three parts: the basics of torch, the implementation of deep neural networks, and the utility of torch beyond deep learning. The book covers topics such as tensors, automatic differentiation, neural network architecture, optimization algorithms, and various applications of torch. Overall, it is a valuable resource for R users interested in deep learning and scientific computing. [Extracted from the article]

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.

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence of stable neural networks (NNs). We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities; however, there does not exist any algorithm, even randomized, that can train (or compute) such a NN. For any positive integers K > 2 and L, there are cases where simultaneously 1) no randomized training algorithm can compute a NN correct to K digits with probability greater than 1/2; 2) there exists a deterministic training algorithm that computes a NN with K − 1 correct digits, but any such (even randomized) algorithm needs arbitrarily many training data; and 3) there exists a deterministic training algorithm that computes a NN with K − 2 correct digits using no more than L training samples. These results imply a classification theory describing conditions under which (stable) NNs with a given accuracy can be computed by an algorithm. We begin this theory by establishing sufficient conditions for the existence of algorithms that compute stable NNs in inverse problems. We introduce fast iterative restarted networks (FIRENETs), which we both prove and numerically verify are stable. Moreover, we prove that only O(| log(ϵ)|) layers are needed for an -accurate solution to the inverse problem. [ABSTRACT FROM AUTHOR]

Utilizing physical information to improve the performance of the conventional neural networks is becoming a promising research direction in scientific computing recently. For multiphase flows, it would require significant computational resources for neural network training due to the large gradients near the interface between the two fluids. Based on the idea of the physics-informed neural networks (PINNs), a modified deep learning framework BubbleNet is proposed to overcome this difficulty in the present study. The deep neural network (DNN) with separate sub-nets is adopted to predict physics fields, with the semi-physics-informed part encoding the continuity equation and the pressure Poisson equation P for supervision and the time discretized normalizer to normalize field data per time step before training. Two bubbly flows, i.e., single bubble flow and multiple bubble flow in a microchannel, are considered to test the algorithm. The conventional computational fluid dynamics software is applied to obtain the training dataset. The traditional DNN and the BubbleNet(s) are utilized to train the neural network and predict the flow fields for the two bubbly flows. Results indicate the BubbleNet frameworks are able to successfully predict the physics fields, and the inclusion of the continuity equation significantly improves the performance of deep NNs. The introduction of the Poisson equation also has slightly positive effects on the prediction results. The results suggest that constructing semi-PINNs by flexibly considering the physical information into neural networks will be helpful in the learning of complex flow problems. [ABSTRACT FROM AUTHOR]

Opinion dynamics (OD) models simulate the evolution of personal opinions using computer science, social dynamics, physics, and complexity science tools on social networks. However, current opinion dynamics models mainly utilize agent-based models to simulate user interactions but still need to leverage large-scale data fully. Social networks typically involve a vast number of users and information, making it difficult for models to capture the complex interactions in real social networks. Additionally, many models overlook the specific mechanisms of user interactions, such as how network individuals influence and interact with one another, resulting in inaccuracies in modeling individual opinion evolution. This paper proposes a novel approach that integrates the probabilistic bounded confidence model (PBC) with deep learning, i.e., Neural Probabilistic Bounded Confidence (NPBC), to tackle these challenges. The NPBC model adopts an attention network, a long short-term memory (LSTM) network, and a feedforward neural network to approximate the evolution of individual opinions within networks. It satisfies the data approximation and the users' opinion update rule that conforms to the PBC model. This model enhances the understanding of opinion dynamics, helping to develop effective strategies for opinion guidance in social networks. Finally, the proposed NPBC model is evaluated on three synthetic and Twitter datasets. The results demonstrate that the proposed NPBC model performs better than the six baseline methods in predicting user opinions. Compared to baseline models, the model's accuracy (ACC) and comprehensive evaluation (F1) scores improve by up to 18% and 7%, respectively. • Combining deep learning and probabilistic bounded confidence model. • Using fully connected layers to map users and time to the same vector space. • The attention mechanism captures the internal correlations between users and time. • The long short-term memory network is used to capture the sequence features. [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]

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]

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]

Implementing artificial neural networks is commonly achieved via high-level programming languages such as Python and easy-to-use deep learning libraries such as Keras. These software libraries come preloaded with a variety of network architectures, provide autodifferentiation, and support GPUs for fast and efficient computation. As a result, a deep learning practitioner will favor training a neural network model in Python, where these tools are readily available. However, many large-scale scientific computation projects are written in Fortran, making it difficult to integrate with modern deep learning methods. To alleviate this problem, we introduce a software library, the Fortran-Keras Bridge (FKB). This two-way bridge connects environments where deep learning resources are plentiful with those where they are scarce. The paper describes several unique features offered by FKB, such as customizable layers, loss functions, and network ensembles. The paper concludes with a case study that applies FKB to address open questions about the robustness of an experimental approach to global climate simulation, in which subgrid physics are outsourced to deep neural network emulators. In this context, FKB enables a hyperparameter search of one hundred plus candidate models of subgrid cloud and radiation physics, initially implemented in Keras, to be transferred and used in Fortran. Such a process allows the model's emergent behavior to be assessed, i.e., when fit imperfections are coupled to explicit planetary-scale fluid dynamics. The results reveal a previously unrecognized strong relationship between offline validation error and online performance, in which the choice of the optimizer proves unexpectedly critical. This in turn reveals many new neural network architectures that produce considerable improvements in climate model stability including some with reduced error, for an especially challenging training dataset. [ABSTRACT FROM AUTHOR]

• Improved process understanding of continuous wet granulation process with deep learning technology. • Application of deep learning techniques for an innovative process monitoring. • Optimization of deep neural networks for pharmaceutical process monitoring. • Application of innovative Process Analytical Technology (PAT) equipment. • Real-world example of process monitoring of a continuous production line. Continuous Manufacturing (CM) of pharmaceutical drug products is a new approach within the pharmaceutical industry. In the presented paper, a GMP continuous wet granulation line for production of solid dosage forms was investigated. The line was composed of the subsequent continuous unit: operations feeding – twin-screw wet-granulation – fluid-bed drying – sieving and tableting. The formulation of a commercial entity was selected for this study. Several critical process parameters were evaluated in order to probe the process and to characterize the impact on quality attributes. Seven critical process parameters have been selected after a risk analysis: API and excipient mass flows of the two feeders, liquid feed rate and rotation speed of the extruder and rotation speed, temperature and airflow of the dryer. Eight quality attributes were controlled in real time by Process Analytical Technologies (PAT): API content after blender, after dryer, in tablet press feed frame and of tablet, LOD after dryer and PSD after dryer (three PSD parameters: x10 x50 x90). The process parameter values were changed during production in order to detect the impact on the quality of the final product. The deep learning techniques have been used in order to predict the quality attribute (output) with the process parameters (input). The use of deep learning reduces the noise and simplify the data interpretation for a better process understanding. After optimization, three hidden layers neural network were selected with 6 hidden neurons. The activation function ReLU (Rectified Linear Unit) and the ADAM optimizer were used with 2500 epochs (number of learning cycle). API contents, PSD values and LOD values were estimated with an error of calibration lower than 10%. The level of error allow an adequate process monitoring by DNN and we have proven that the main critical process parameters can be identified at a higher levelof process understanding. The synergy between PAT and process data science creates a superior monitoring framework of the continuous manufacturing line and increase the knowledge of this innovative production line and the products that it makes. [ABSTRACT FROM AUTHOR]

Artificial intelligence is one of the hottest research topics in computer science. In general, when it comes to the needs to perform deep learning, the most intuitive and unique implementation method is to use neural network. But there are two shortcomings in neural network. First, it is not easy to be understood. When encountering the needs for implementation, it often requires a lot of relevant research efforts to implement the neural network. Second, the structure is complex. When constructing a perfect learning structure, in order to achieve the fully defined connection between nodes, the overall structure becomes complicated. It is hard for developers to track the parameter changes inside. Therefore, the goal of this article is to provide a more streamlined method so as to perform deep learning. A modified high-level fuzzy Petri net, called deep Petri net, is used to perform deep learning, in an attempt to propose a simple and easy structure and to track parameter changes, with faster speed than the deep neural network. The experimental results have shown that the deep Petri net performs better than the deep neural network. [ABSTRACT FROM AUTHOR]

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct probabilistic representations for the system states, and put forth an adversarial inference procedure for training them on data, while constraining their predictions to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep generative models as surrogates of physical systems in which the cost of data acquisition is high, and training data-sets are typically small. This provides a flexible framework for characterizing uncertainty in the outputs of physical systems due to randomness in their inputs or noise in their observations that entirely bypasses the need for repeatedly sampling expensive experiments or numerical simulators. We demonstrate the effectiveness of our approach through a series of examples involving uncertainty propagation in non-linear conservation laws, and the discovery of constitutive laws for flow through porous media directly from noisy data. • We developed self-supervised deep learning methods for modeling stochastic systems. • Regularized adversarial inference enables learning generative models from small data. • This yields a flexible workflow for characterizing uncertainty in physical systems. • This method bypasses the need for sampling costly simulators for tackling UQ tasks. [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]

Esteban Mockskos earned his PhD degree in Computer Science at Universidad de Buenos Aires, Argentina. This editorial introduces the SIMULATION special issue "High-Performance Computing in the Ibero American region", which was published with the aim of supporting a building knowledge base process on theory, methodology, and technology related to high-performance computing (HPC) in Latin America. B Esteban Mockskos b earned his PhD degree in Computer Science at Universidad de Buenos Aires, Argentina. [Extracted from the article]

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]

In this paper, we introduce SciANN, a Python package for scientific computing and physics-informed deep learning using artificial neural networks. SciANN uses the widely used deep-learning packages TensorFlow and Keras to build deep neural networks and optimization models, thus inheriting many of Keras's functionalities, such as batch optimization and model reuse for transfer learning. SciANN is designed to abstract neural network construction for scientific computations and solution and discovery of partial differential equations (PDE) using the physics-informed neural networks (PINN) architecture, therefore providing the flexibility to set up complex functional forms. We illustrate, in a series of examples, how the framework can be used for curve fitting on discrete data, and for solution and discovery of PDEs in strong and weak forms. We summarize the features currently available in SciANN, and also outline ongoing and future developments. • We introduce a new Python package, SciANN, for scientific computing and physics-informed deep learning. • SciANN is built on top of Tensorflow and Keras, therefore inheriting their high-performance computing capabilities. • We show how to use SciANN for curve-fitting, solution of PDEs in strong and weak form, and model inversion. [ABSTRACT FROM AUTHOR]

Link prediction finds missing links (in static networks) or predicts the likelihood of future links (in dynamic networks). The latter definition is useful in network evolution (Wang et al., 2011; Barabasi and Albert, 1999; Kleinberg, 2000; Leskovec et al., 2005; Zhang et al., 2015). Link prediction is a fast-growing research area in both physics and computer science domain. There exists a wide range of link prediction techniques like similarity-based indices, probabilistic methods, dimensionality reduction approaches, etc., which are extensively explored in different groups of this article. Learning-based methods are covered in addition to clustering-based and information-theoretic models in a separate group. The experimental results of similarity and some other representative approaches are tabulated and discussed. To make it general, this review also covers link prediction in different types of networks, for example, directed, temporal, bipartite, and heterogeneous networks. Finally, we discuss several applications with some recent developments and concludes our work with some future works. • We ponder over the problem of link prediction in social networks. • We reviewed several approaches to link prediction from classical to recent network embedding and deep learning approaches. • We put forward taxonomy of the existing approaches that clearly groups these approaches into well defined domains. • We experimentally evaluated the structural-based approaches using four evaluation metrics. • Finally, we explored different applications, recent developments, and future directions. [ABSTRACT FROM AUTHOR]