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Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While the machine learning community has successfully utilized low-precision computations, scientific computing remains cautious due to concerns about numerical stability. To tackle this long-standing challenge, we propose a novel approach to dynamically adjust the floating-point data precision at runtime, maintaining computational fidelity using lower bit widths. We first conduct a thorough analysis of data range distributions during scientific simulations to identify opportunities and challenges for dynamic precision adjustment. We then propose a runtime reconfigurable, flexible floating-point multiplier (R2F2), which automatically and dynamically adjusts multiplication precision based on the current operands, ensuring accurate results with lower bit widths. Our evaluation shows that 16-bit R2F2 significantly reduces error rates by 70.2\% compared to standard half-precision, with resource overhead ranging from a 5% reduction to a 7% increase and no latency overhead. In two representative scientific computing applications, R2F2, using 16 or fewer bits, can achieve the same simulation results as 32-bit precision, while standard half precision will fail. This study pioneers runtime reconfigurable arithmetic, demonstrating great potential to enhance scientific computing efficiency. Code available at https://github.com/sharc-lab/R2F2., Comment: Accepted by ASD-DAC 2025

One of the most important topics in quantum scientific computing is solving differential equations. In this paper, generalized quantum functional expansion (QFE) framework is proposed. In the QFE framework, a functional expansion of solution is encoded into a quantum state and the time evolution of the quantum state is solved with variational quantum simulation (VQS). The quantum functional encoding supports different numerical schemes of functional expansions. The lower bound of the required number of qubits is double logarithm of the inverse error bound in the QFE framework. Furthermore, a new parallel Pauli operation strategy is proposed to significantly improve the scalability of VQS. The number of circuits in VQS is exponentially reduced to only the quadratic order of the number of ansatz parameters. Four example differential equations are solved to demonstrate the generic QFE framework.

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing, which may often be framed in terms of operators mapping between spaces of functions. Building on the classical random features methodology for scalar regression, this paper introduces the function-valued random features method. This leads to a supervised operator learning architecture that is practical for nonlinear problems yet is structured enough to facilitate efficient training through the optimization of a convex, quadratic cost. Due to the quadratic structure, the trained model is equipped with convergence guarantees and error and complexity bounds, properties that are not readily available for most other operator learning architectures. At its core, the proposed approach builds a linear combination of random operators. This turns out to be a low-rank approximation of an operator-valued kernel ridge regression algorithm, and hence the method also has strong connections to Gaussian process regression. The paper designs function-valued random features that are tailored to the structure of two nonlinear operator learning benchmark problems arising from parametric partial differential equations. Numerical results demonstrate the scalability, discretization invariance, and transferability of the function-valued random features method., Comment: 36 pages, 1 table, 9 figures. SIGEST version of SIAM J. Sci. Comput. Vol. 43 No. 5 (2021) pp. A3212-A3243, hence text overlap with arXiv:2005.10224

Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering applications. This advancement presents both opportunities and challenges, requiring engineers to familiarize themselves with quantum principles, applications, and complexities. This paper systematically explores the foundational concepts of quantum mechanics and their implications for computational advancements, emphasizing the superiority of quantum algorithms in solving engineering problems. It identifies areas where gate-based quantum computing has the potential to outperform classical methods despite facing scalability and coherence issues. By offering clear examples with minimal reliance on in-depth quantum physics or hardware specifics, the aim is to make quantum computing accessible to engineers, addressing the steep learning curve and fostering its practical adoption for complex problem-solving and technological advancement as quantum hardware becomes more robust and reliable.

We provide an overview of the emergence of large language models for scientific computing applications. We highlight use cases that involve natural language processing of scientific documents and specialized languages designed to describe physical systems. For the former, chatbot style applications appear in medicine, mathematics and physics and can be used iteratively with domain experts for problem solving. We also review specialized languages within molecular biology, the languages of molecules, proteins, and DNA where language models are being used to predict properties and even create novel physical systems at much faster rates than traditional computing methods., Comment: 13 pages

Scientific research increasingly relies on distributed computational resources, storage systems, networks, and instruments, ranging from HPC and cloud systems to edge devices. Event-driven architecture (EDA) benefits applications targeting distributed research infrastructures by enabling the organization, communication, processing, reliability, and security of events generated from many sources. To support the development of scientific EDA, we introduce Octopus, a hybrid, cloud-to-edge event fabric designed to link many local event producers and consumers with cloud-hosted brokers. Octopus can be scaled to meet demand, permits the deployment of highly available Triggers for automatic event processing, and enforces fine-grained access control. We identify requirements in self-driving laboratories, scientific data automation, online task scheduling, epidemic modeling, and dynamic workflow management use cases, and present results demonstrating Octopus' ability to meet those requirements. Octopus supports producing and consuming events at a rate of over 4.2 M and 9.6 M events per second, respectively, from distributed clients., Comment: 12 pages and 8 figures. Camera-ready version for FTXS'24 (https://sites.google.com/view/ftxs2024)

In the realm of scientific computing, both Julia and Python have established themselves as powerful tools. Within the context of High Energy Physics (HEP) data analysis, Python has been traditionally favored, yet there exists a compelling case for migrating legacy software to Julia. This article focuses on language interoperability, specifically exploring how Awkward Array data structures can bridge the gap between Julia and Python. The talk offers insights into key considerations such as memory management, data buffer copies, and dependency handling. It delves into the performance enhancements achieved by invoking Julia from Python and vice versa, particularly for intensive array-oriented calculations involving large-scale, though not excessively dimensional, arrays of HEP data. The advantages and challenges inherent in achieving interoperability between Julia and Python in the domain of scientific computing are discussed., Comment: 8 pages, 1 figure, ACAT2024 workshop

Foundation models have revolutionized knowledge acquisition across domains, and our study introduces OmniArch, a paradigm-shifting approach designed for building foundation models in multi-physics scientific computing. OmniArch's pre-training involves a versatile pipeline that processes multi-physics spatio-temporal data, casting forward problem learning into scalable auto-regressive tasks, while our novel Physics-Informed Reinforcement Learning (PIRL) technique during fine-tuning ensures alignment with physical laws. Pre-trained on the comprehensive PDEBench dataset, OmniArch not only sets new performance benchmarks for 1D, 2D and 3D PDEs but also demonstrates exceptional adaptability to new physics via few-shot and zero-shot learning approaches. The model's representations further extend to inverse problem-solving, highlighting the transformative potential of AI-enabled Scientific Computing(AI4SC) foundation models for engineering applications and physics discovery., Comment: Work in Progress

This report is a digest of the DOE/NSF Workshop on Correctness in Scientific Computing (CSC'23) held on June 17, 2023, as part of the Federated Computing Research Conference (FCRC) 2023. CSC was conceived by DOE and NSF to address the growing concerns about correctness among those who employ computational methods to perform large-scale scientific simulations. These concerns have escalated, given the complexity, scale, and heterogeneity of today's HPC software and hardware. If correctness is not proactively addressed, there is the risk of producing flawed science on top of unacceptable productivity losses faced by computational scientists and engineers. HPC systems are beginning to include data-driven methods, including machine learning and surrogate models, and their impact on overall HPC system correctness was also felt urgent to discuss. Stakeholders of correctness in this space were identified to belong to several sub-disciplines of computer science; from computer architecture researchers who design special-purpose hardware that offers high energy efficiencies; numerical algorithm designers who develop efficient computational schemes based on reduced precision as well as reduced data movement; all the way to researchers in programming language and formal methods who seek methodologies for correct compilation and verification. To include attendees with such a diverse set of backgrounds, CSC was held during the Federated Computing Research Conference (FCRC) 2023., Comment: 36 pages. DOE/NSF Workshop on Correctness in Scientific Computing (CSC 2023) was a PLDI 2023 workshop

Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in real world applications. Areas that are likely to have the greatest impact on high performance computing (HPC) include simulation of quantum systems, optimization, and machine learning. We draw our examples from electronic structure calculations and computational fluid dynamics which account for a large fraction of current scientific and engineering use of HPC. Potential challenges include encoding and decoding classical data for quantum devices, and mismatched clock speeds between classical and quantum processors. Even a modest quantum enhancement to current classical techniques would have far-reaching impacts in areas such as weather forecasting, aerospace engineering, and the design of "green" materials for sustainable development. This requires significant effort from the computational science, engineering and quantum computing communities working together., Comment: Accepted by Reports on Progress in Physics. 43 pages + 29 pages references

Nowadays interactive digital scientific environments have become an integral part of scientific computing in solving various scientific tasks in research, but also STEM education. We introduce SageMath or shortly Sage -- a free open Python-based alternative to the well-known commercial software -- in the frame of our course Methods of Physical Problems Solving for future scientists and science teachers. Particularly, in the 1st illustrative example from the Physics Olympiad, we present Sage as a scientific open data source, symbolic, numerical, and visualization tool. The 2nd example from the Young Physicists' Tournament shows Sage as a multimedia, modeling, and programming tool. By employing SageMath as an open digital environment for scientific computing in the education of all STEM disciplines, teachers and students are empowered not only with a universal educational tool, but a real research tool, enabling them to engage in interactive visualization, modeling, programming, and solving of authentic, complex interdisciplinary problems, thus naturally enhancing their motivation to pursue science in alignment with the core mission of STEM education., Comment: 9 pages, 3 figures, 1 table, conference DIDSCI2022

Critical goals of scientific computing are to increase scientific rigor, reproducibility, and transparency while keeping up with ever-increasing computational demands. This work presents an integrated framework well-suited for data processing and analysis spanning individual, on-premises, and cloud environments. This framework leverages three well-established DevOps tools: 1) Git repositories linked to 2) CI/CD engines operating on 3) containers. It supports the full life-cycle of scientific data workflows with minimal friction between stages--including solutions for researchers who generate data. This is achieved by leveraging a single container that supports local, interactive user sessions and deployment in HPC or Kubernetes clusters. Combined with Git repositories integrated with CI/CD, this approach enables decentralized data pipelines across multiple, arbitrary computational environments. This framework has been successfully deployed and validated within our research group, spanning experimental acquisition systems and computational clusters with open-source, purpose-built GitLab CI/CD executors for slurm and Google Kubernetes Engine Autopilot. Taken together, this framework can increase the rigor, reproducibility, and transparency of compute-dependent scientific research.

This report provides an introduction to the Bandicoot C++ library for linear algebra and scientific computing on GPUs, overviewing its user interface and performance characteristics, as well as the technical details of its internal design. Bandicoot is the GPU-enabled counterpart to the well-known Armadillo C++ linear algebra library, aiming to allow users to take advantage of GPU-accelerated computation for their existing codebases without significant changes. Adapting the same internal template meta-programming techniques that Armadillo uses, Bandicoot is able to provide compile-time optimisation of mathematical expressions within user code. The library is ready for production use and is available at https://coot.sourceforge.io. Bandicoot is distributed under the Apache 2.0 License.

Estimates of energy usage in layers of computing from devices to algorithms have been determined and analyzed. Building on the previous analysis [3], energy needed from single devices and systems including three large-scale computing applications such as Artificial Intelligence (AI)/Machine Learning for Natural Language Processing, Scientific Simulations, and Cryptocurrency Mining have been estimated. In contrast to the bit-level switching, in which transistors achieved energy efficiency due to geometrical scaling, higher energy is expended both at the at the instructions and simulations levels of an application. Additionally, the analysis based on AI/ML Accelerators indicate that changes in architectures using an older semiconductor technology node have comparable energy efficiency with a different architecture using a newer technology. Further comparisons of the energy in computing systems with the thermodynamic and biological limits, indicate that there is a 27-36 orders of magnitude higher energy requirements for total simulation of an application. These energy estimates underscore the need for serious considerations of energy efficiency in computing by including energy as a design parameter, enabling growing needs of compute-intensive applications in a digital world., Comment: 6 pages, 5 figures

Scientific computing libraries, either being in-house or open-source, have experienced enormous progress in both engineering and scientific research. It is therefore essential to ensure that the modifications in the source code aroused by bug fixing or new feature development wouldn't compromise the accuracy and functionality that has already been validated and verified. With this in mind, this paper introduces a method for developing and implementing an automatic regression test environment and takes the open-source multi-physics library SPHinXsys \cite{zhang2021sphinxsys} as an example. Firstly, the reference database for each benchmark test is generated from monitored data by multiple executions. This database contains the maximum variation range of metrics for different types of strategies, i.e., time-averaged method, ensemble-averaged method as well as the dynamic time warping method, covering the uncertainty arising from parallel computing, particle relaxation, physical instabilities, etc. Then, new results obtained after source code modification will be tested with them according to a curve-similarity based comparison. Whenever the source code is updated, the regression test will be carried out automatically for all test cases and used to report the validity of the current results. This regression test environment has already been implemented in all dynamics test cases released in SPHinXsys, including fluid dynamics, solid mechanics, fluid-structure interaction, thermal and mass diffusion, reaction-diffusion, and their multi-physics coupling, and shows good capability for testing various problems. It's worth noting that while the present test environment is built and implemented for a specific scientific computing library, its underlying principle is generic and can be applied to many others., Comment: 39 pages, 13 figures

The accuracy requirements in many scientific computing workloads result in the use of double-precision floating-point arithmetic in the execution kernels. Nevertheless, emerging real-number representations, such as posit arithmetic, show promise in delivering even higher accuracy in such computations. In this work, we explore the native use of 64-bit posits in a series of numerical benchmarks and compare their timing performance, accuracy and hardware cost to IEEE 754 doubles. In addition, we also study the conjugate gradient method for numerically solving systems of linear equations in real-world applications. For this, we extend the PERCIVAL RISC-V core and the Xposit custom RISC-V extension with posit64 and quire operations. Results show that posit64 can obtain up to 4 orders of magnitude lower mean square error than doubles. This leads to a reduction in the number of iterations required for convergence in some iterative solvers. However, leveraging the quire accumulator register can limit the order of some operations such as matrix multiplications. Furthermore, detailed FPGA and ASIC synthesis results highlight the significant hardware cost of 64-bit posit arithmetic and quire. Despite this, the large accuracy improvements achieved with the same memory bandwidth suggest that posit arithmetic may provide a potential alternative representation for scientific computing., Comment: 12 pages. Code available at https://github.com/artecs-group/PERCIVAL. Reviewed version to be published in IEEE TC

\textsc{Lara} is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of \textsc{Lara}'s expressive ability reports that it can represent relational algebra and most linear algebra operations. However, several essential computations, such as matrix inversion and determinant, cannot be expressed in \textsc{Lara}. \textsc{Lara} cannot represent global and iterative computation, either. This article proposes \textsc{IterLara}, extending \textsc{Lara} with iterative operators, to provide an algebraic model that unifies operations in general-purpose computing, like big data, AI, scientific computing, and database. We study the expressive ability of \textsc{Lara} and \textsc{IterLara} and prove that \textsc{IterLara} with aggregation functions can represent matrix inversion, determinant. Besides, we demonstrate that \textsc{IterLara} with no limitation of function utility is Turing complete. We also propose the Operation Count (OP) as a metric of computation amount for \textsc{IterLara} and ensure that the OP metric is in accordance with the existing computation metrics.

Stencil computation is one of the most important kernels in various scientific computing. Nowadays, most Stencil-driven scientific computing still relies heavily on supercomputers, suffering from expensive access, poor scalability, and duplicated optimizations. This paper proposes Tetris, the first system for high-performance Stencil on heterogeneous CPU+GPU, towards democratizing Stencil-driven scientific computing on Cloud. In Tetris, polymorphic tiling tetrominoes are first proposed to bridge different hardware architectures and various application contexts with a perfect spatial and temporal tessellation automatically. Tetris is contributed by three main components: (1) Underlying hardware characteristics are first captured to achieve a sophisticated Pattern Mapping by register-level tetrominoes; (2) An efficient Locality Enhancer is first presented for data reuse on spatial and temporal dimensions simultaneously by cache/SMEM-level tetrominoes; (3) A novel Concurrent Scheduler is first designed to exploit the full potential of on-cloud memory and computing power by memory-level tetrominoes. Tetris is orthogonal to (and complements) the optimizations or deployments for a wide variety of emerging and legacy scientific computing applications. Results of thermal diffusion simulation demonstrate that the performance is improved by 29.6x, reducing time cost from day to hour, while preserving the original accuracy.

Diffractive optical neural networks (DONNs) have been emerging as a high-throughput and energy-efficient hardware platform to perform all-optical machine learning (ML) in machine vision systems. However, the current demonstrated applications of DONNs are largely straightforward image classification tasks, which undermines the prospect of developing and utilizing such hardware for other ML applications. Here, we numerically and experimentally demonstrate the deployment of an all-optical reconfigurable DONNs system for scientific computing, including guiding two-dimensional quantum material synthesis, predicting the properties of nanomaterials and small molecular cancer drugs, predicting the device response of nanopatterned integrated photonic power splitters, and the dynamic stabilization of an inverted pendulum with reinforcement learning. Despite a large variety of input data structures, we develop a universal feature engineering approach to convert categorical input features to the images that can be processed in the DONNs system. Our results open up new opportunities of employing DONNs systems for a broad range of ML applications.

Deep learning (DL) is revolutionizing the scientific computing community. To reduce the data gap caused by usually expensive simulations or experimentation, active learning has been identified as a promising solution for the scientific computing community. However, the deep active learning (DAL) literature is currently dominated by image classification problems and pool-based methods, which are not directly transferrable to scientific computing problems, dominated by regression problems with no pre-defined 'pool' of unlabeled data. Here for the first time, we investigate the robustness of DAL methods for scientific computing problems using ten state-of-the-art DAL methods and eight benchmark problems. We show that, to our surprise, the majority of the DAL methods are not robust even compared to random sampling when the ideal pool size is unknown. We further analyze the effectiveness and robustness of DAL methods and suggest that diversity is necessary for a robust DAL for scientific computing problems.

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides researchers and engineers with a solid starting point to comprehend how to integrate different layers of physics into neural networks.

Today's large-scale scientific applications running on high-performance computing (HPC) systems generate vast data volumes. Thus, data compression is becoming a critical technique to mitigate the storage burden and data-movement cost. However, existing lossy compressors for scientific data cannot achieve a high compression ratio and throughput simultaneously, hindering their adoption in many applications requiring fast compression, such as in-memory compression. To this end, in this work, we develop a fast and high-ratio error-bounded lossy compressor on GPUs for scientific data (called FZ-GPU). Specifically, we first design a new compression pipeline that consists of fully parallelized quantization, bitshuffle, and our newly designed fast encoding. Then, we propose a series of deep architectural optimizations for each kernel in the pipeline to take full advantage of CUDA architectures. We propose a warp-level optimization to avoid data conflicts for bit-wise operations in bitshuffle, maximize shared memory utilization, and eliminate unnecessary data movements by fusing different compression kernels. Finally, we evaluate FZ-GPU on two NVIDIA GPUs (i.e., A100 and RTX A4000) using six representative scientific datasets from SDRBench. Results on the A100 GPU show that FZ-GPU achieves an average speedup of 4.2X over cuSZ and an average speedup of 37.0X over a multi-threaded CPU implementation of our algorithm under the same error bound. FZ-GPU also achieves an average speedup of 2.3X and an average compression ratio improvement of 2.0X over cuZFP under the same data distortion., Comment: 14 pages, 12 figures, accepted by ACM HPDC '23

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote physical faithfulness, but hardware limitations have precluded their application to large computational domains. We show that it is \textit{possible} to train a class of GNN surrogates on 3D meshes. We scale MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via our domain decomposition approach to facilitate training that is mathematically equivalent to training on the whole domain under certain conditions. With this, we were able to train MGN on meshes with \textit{millions} of nodes to generate computational fluid dynamics (CFD) simulations. Furthermore, we show how to enhance MGN via higher-order numerical integration, which can reduce MGN's error and training time. We validated our methods on an accompanying dataset of 3D $\text{CO}_2$-capture CFD simulations on a 3.1M-node mesh. This work presents a practical path to scaling MGN for real-world applications., Comment: ICLR 2023 Workshop on Physics for Machine Learning

With the release of the Apple Silicon System-on-a-Chip processors, and the impressive performance shown in general use by both the M1 and M1 Ultra, the potential use for Apple Silicon processors in scientific computing is explored. Both the M1 and M1 Ultra are compared to current state-of-the-art data-center GPUs, including an NVIDIA V100 with PCIe, an NVIDIA V100 with NVLink, and an NVIDIA A100 with PCIe. The scientific performance is measured using the Scalable Heterogeneous Computing (SHOC) benchmark suite using OpenCL benchmarks. We find that both M1 processors outperform the GPUs in all benchmarks., Comment: 10 pages, 3 figures, IEEE HPEC

This paper presents models for renewable energy systems with storage, and considers its optimal operation. We model and simulate wind and solar power production using stochastic differential equations as well as storage of the produced power using batteries, thermal storage, and water electrolysis. We formulate an economic optimal control problem, with the scope of controlling the system in the most efficient way, while satisfying the power demand from the electric grid. Deploying multiple storage systems allows flexibility and higher reliability of the renewable energy system., Comment: Submitted to European Control Conference 2023

The recent influx of open scientific data has contributed to the transitioning of scientific computing from compute intensive to data intensive. Whereas many Big Data frameworks exist that minimize the cost of data transfers, few scientific applications integrate these frameworks or adopt data-placement strategies to mitigate the costs. Scientific applications commonly rely on well-established command-line tools that would require complete reinstrumentation in order to incorporate existing frameworks. We developed Sea as a means to enable data-placement strategies for scientific applications executing on HPC clusters without the need to reinstrument workflows. Sea leverages GNU C library interception to intercept POSIX-compliant file system calls made by the applications. We designed a performance model and evaluated the performance of Sea on a synthetic data-intensive application processing a representative neuroimaging dataset (the Big Brain). Our results demonstrate that Sea significantly improves performance, up to a factor of 3$\times$.

A discussion of the history of scientific computing for Radio Astronomy in the Cavendish Laboratory of the University of Cambridge in the decades after the Second World War. This covers the development of the aperture synthesis technique for Radio Astronomy and how that required using the new computing technology developed by the University's Mathematical Laboratory: the EDSAC, EDSAC 2 and TITAN computers. It looks at the scientific advances made by the Radio Astronomy group, particularly the assembling of evidence which contradicted the Steady State Hypothesis. It also examines the software advances that allowed bigger telescopes to be built: the Fast Fourier Transform (FFT) and the degridding algorithm. Throughout, the contribution of women is uncovered, from the diagrams they drew for scientific publications, through programming and operating computers, to writing scientific papers., Comment: First presented at the Joint BSHM CSHPM/SCHPM Conference People, Places, Practices at St Andrews, July 2021

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations., Comment: 22 pages, 4 figures, 3 table

The Electron Ion Collider (EIC) is the next generation of precision QCD facility to be built at Brookhaven National Laboratory in conjunction with Thomas Jefferson National Laboratory. There are a significant number of software and computing challenges that need to be overcome at the EIC. During the EIC detector proposal development period, the ECCE consortium began identifying and addressing these challenges in the process of producing a complete detector proposal based upon detailed detector and physics simulations. In this document, the software and computing efforts to produce this proposal are discussed; furthermore, the computing and software model and resources required for the future of ECCE are described.

Deep learning (DL) is revolutionizing the scientific computing community. To reduce the data gap, active learning has been identified as a promising solution for DL in the scientific computing community. However, the deep active learning (DAL) literature is dominated by image classification problems and pool-based methods. Here we investigate the robustness of pool-based DAL methods for scientific computing problems (dominated by regression) where DNNs are increasingly used. We show that modern pool-based DAL methods all share an untunable hyperparameter, termed the pool ratio, denoted $\gamma$, which is often assumed to be known apriori in the literature. We evaluate the performance of five state-of-the-art DAL methods on six benchmark problems if we assume $\gamma$ is \textit{not} known - a more realistic assumption for scientific computing problems. Our results indicate that this reduces the performance of modern DAL methods and that they sometimes can even perform worse than random sampling, creating significant uncertainty when used in real-world settings. To overcome this limitation we propose, to our knowledge, the first query synthesis DAL method for regression, termed NA-QBC. NA-QBC removes the sensitive $\gamma$ hyperparameter and we find that, on average, it outperforms the other DAL methods on our benchmark problems. Crucially, NA-QBC always outperforms random sampling, providing more robust performance benefits.