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At least 37 records · Page 2

Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics

Abstract Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data are 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 multiphysics 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 multiphysics 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 are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.

Computer Science↗

Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

97 MATHEMATICS AND COMPUTING↗

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗

Learning thermodynamic master equations for open quantum systems

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.

Mathematics and Computing↗

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗

Probabilistic data fusion and physics-informed machine learning: A new paradigm for modeling under uncertainty, and its application to accelerating the discovery of new materials

In this report we summarize the work conducted by PI Perdikaris and his group under this Early Career project DE–SC0019116 during the period of 09/01/2018 – 08/31/2023. The central aim of the work was to introduce a new paradigm for scientific data analysis that can seamlessly synthesize rigorous mathematical modeling with data of variable fidelity (e.g., measurements at multiple scales/resolutions or predictions of variable fidelity models) and multiple modalities (e.g., images, time–series, or scattered measurements). The setting we are interested in involves complex systems that are partially observed and whose dynamical behavior could be hard to model or totally unknown. The inherent uncertainty associated with this setting necessitates a departure from the classical deterministic realm of modeling and scientific computation, and, consequently, our main building blocks can no longer be crisp deterministic numbers and governing laws, but instead we must operate with probabilistic models.

97 MATHEMATICS AND COMPUTING↗

Performance on HPC Platforms Is Possible Without C++

Computing at large scales has become extremely challenging due to increasing heterogeneity in both hardware and software. More and more scientific workflows must tackle a range of scales and use machine learning and AI intertwined with more traditional numerical modeling methods, placing more demands on computational platforms. These constraints indicate a need to fundamentally rethink the way computational science is done and the tools that are needed to enable these complex workflows. The current set of C++-based solutions may not suffice, and relying exclusively upon C++ may not be the best option, especially because several newer languages and boutique solutions offer more robust design features to tackle the challenges of heterogeneity. In June 2023, we held a mini symposium that explored the use of newer languages and heterogeneity solutions that are not tied to C++ and that offer options beyond template metaprogramming and Parallel. For for performance and portability. In conclusion, we describe some of the presentations and discussion from the mini symposium in this article.

97 MATHEMATICS AND COMPUTING↗

Scalable 3D reconstruction for X-ray single particle imaging with online machine learning

X-ray free-electron lasers offer unique capabilities for measuring the structure and dynamics of biomolecules, helping us understand the basic building blocks of life. Notably, high-repetition-rate free-electron lasers enable single particle imaging, where individual, weakly scattering biomolecules are imaged under near-physiological conditions with the opportunity to access fleeting states that cannot be captured in cryogenic or crystallized conditions. Existing X-ray single particle reconstruction algorithms, which estimate the particle orientation for each image independently, are slow and memory-intensive when handling the massive datasets generated by emerging free-electron lasers. Here, we introduce X-RAI (X-Ray single particle imaging with Amortized Inference), an online reconstruction framework that estimates the structure of 3D macromolecules from large X-ray single particle datasets. X-RAI consists of a convolutional encoder, which amortizes pose estimation over large datasets, as well as a physics-based decoder, which employs an implicit neural representation to enable high-quality 3D reconstruction in an end-to-end, self-supervised manner. We demonstrate that X-RAI achieves state-of-the-art performance for small-scale datasets in simulation and challenging experimental settings and demonstrate its unprecedented ability to process large datasets containing millions of diffraction images in an online fashion. These abilities signify a paradigm shift in X-ray single particle imaging towards real-time reconstruction.

Computer science↗

Inferring building height from footprint morphology data

As cities continue to grow globally, characterizing the built environment is essential to understanding human populations, projecting energy usage, monitoring urban heat island impacts, preventing environmental degradation, and planning for urban development. Buildings are a key component of the built environment and there is currently a lack of data on building height at the global level. Current methodologies for developing building height models that utilize remote sensing are limited in scale due to the high cost of data acquisition. Other approaches that leverage 2D features are restricted based on the volume of ancillary data necessary to infer height. Here, we find, through a series of experiments covering 74.55 million buildings from the United States, France, and Germany, it is possible, with 95% accuracy, to infer building height within 3 m of the true height using footprint morphology data. Our results show that leveraging individual building footprints can lead to accurate building height predictions while not requiring ancillary data, thus making this method applicable wherever building footprints are available. The finding that it is possible to infer building height from footprint data alone provides researchers a new method to leverage in relation to various applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Bridging Python to Silicon: The SODA Toolchain

Systems performing scientific computing, data analysis, and machine learning tasks have a growing demand for application-specific accelerators that can provide high computational performance while meeting strict size and power requirements. However, the algorithms and applications that need to be accelerated are evolving at a rate that is incompatible with manual design processes based on hardware description languages. Agile hardware design tools based on compiler techniques can help by quickly producing an application-specific integrated circuit (ASIC) accelerator starting from a high-level algorithmic description. Here, we present the software-defined accelerator (SODA) synthesizer, a modular and open-source hardware compiler that provides automated end-to-end synthesis from high-level software frameworks to ASIC implementation, relying on multilevel representations to progressively lower and optimize the input code. Our approach does not require the application developer to write any register-transfer level code, and it is able to reach up to 364 giga floating point operations per second (GFLOPS)/W efficiency (32-bit precision) on typical convolutional neural network operators.

97 MATHEMATICS AND COMPUTING↗

ASAP: Automatic Synthesis of Area-Efficient and Precision-Aware CGRAs

Coarse-grained reconfigurable accelerators (CGRAs) are a promising accelerator design choice that strikes a balance between performance and adaptability to different computing patterns across various applications domains. Designing a CGRA for a specific application domain involves enormous software/hardware engineering effort. Recent research works explore loop transformations, functional unit types, network topology, and memory size to identify optimal CGRA designs given a set of kernels from a specific application do- main. Unfortunately, the impact of functional units with different precision support has rarely been investigated. To address this gap, we propose ASAP – a hardware/software co-design framework that automatically identifies and synthesizes optimal precision-aware CGRA for a set of applications of interest. Our evaluation shows that ASAP generates specialized designs 3.2×, 4.21×, and 5.8× more efficient (in terms of performance per unit of energy or area) than non-specialized homogeneous CGRAs, for the scientific computing, embedded, and edge machine learning domains, respectively, with limited accuracy loss. Moreover, ASAP provides more efficient designs than other state-of-the-art synthesis frameworks for specialized CGRAs.

artificial intelligence↗

Composable optimization and control toolkit for scientific applications

Applications of Artificial Intelligence (AI) and Machine Learning (ML) can improve the computational efficiency and scientific research output. In order to improve interoperability and reuse of AI/ML software, a composable approach is required. This talk presents a composable approach for scientific workflow development that allows seamless integration of various modules developed by independent researchers. These practices will reduce redundant software development by allowing re-use of workflow modules across projects, teams, departments and facilities. We will present three use cases that follow the composable approach namely, Scientific Optimization and Control Toolkit (SOCT), SciDAC QuantOm workflow, and JLab Nuclear Physics experimental workflows. This talk will dive deeper into SOCT and present the details of the composable code development for optimization and control algorithms using reinforcement learning.

Rajput, Kishansingh↗

Toward digital design at the exascale: An overview of project ICECap

High performance computing has entered the Exascale Age. Capable of performing over 1018 floating point operations per second, exascale computers, such as El Capitan, the National Nuclear Security Administration's first, have the potential to revolutionize the detailed in-depth study of highly complex science and engineering systems. However, in addition to these kind of whole machine “hero” simulations, exascale systems could also enable new paradigms in digital design by making petascale hero runs routine. Currently, untenable problems in complex system design, optimization, model exploration, and scientific discovery could all become possible. Motivated by the challenge of uncovering the next generation of robust high-yield inertial confinement fusion (ICF) designs, project ICECap (Inertial Confinement on El Capitan) attempts to integrate multiple advances in machine learning (ML), scientific workflows, high performance computing, GPU-acceleration, and numerical optimization to prototype such a future. Built on a general framework, ICECap is exploring how these technologies could broadly accelerate scientific discovery on El Capitan. In addition to our requirements, system-level design, and challenges, we describe some of the key technologies in ICECap, including ML replacements for multiphysics packages, tools for human-machine teaming, and algorithms for multifidelity design optimization under uncertainty. As a test of our prototype pre-El Capitan system, we advance the state-of-the art for ICF hohlraum design by demonstrating the optimization of a 17-parameter National Ignition Facility experiment and show that our ML-assisted workflow makes design choices that are consistent with physics intuition, but in an automated, efficient, and mathematically rigorous fashion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗

Integration of scanning probe microscope with high-performance computing: Fixed-policy and reward-driven workflows implementation

The rapid development of computation power and machine learning algorithms has paved the way for automating scientific discovery with a scanning probe microscope (SPM). The key elements toward operationalization of the automated SPM are the interface to enable SPM control from Python codes, availability of high computing power, and development of workflows for scientific discovery. Here, we build a Python interface library that enables controlling an SPM from either a local computer or a remote high-performance computer, which satisfies the high computation power need of machine learning algorithms in autonomous workflows. We further introduce a general platform to abstract the operations of SPM in scientific discovery into fixed-policy or reward-driven workflows. Furthermore, our work provides a full infrastructure to build automated SPM workflows for both routine operations and autonomous scientific discovery with machine learning.

47 OTHER INSTRUMENTATION↗

Leveraging interpolation models and error bounds for verifiable scientific machine learning

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. Here, in this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.

97 MATHEMATICS AND COMPUTING↗

Leveraging History to Predict Infrequent Abnormal Transfers in Distributed Workflows

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

97 MATHEMATICS AND COMPUTING↗

Final report- UFL - RAPIDS2: A SciDAC Institute for Computer Science, Data, and Artificial Intelligence

The research initiatives supported by the U.S. Department of Energy (DOE) Grant DE-SC0022265 are fundamentally aimed at pioneering advanced machine learning (ML) techniques for scientific data compression within high-performance computing (HPC) environments. This comprehensive body of work addresses the critical challenge posed by the exponential growth of data generated by scientific simulations in domains such as fusion energy, climate modeling, and computational fluid dynamics (CFD). A core objective is to develop compression algorithms that achieve substantial data reduction—often by orders of magnitude—while rigorously ensuring the fidelity of both the primary data (PD) and scientifically crucial derived quantities of interest (QoI). The methodologies deployed under this grant integrate sophisticated deep learning architectures, prominently featuring autoencoders, advanced generative models like conditional diffusion, and hybrid learning techniques. Key innovations include the development of Guaranteed Autoencoders (GAE) and the Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) framework, which provide explicit, instance-level error bounds on reconstructed data. Furthermore, specialized strategies such as nonlinear constraint satisfaction are employed to preserve the integrity of QoI, a vital requirement for the trustworthiness of downstream scientific analyses. This research also focuses on the design and implementation of scalable, GPU-accelerated software pipelines that seamlessly integrate into existing HPC workflows, ensuring both computational efficiency and practical applicability. The CAESAR framework, for example, unifies foundation and generative models to create an adaptive and efficient compression solution for spatio-temporal scientific data. Collectively, these efforts represent a significant advancement in mitigating the scientific data deluge, enabling more effective data management, accelerated scientific discovery, and optimized utilization of HPC resources.

97 MATHEMATICS AND COMPUTING↗