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DOE OSTI2024

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↗

NASA NTRS1992

Learning and optimization with cascaded VLSI neural network building-block chips

To demonstrate the versatility of the building-block approach, two neural network applications were implemented on cascaded analog VLSI chips. Weights were implemented using 7-b multiplying digital-to-analog converter (MDAC) synapse circuits, with 31 x 32 and 32 x 32 synapses per chip. A novel learning algorithm compatible with analog VLSI was applied to the two-input parity problem. The algorithm combines dynamically evolving architecture with limited gradient-descent backpropagation for efficient and versatile supervised learning. To implement the learning algorithm in hardware, synapse circuits were paralleled for additional quantization levels. The hardware-in-the-loop learning system allocated 2-5 hidden neurons for parity problems. Also, a 7 x 7 assignment problem was mapped onto a cascaded 64-neuron fully connected feedback network. In 100 randomly selected problems, the network found optimal or good solutions in most cases, with settling times in the range of 7-100 microseconds.

Duong, T.↗

DOE OSTI2022

An Autonomous Robot for Shell and Tube Heat Exchanger Inspection

Shell and tube heat exchangers (STHEs) are critical to energy conversion efficiency of power plants. Eddy current examination is a way to evaluate working conditions of these tubes. However, the current testing apparatus requires human to manually insert an eddy current testing (ECT) probe into and extract it out of individual tubes, and meanwhile monitor measurement results for diagnosis. It is a time-consuming and labor-intensive procedure even for an experienced technician. To tackle this challenge, in this work, we developed a robot enabled ECT system for autonomous inspection of STHEs. The robotic platform employs Mecanum wheeled chassis for high mobility, machine vision to locate tube bundle and tube inlets, a rotational Cartesian mechanism to operate at planes with all possible inclinations, and a task-specific mechanism for ECT probe delivery. Machine vision locates tube bundle and tube inlets by an April tag detection algorithm and a Circle Hough Transform (CHT) algorithm, respectively. Assisted by a guidance cone, the ECT probe is continuously fed into the tubes with a fill factor of 0.819. During this process, the eddy current data are automatically collected and real-time analyzed by convolutional neural networks (CNN), showing accuracy of nearly 100% for identifying defective and non-defective tubes and 85% for four types of defective tubes and non-defective tubes.

autonomy, deep learning, eddy current testing, hea↗

DOE OSTI2023

Machine learning based simultaneous control of air handling unit discharge air and condenser water temperatures set-point for minimized cooling energy in an office building

In this study, an artificial intelligence based real-time prediction and control model to optimize condenser water temperature and discharge air temperature (DAT) set-points in water-cooled air handling unit (AHU) system has been developed. EnergyPlus-MATLAB co-simulation has been conducted to analyze the developed model's effectiveness. Here, to develop artificial neural networks (ANN) model, embedded neural network objects in MATLAB was utilized. The developed model could decide an optimal temperature set-points based on outdoor air wet-bulb temperature to reflect the Korean climate context. As a result, the developed ANN prediction model showed the predictive performance of Cv(RMSE) of approximately 21%. Compared to the conventional fixed temperature algorithm, which fixes AHU DAT at 14°C and condenser water temperature at 32°C, the ANN based optimized control showed a 22% total cooling energy reduction. These results show that significant energy savings can be achieved by simultaneously controlling condenser water temperature and AHU DAT set-points considering Korean climatic characteristics using AI technologies such as ANN models.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Long-term missing value imputation for time series data using deep neural networks

We present an approach that uses a deep learning model, in particular, a MultiLayer Perceptron, for estimating the missing values of a variable in multivariate time series data. We focus on filling a long continuous gap (e.g., multiple months of missing daily observations) rather than on individual randomly missing observations. Our proposed gap filling algorithm uses an automated method for determining the optimal MLP model architecture, thus allowing for optimal prediction performance for the given time series. We tested our approach by filling gaps of various lengths (three months to three years) in three environmental datasets with different time series characteristics, namely daily groundwater levels, daily soil moisture, and hourly Net Ecosystem Exchange. We compared the accuracy of the gap-filled values obtained with our approach to the widely used R-based time series gap filling methods ImputeTS and mtsdi. The results indicate that using an MLP for filling a large gap leads to better results, especially when the data behave nonlinearly. Thus, our approach enables the use of datasets that have a large gap in one variable, which is common in many long-term environmental monitoring observations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

End-to-end optimization for battery materials and molecules by combining graph neural networks and reinforcement learning

The National Renewable Energy Laboratory (NREL), together with the Colorado School of Mines (CSM) and Colorado State University (CSU), has developed a machine learning-enhanced approach to design new battery materials. Currently, such materials are designed in part via numerous expensive high-fidelity computational simulations that predict the performance of a given composition. Even with computational screening tools, the vast landscape of possible molecular or crystal structures exceeds current and future computational capacity. Improving the efficiency by which new materials can be optimized will therefore disrupt the cost, risk, and time required to bring new energy solutions to the marketplace. Predicting the properties of an organic molecule or periodic crystalline material given its structure has grown increasingly common. These approaches leverage large-scale computational and experimental databases and ML approaches such as graph neural networks. The inverse design problem of finding a material that possesses desired properties is substantially more challenging, since enumerating all valid material structures is not feasible. In this project, we leveraged recent success in reinforcement learning to efficiently navigate this high-dimensional search space. Just as algorithms can find the optimal chess moves from nearly limitless options, we train an approach to evolve a simple starting structure into a complex structure that possess the desired properties. Our solution has been demonstrated by applying it to two related design application tasks for short- and long-term energy storage, respectively: (1) the design of solid-state ion conductors and (2) the design of organic redox-active materials. The project has resulted an open-source software library for material design, documented examples of applying the library to both organic and inorganic material optimization, and peer-reviewed publications detailing the data, computational models, and resulting candidate materials.

25 ENERGY STORAGE↗

DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials

Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.

36 MATERIALS SCIENCE↗

DOE OSTI2023

PCAfold 2.0—Novel tools and algorithms for low-dimensional manifold assessment and optimization

We describe an update to our open-source Python package, PCAfold, designed to help researchers generate, analyze and improve low-dimensional data manifolds. In the current version, PCAfold 2.0, we introduce novel tools and algorithms for assessing and optimizing low-dimensional manifolds. This includes a method that generates a “map” of local feature sizes that can help pinpoint researchers to problematic regions on a manifold. We introduce a novel cost function that characterizes the quality of a manifold topology with a single number. We develop two algorithms for feature selection based on principal component analysis (PCA) that use the cost function as an objective function to minimize. We introduce a quantity of interest (QoI)-aware dimensionality reduction strategy where data projections are computed using an artificial neural network and are directly optimized towards representing various projection-independent and projection-dependent QoIs. We also introduce an implementation of partition of unity networks (POUnets) for efficient reconstruction of QoIs from low-dimensional manifolds based on combining neural network classification with localized polynomial regression. Our software can be broadly applicable in all domains of science and engineering that aim to reduce data dimensionality, as well as in the fundamental research on representation learning.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations

Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high- delity simulations of radiation transport within an urban domain. The model is constructed to employ a source location (x, y, z) as input and return the estimated count rate for a set of speci ed detector locations. Because MCNP simulations are computationally expensive, we develop e cient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes (GP) and neural networks (NN) that we train and verify using the MCNP simulations. The trained surrogate models provide an e cient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo (MCMC) algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source's location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction

Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. Furthermore, a neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets with encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.

Gaussian process↗

DOE OSTI2023

Deep Learning Based Workflow for Accelerated Industrial X-Ray Computed Tomography

X-ray computed tomography (XCT) is an important tool for high-resolution non-destructive characterization of additively-manufactured metal components. XCT reconstructions of metal components may have beam hardening artifacts such as cupping and streaking which makes reliable detection of flaws and defects challenging. Furthermore, traditional workflows based on using analytic reconstruction algorithms require a large number of projections for accurate characterization - leading to longer measurement times and hindering the adoption of XCT for in-line inspections. In this paper, we introduce a new workflow based on the use of two neural networks to obtain high-quality accelerated reconstructions from sparse-view XCT scans of single material metal parts. The first network, implemented using fully-connected layers, helps reduce the impact of BH in the projection data without the need of any calibration or knowledge of the component material. The second network, a convolutional neural network, maps a low-quality analytic 3D reconstruction to a high-quality reconstruction. Using experimental data, we demonstrate that our method robustly generalizes across several alloys, and for a range of sparsity levels without any need for retraining the networks thereby enabling accurate and fast industrial XCT inspections.

Rahman, Obaid↗

DOE OSTI2026

Lyapunov-Based Iterative Learning of Regions of Attraction for Autonomous Systems

This paper proposes a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Machine learning of factors for improving oyster hatchery production

Oyster aquaculture and restoration in the Chesapeake Bay are vital, yet hatcheries frequently struggle with inconsistent larval growth and sudden mass mortality events. Unpredictable disruptions in larval production cause large economic losses, represent a perceived risk to growers, and impede industry expansion. To better understand associations between production yield and its potential predictors, we applied machine learning (random forest, and neural network) and statistical (generalized additive model) models to a comprehensive dataset of environmental, water quality, and operational parameters from a Maryland oyster hatchery, aiming to identify key yield predictors and develop a robust forecasting tool. We used recursive Boruta algorithm for variable selection, pinpointing critical predictors, and employed cross-validation to fine-tune model settings. Shapley value analysis offered crucial insights into model interpretations, highlighting week number, Normalized Difference Vegetation Index, salinity, turbidity, and fecundity as primary drivers of yield variability. For low-yield cases, salinity-related variables were particularly important. Our findings provide an early warning system for potential production downturns, empowering hatchery operators to make data-driven decisions for optimizing water conditions, feeding schedules, and broodstock management. By boosting predictability and efficiency, this research directly supports economic stability of the oyster industry and ecological health of the Chesapeake Bay.

Vishwakarma, Srishti [Oak Ridge National Laborator↗

DOE OSTI2026

Lyapunov-Based Iterative Learning of the Region of Attraction for Autonomous Systems

This presentation introduces a novel algorithm for estimating the region of attraction of equilibrium points for nonlinear discrete-time autonomous systems. The method iteratively expands an initial estimate of the region of attraction by constructing unions of sublevel sets of learned functions parametrized as neural networks. Unlike conventional techniques that rely on a single global Lyapunov function, the proposed approach provides a collection of local Lyapunov-like functions, enabling richer representations and potentially larger region of attraction estimates. These functions are trained using sampled state-space data, and their Lipschitz continuity ensures that desirable properties extend beyond the training samples. The devised strategy is tested via numerical simulations, demonstrating the effectiveness of the proposed approach.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Radial basis function neural networks applied to NASA SSME data

This paper presents a brief report on the application of Radial Basis Function Neural Networks (RBFNN) to the prediction of sensor values for fault detection and diagnosis of the Space Shuttle's Main Engines (SSME). The location of the Radial Basis Function (RBF) node centers was determined with a K-means clustering algorithm. A neighborhood operation about these center points was used to determine the variances of the individual processing notes.

Wheeler, Kevin R.↗

NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗

DOE OSTI2021

Adaptive Machine Learning for Robust Diagnostics and Control of Time-Varying Particle Accelerator Components and Beams

Machine learning (ML) is growing in popularity for various particle accelerator applications including anomaly detection such as faulty beam position monitor or RF fault identification, for non-invasive diagnostics, and for creating surrogate models. ML methods such as neural networks (NN) are useful because they can learn input-output relationships in large complex systems based on large data sets. Once they are trained, methods such as NNs give instant predictions of complex phenomenon, which makes their use as surrogate models especially appealing for speeding up large parameter space searches which otherwise require computationally expensive simulations. However, quickly time varying systems are challenging for ML-based approaches because the actual system dynamics quickly drifts away from the description provided by any fixed data set, degrading the predictive power of any ML method, and limits their applicability for real time feedback control of quickly time-varying accelerator components and beams. In contrast to ML methods, adaptive model-independent feedback algorithms are by design robust to un-modeled changes and disturbances in dynamic systems, but are usually local in nature and susceptible to local extrema. In this work, we propose that the combination of adaptive feedback and machine learning, adaptive machine learning (AML), is a way to combine the global feature learning power of ML methods such as deep neural networks with the robustness of model-independent control. We present an overview of several ML and adaptive control methods, their strengths and limitations, and an overview of AML approaches.

97 MATHEMATICS AND COMPUTING↗