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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2025

Application of a Physics-Informed Convolutional Neural Network for Monitoring the Temperature Fields in High-Temperature Gas Reactors

Here, this work presents current advances in applying a physics-informed convolutional neural network (CNN) to evaluate temperature distributions in advanced reactors. Our goal is to demonstrate that the CNN can reconstruct temperature fields within the solid region of a prismatic fuel assembly in a high-temperature gas reactor (HTGR) with sensor data available in only a few cooling channels. Before that, we showcase the superior performance of the physics-informed CNN in comparison to a purely data-driven multilayer perceptron (MLP), considering a canonical heated channel setup. This analysis shows the advantages of our approach and justifies its choice. The datasets employed here are obtained upon numerical simulations performed with codes under the Nuclear Energy Advanced Modeling and Simulation program. This work is important, as industry experience indicates that the assembly material in HTGR concepts is prone to large thermal-mechanical loads nearing operational limits. This makes it crucial to characterize peak temperatures and their distributions near hot spots. Modern thermocouples are unreliable in these types of harsh environments because of the high neutron fluxes and elevated temperatures involved. The CNN-based field reconstruction represents an attractive solution, enabling sensor arrays in less aggressive locations and augmenting indirect predictions for less accessible regions. The results show that the CNN reduces prediction errors by orders of magnitude in comparison to the MLP, considering the simple yet well-representative heated channel case. In the case of the HTGR fuel assembly, the CNN can successfully reconstruct temperature fields over various cooling regimes. Furthermore, we also explore the algorithm’s ability to detect abnormalities. Interestingly, the CNN proves it has the capacity to detect blockage in one of the noninstrumented cooling channels.

Machine learning↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Structure-aware Initialization via Numerical Continuation and Informed Priors

Scientific machine learning (SciML) often operates in ill-conditioned, weakly identifiable regimes due to limited data or indirect observations. In such settings, optimization and inference are highly sensitive to the starting point, making initialization--often under-reported--a consequential degree of freedom. Random initialization is not a neutral default as it induces an implicit prior over candidate solutions and can systematically bias the result, producing large run-to-run variability. Here, we formalize this view by treating initialization as a hidden confounder in SciML and develop a unifying theory for structure-aware initialization via numerical continuation, constructing warm starts from related problem instances. Across representative tasks, including physics-informed neural networks, maximum likelihood estimation, and variational inference, warm starts have been shown to consistently reduce optimization effort and improve reliability.

Data integrity↗
DOE OSTI2025

Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram

X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly suitable for time- or dose-critical in vivo/in situ/operando (tomography) experiments because it requires only a single intensity measurement. However, the phase information of the wave field is lost during the measurement and must be recovered. Conventional algebraic and iterative methods often rely on specific approximations or boundary conditions that may not be met by many samples or experimental setups. In addition, they require manual tuning of reconstruction parameters by experts, making them less adaptable for complex or variable conditions. Here we present a self-learning approach for solving the inverse problem of phase retrieval in the near-field regime of Fresnel theory using a single intensity measurement (hologram). A physics-informed generative adversarial network is employed to reconstruct both the phase and absorbance of the unpropagated wave field in the sample plane from a single hologram. Unlike most state-of-the-art deep learning approaches for phase retrieval, our approach does not require paired, unpaired, or simulated training data. This significantly broadens the applicability of our approach, as acquiring or generating suitable training data remains a major challenge due to the wide variability in sample types and experimental configurations. The algorithm demonstrates robust and consistent performance across diverse imaging conditions and sample types, delivering quantitative, high-quality reconstructions for both simulated data and experimental datasets acquired at beamline P05 at PETRA III (DESY, Hamburg), operated by Helmholtz-Zentrum Hereon. Furthermore, it enables the simultaneous retrieval of both phase and absorption information.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Convolutional Neural Network–Aided Temperature Field Reconstruction: An Innovative Method for Advanced Reactor Monitoring

In this study, the capabilities of a physics-informed convolutional neural network (CNN) for reconstructing the temperature field from a limited set of measurements taken at the boundaries of internal flows are demonstrated. Such an approach enables the development of less invasive monitoring methods for real-time plant diagnostics. As a test case, a Molten Salt Fast Reactor (MSFR) design was selected. This circulating fuel reactor has received interest from both scientific and industrial communities due to its intrinsic safety and sustainability. Molten salt flows in such reactors, however, can present highly localized temperature peaks that can induce significant thermal stresses onto the vessel walls. At these local maxima, the salt temperature may exceed a thousand kelvins, which makes a direct measurement challenging or even unfeasible. The proposed CNN algorithm allows one to detect indirectly such discontinuities through an accurate, albeit indirect, temperature measurement method during reactor operation. The datasets employed to train and test the machine learning models in the present work were generated with Nek5000, a computational fluid dynamics (CFD) code developed at Argonne National Laboratory. The CNN algorithm is trained with CFD results that span a set of MSFR operational power and flow ranges. Here, to demonstrate the efficacy of the algorithm, predictions are made for test cases contained within the training range but for which the CFD data were not used when training. Results demonstrate that the proposed technique properly characterizes temperature peaks and distributions within the domain for a broad range of scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

1.2.4.404 - Data-Driven Approach for Hydropower Plant Controller Prototyping Using Remote Hardware in the Loop (DR-HIL)

Real-time prototyping of hydropower plant controls is important for reducing the cost and the risk of field deployment. This project will 1) collect design and operational data from actual hydro plants and 2) use a physics-informed machine learning approach for real-time emulation of hydropower plants, including hydro turbine and hydrodynamics. The data-driven models will be interfaced with digital real-time simulation at NREL’s Flatirons campus for hardware-in-the-loop (HIL) testing of the governor hardware device or controller-HIL (CHIL). The proposed approach will also establish the connectivity based remote CHIL testing capability using real-time data streams from an actual hydro plant. This integrated hydro-plant emulation with CHIL will be used to prototype hydro-governor controls and eventually provide an opportunity to test hydropower integrated with various technologies (e.g. conventional and renewable generation, energy conversion, etc.) as HIL.

controls prototyping↗
DOE OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Machine learning methods for particle stress development in suspension Poiseuille flows

Numerical simulations are used to study the dynamics of a developing suspension Poiseuille flow with monodispersed and bidispersed neutrally buoyant particles in a planar channel, and machine learning is applied to learn the evolving stresses of the developing suspension. The particle stresses and pressure develop on a slower time scale than the volume fraction, indicating that once the particles reach a steady volume fraction profile, they rearrange to minimize the contact pressure on each particle. Here we consider how the stress development leads to particle migration, time scales for stress development, and present a new physics-informed Galerkin neural network that allows for learning the particle stresses when direct measurements are not possible. The particle fluxes are compared with the Suspension Balance Model with good agreement. We show that when stress measurements are possible, the MOR-physics operator learning method can also capture the particle stresses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improved Architectures and Training Algorithms for Deep Operator Networks

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

PINN surrogate of Li-ion battery models for parameter inference, Part II: Regularization and application of the pseudo-2D model

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of ~2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. Finally, in the low-data availability scenario, the testing error was estimated to ~2 mV for the SPM surrogate and ~10 mV for the P2D surrogate which could be mitigated with additional data.

25 ENERGY STORAGE↗
DOE OSTI2023

Enabling site-specific well leakage risk estimation during geologic carbon sequestration using a modular deep-learning-based wellbore leakage model

Geologic carbon sequestration (GCS) is a promising technology for mitigating net carbon emissions and growing climate concern by storing CO 2 in reservoirs. Oil and gas brownfields are an attractive option for CO 2 storage, but these sites have many historical wellbores from petroleum production and can be a potential leakage pathway for CO 2 or formation brine. Therefore, risk management of GCS operations requires an assessment of potential well leakage. Due to the high uncertainty of the system, stochastic approaches are ideal for quantifying the range of risk behaviors, but they must be computationally efficient in the face of complex physics. Here, we develop a new physics-centric deep learning wellbore model to predict the leakage of CO 2 and brine through leaky wellbores. Multi-physics numerical simulations were used to generate data sets, and physics-informed features were introduced. Neural networks were optimized with an automated searching algorithm. Feature analysis quantifies the impact of each feature on model prediction and confirms the role of physics-inspired parameters. The model shows high predictive performance across a wide range of geologic and injection conditions and well attributes. In conclusion, a case study illustrates how the model is applied to assess well leakage in GCS operations.

58 GEOSCIENCES↗
DOE OSTI2025

Scaling Field-Theoretic Simulation for Multicomponent Mixtures with Neural Operators

Multicomponent polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, neural operators, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Physics-informed neural network with transfer learning (TL-PINN) based on domain similarity measure for prediction of nuclear reactor transients

Nuclear reactor safety and efficiency can be enhanced through the development of accurate and fast methods for prediction of reactor transient (RT) states. Physics informed neural networks (PINNs) leverage deep learning methods to provide an alternative approach to RT modeling. Applications of PINNs in monitoring of RTs for operator support requires near real-time model performance. However, as with all machine learning models, development of a PINN involves time-consuming model training. Here, we show that a transfer learning (TL-PINN) approach achieves significant performance gain, as measured by reduction of the number of iterations for model training. Using point kinetic equations (PKEs) model with six neutron precursor groups, constructed with experimental parameters of the Purdue University Reactor One (PUR-1) research reactor, we generated different RTs with experimentally relevant range of variables. The RTs were characterized using Hausdorff and Fréchet distance. We have demonstrated that pre-training TL-PINN on one RT results in up to two orders of magnitude acceleration in prediction of a different RT. The mean error for conventional PINN and TL-PINN models prediction of neutron densities is smaller than 1%. We have developed a correlation between TL-PINN performance acceleration and similarity measure of RTs, which can be used as a guide for application of TL-PINNs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Trustworthy Physics-Informed Deep Learning for Predictive Scientific Computing

This project has developed powerful trustworthy physics-informed deep learning (TPiDL) models and methods to fundamentally enhance the scale and power of computational modeling in the scientific and engineering domains. Deep learning (DL) has radically advanced the state-of-the-art in machine learning, computer vision, natural language processing, and also scientific computing. Nevertheless, progress has been driven almost entirely by empirical observations, hacks, and tricks. Under the support of this project, the graph operator learning tools and advanced trustworthy physical informed neural networks have been developed. In addition, stochastic gradient replica-exchange Markov Chain Monte Carlo (MCMC) sampling algorithms have been designed to quantify the uncertainties and speed up the training of large-scale neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Utilizing Physics-Informed Synthetic Data to Train a Digital Twin for Predicting Reactor Operations

Understanding techniques to strengthen the nuclear nonproliferation regime is crucial in reducing the creation of nuclear weaponry on the basis of advancements in the nuclear energy industry. Prior to construction of a nuclear power plant, it is necessary to understand the proliferation potential of the plant’s reactor. Digital twins serve as a unique solution to recognizing reactor behavior indicative of nuclear proliferation. The following research conducted serves as a validation to training a digital twin on synthetic data fabricated via means of reactor physics simulations based on parameters of Idaho State University’s AGN-201 reactor. The synthetic data is utilized to train a long short-term memory (LSTM) recurrent neural network model. The accuracy of the predicted data is measured against real operational data to verify the reliability of the synthetic data creation methods and if these methods should be used in the future to inform inspectors of a reactor’s proliferation capabilities.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2025

Physics-Informed Neural Network (PINN) Prediction of Mixed Mass-Heat-Crystallization Limited Methane Hydrate Formation and Dissociation in Micro-Confinement

The creation and use of Physics-Informed Neural Networks (PINNs) for simulating the dynamics of methane hydrate formation and dissociation will be presented. The PINN framework's main benefit is its capacity to impose physical consistency with only a partial comprehension of the governing equations. This makes the algorithm especially useful for systems with little experimental evidence or a lack of theoretical knowledge. A strong basis for forecasting methane hydrate behavior over the verified operating ranges of 30.0-80.9 bar pressure and 1.0-4.0 K sub-cooling conditions is provided by the combination of conductive heat transfer equations and mixed mass-transfer–crystallization kinetics. PINNs were more accurate at predicting the mixed mass-heat-crystallization limited kinetics than conventional Artificial Neural Networks (ANNs), demonstrating remarkable predictive accuracy for methane hydrate production over the ANN model. The efficiency of incorporating physical limitations from first principles into machine learning frameworks for methane hydrate crystallizations is reinforced by these findings. For hydrate-related applications in energy generation, carbon sequestration, and climate modelling, our study establishes PINNs as a computational tool that is both scalable and efficient. The proven capacity to close the gap between conventional physics-based simulations and solely data-driven models creates new opportunities for expedited hydrate research and practical applications.

Hartman, Ryan L [NYU Tandon School of Engineering]↗