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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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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Physics-informed heterogeneous graph neural networks for DC blocker placement

The threat of geomagnetic disturbances (GMDs) to the reliable operation of the bulk energy system has spurred the development of effective strategies for mitigating their impacts. One such approach involves placing transformer neutral blocking devices, which interrupt the path of geomagnetically induced currents (GICs) to limit their impact. The high cost of these devices and the sparsity of transformers that experience high GICs during GMD events, however, calls for a sparse placement strategy that involves high computational cost. To address this challenge, we developed a physics-informed heterogeneous graph neural network (PIHGNN) for solving the graph-based dc-blocker placement problem. Our approach combines a heterogeneous graph neural network (HGNN) with a physics-informed neural network (PINN) to capture the diverse types of nodes and edges in ac/dc networks and incorporates the physical laws of the power grid. We train the PIHGNN model using a surrogate power flow model and validate it using case studies. Results demonstrate that PIHGNN can effectively and efficiently support the deployment of GIC dc-current blockers, ensuring the continued supply of electricity to meet societal demands. Furthermore, our approach has the potential to contribute to the development of more reliable and resilient power grids capable of withstanding the growing threat that GMDs pose.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Physics informed deep neural network embedded in a chemical transport model for the Amazon rainforest

Secondary organic aerosols (SOA) are fine particles in the atmosphere, which interact with clouds, radiation and affect the Earth’s energy budget. SOA formation involves chemistry in gas phase, aqueous aerosols, and clouds. Simulating these chemical processes involve solving a stiff set of differential equations, which are computationally expensive steps for three-dimensional chemical transport models. Deep neural networks (DNNs) are universal function approximators that could be used to represent the complex nonlinear changes in aerosol physical and chemical processes; however, key challenges such as generalizability to extended time periods, preservation of mass balance, simulating sparse model outputs, and maintaining physical constraints have limited their use in atmospheric chemistry. Here, we develop an approach of using a physics-informed DNN that overcomes previous such challenges and demonstrates its applicability for the chemical formation processes of isoprene epoxydiol SOA (IEPOX-SOA) over the Amazon rainforest. The DNN is trained with data generated by simulating IEPOX-SOA over the entire atmospheric column, using the Weather Research and Forecasting Model coupled with Chemistry (WRF-Chem). The trained DNN is then embedded within WRF-Chem to replace the computationally expensive default solver of IEPOX-SOA formation. The trained DNN predictions generalizes well with the default model simulation of the IEPOX-SOA mass concentrations and its size distribution (20 size bins) over several days of simulations in both dry and wet seasons. The embedded DNN reduces the computational expense of WRF-Chem by a factor of 2. Our approach shows promise in terms of application to other computationally expensive chemistry solvers in climate models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks↗
DOE OSTI2024

Speeding up and reducing memory usage for scientific machine learning via mixed precision

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets) stand out as the leading techniques for solving partial differential equations by incorporating both physical equations and experimental data. However, training PINNs and DeepONets require significant computational resources, including long computational times and large amounts of memory. In search of computational efficiency, training neural networks using half precision (float16) rather than the conventional single (float32) or double (float64) precision has gained substantial interest, given the inherent benefits of reduced computational time and memory consumed. However, we find that float16 cannot be applied to SciML methods, because of gradient divergence at the start of training, weight updates going to zero, and the inability to converge to a local minima. To overcome these limitations, we explore mixed precision, which is an approach that combines the float16 and float32 numerical formats to reduce memory usage and increase computational speed. Our experiments showcase that mixed precision training not only substantially decreases training times and memory demands but also maintains model accuracy. Here, we also reinforce our empirical observations with a theoretical analysis. The research has broad implications for SciML in various computational applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗
DOE OSTI2025

Exploring the nexus of many-body theories through neural network techniques: the tangent model

Abstract In this paper, we present a physically informed neural network (NN) representation of the effective interactions associated with coupled-cluster downfolding models to describe chemical systems and processes. The NN representation not only allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems corresponding to various levels of complexity of the underlying wave functions, but also reveals that the bare and effective interactions are related by a tangent function of some latent variables. We refer to this characterization of the effective interaction as a tangent model. We discuss the connection between this tangent model for the effective interaction with the previously developed theoretical analysis that examines the difference between the bare and effective Hamiltonians in the corresponding active spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Artificial to Spiking Neural Networks Conversion with Calibration in Scientific Machine Learning

Here, we introduce a method to convert physics-informed neural networks (PINNs), commonly used in scientific machine learning, to spiking neural networks (SNNs), which are expected to have higher energy efficiency compared to traditional artificial neural networks (ANNs). We first extend the calibration technique of SNNs to arbitrary activation functions beyond ReLU, making it more versatile, and we prove a theorem that ensures the effectiveness of the calibration. We successfully convert PINNs to SNNs, enabling computational efficiency for diverse regression tasks in solving multiple differential equations, including the unsteady Navier–Stokes equations. We demonstrate great gains in terms of overall efficiency, including separable PINNs (SPINNs), which accelerate the training process. Overall, this is the first work of this kind and the proposed method achieves relatively good accuracy with low spike rates.

PINN↗
DOE OSTI2026

Adaptation of virtual synchronous generators to dynamic conditions in power grids

Virtual synchronous generators (VSGs) are widely adopted as grid-forming controls for inverter-based resources. However, when grid conditions vary significantly as characterized by changes in short-circuit ratio (SCR) and the reactance-to-resistance (X/R) ratio, fixed-gain designs and the commonly used P–Q decoupling assumption can become inaccurate. Such conditions can degrade transient power performance, leading to oscillations, prolonged settling, and overshoot, particularly in stiff-grid operating points. This paper quantifies how grid strength and impedance-dependent coupling affect the active–reactive power dynamics of a conventional VSG over a broad range of SCR and X/R values. An adaptive VSG tuning framework is then developed by combining (i) a coupling-explicit, impedance-parameterized state-space model to enable systematic controller synthesis, (ii) a full-state-feedback law designed via pole placement to meet prescribed damping and settling-time specifications, and (iii) a physics-informed neural network (PINN)–based online grid-impedance estimator that updates controller gains in real time as grid conditions vary. Offline simulations in MATLAB/Simulink and real-time validation on an OPAL-RT platform show that the proposed method preserves consistent damping and settling behavior with reduced overshoot across wide SCR and X/R ranges, compared with fixed-gain VSG baselines.

Adaptive control↗
DOE OSTI2024

PINN surrogate of Li-ion battery models for parameter inference, Part I: Implementation and multi-fidelity hierarchies for the single-particle model

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. Here, this study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models - such as the single-particle model (SPM) and the pseudo-2D (P2D) model - with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/PINNSTRIPES). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

25 ENERGY STORAGE↗
DOE OSTI2021

When and why PINNs fail to train: A neural tangent kernel perspective

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. Here in this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions, it converges to a deterministic kernel that stays constant during training in the infinite-width limit. This allows us to analyze the training dynamics of PINNs through the lens of their limiting NTK and find a remarkable discrepancy in the convergence rate of the different loss components contributing to the total training error. To address this fundamental pathology, we propose a novel gradient descent algorithm that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error. Finally, we perform a series of numerical experiments to verify the correctness of our theory and the practical effectiveness of the proposed algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Crustal Scale Travel Time Prediction with the SALSA3D Framework and Machine Learning

The SALSA3D project aims to improve our models used in travel time prediction. The current version uses tomographic modeling for propagation through the Earth’s mantle because of the large number (order of millions) of observations of seismic phases which primarily traverse the Earth’s mantle and the ability to pose the travel time problem as a set of linear equations. However, all seismic rays traverse the crust to reach receivers at the surface and therefore models of propagation through the crust are required. Therefore, the primary motivation for this study is to explore how to increase the scope of the SALSA3D project to phases which travel primarily through the crust. In this report, we evaluate new, machine learning based and physics-based methods to model these travel times for integration into the SALSA3D framework. Our results suggest that using our existing physics-based travel time tomography method is a viable approach for the regional to global scale, but better predictive capabilities can be achieved through a neural network trained on the region of interest for near-regional offsets. We suggest future iterations of SALSA3D should incorporate machine learning tools such as Physics-Informed Neural Networks or Bayesian Neural Networks.

58 GEOSCIENCES↗