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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier–Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a two-dimensional synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a centre plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. Furthermore, the results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2022

Analyses of internal structures and defects in materials using physics-informed neural networks

Characterizing internal structures and defects in materials is a challenging task, often requiring solutions to inverse problems with unknown topology, geometry, material properties, and nonlinear deformation. Here, we present a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters. By using a mesh-free method, we parameterize the geometry of the material using a differentiable and trainable method that can identify multiple structural features. We validate this approach for materials with internal voids/inclusions using constitutive models that encompass the spectrum of linear elasticity, hyperelasticity, and plasticity. We predict the size, shape, and location of the internal void/inclusion as well as the elastic modulus of the inclusion. Our general framework can be applied to other inverse problems in different applications that involve unknown material properties and highly deformable geometries, targeting material characterization, quality assurance, and structural design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Enhancing Drinking Water Quality Modeling: Leveraging Physics Informed Neural Networks for Learning with Imperfect Reaction Models and Partial Data

Chemical kinetics models, typically formulated as systems of ordinary or partial differential equations, are valuable tools for simulating drinking water quality. However, these models often face inaccuracies due to discrepancies between the laboratory and the real-world conditions, as well as limitations in experimental analytical methods, hindering the accurate representation of the true underlying chemical mechanisms. In this study, we propose a Physics Informed Neural Network (PINN), using the eXtreme Theory of Functional Connections, to improve the prediction of chemical concentrations over time. The PINN method accounts for imperfect chemical models and incorporates partial data to improve predictions. Focusing on reactions describing water disinfection residual and disinfectant byproduct formation, which are crucial for public health and regulatory compliance, we demonstrate that the PINN model is able to accurately predict the concentrations of chemical species across various pH values. Notably, the model extends its accuracy to predict concentrations of chemical species not originally included in its training data. The developed method can be extended to a variety of chemical systems, offering a wide array of potential applications.

13 HYDRO ENERGY↗
DOE OSTI2024

Generative Physics-Informed Neural Network Solving Multi-Scale and Multi-Phase Plasma Chemical Flow Field

Low-temperature plasmas (LTPs) are non-equilibrium systems with near-room-temperature gas and highly energetic electrons. This makes them ideal for delicate applications in biomedicine and semiconductor manufacturing, enabling processes like wound healing, sterilization, etching, and plasma-enhanced chemical vapor deposition without thermal damage. However, LTPs involve complex chemistries, with hundreds of species and thousands of reactions, complicating their diagnosis, prediction, and control. Conventional diagnostics, such as Fourier-transform infrared spectroscopy (FTIR), laser-induced fluorescence (LIF), and optical emission spectroscopy (OES), offer limited species detection, while mass spectrometry (MS) struggles with low-sensitivity species. Additionally, LTP simulations face multi-scale challenges, as macroscopic fluid dynamics and microscopic particle collisions operate on vastly different timescales. To address these issues, we developed an artificial intelligence (AI) based diagnostic system: a generative physics-informed neural network (PINN-Gen) that can predict spatially resolved species concentrations and temperatures in LTPs by integrating experimental data from planar LIF with microscopic plasma chemical kinetics and macroscopic fluid mechanics, including plasma-liquid interactions at the interface between two phases. PINN-Gen solves no equations but checks the errors of physical laws by substituting the output from neural network, and the comparison with the experimental results. Thus, it naturally avoids the multi-scale difficulty of numerical simulations and predicts the results of conventionally unsolvable multi-scale and multi-phase problems. The real-time prediction will be robust due to the physical information used in the training of such a neural network, and only very limited input of condition required due to its generative feature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Identifying Heterogeneous Micromechanical Properties of Biological Tissues via Physics–Informed Neural Networks

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in data-driven models for learning full-field mechanical responses, such as displacement and strain, from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, a physics-informed machine learning approach is proposed to identify the elasticity map in nonlinear, large deformation hyperelastic materials. This study reports the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) in inferring the heterogeneous elasticity maps across materials with structural complexity that closely resemble real tissue microstructure, such as brain, tricuspid valve, and breast cancer tissues. Further, the improved architecture is applied to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Furthermore, the improved network architecture consistently produces accurate estimations of heterogeneous elasticity maps, even when there is up to 10% noise present in the training data.

59 BASIC BIOLOGICAL SCIENCES↗
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 OSTI2022

Physics-Informed Neural Network Modeling of Li-Ion Batteries: Preprint

Li-ion batteries (LIB) are a promising solution to enable storage of intermittent energy sources due to their high energy density. However, LIBs are known to significantly degrade after about 1000 charge-discharge cycles. LIBs degrade following different degradation modes and at a rate that depends on the operating conditions (external temperature, load). To plan the installation of batteries, appropriate understanding and prediction capabilities of their lifecycle is needed. High-fidelity numerical models of LIBs such as the pseudo-two-dimensional (P2D) model have been shown to accurately represent the charge-discharge-cycle of an LIB given ac- curate choice of the physical parameters. Given the large number of P2D parameters, adjusting them using forward runs is intractable. This work describes the development of a physics-informed neural network (PINN) as a surrogate substitute of the P2D model that captures parameter dependence. The PINN is advantageous as it needs little to no data, and can naturally encode the dependence of every model parameter. Here, a specific training procedure is adopted to efficiently cover parameter space, handle model stiffness and enforce boundary conditions. The trained PINN is validated against numerical solutions of the P2D model, and its applicability to battery degradation modeling is discussed.

battery degradation↗
DOE OSTI2024

Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics

Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow for obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. Here, in this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^0$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a priori but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, using synthetic and experimental data. This work aims to set a new paradigm for interpretable machine learning models in the broad area of solid mechanics where low and limited data is available along with prior knowledge of physical constraints that the learned maps need to obey. This paradigm can potentially be extended to a broader spectrum of scientific exploration.

Data-driven constitutive models↗
DOE OSTI2022

Magnetic field mapping of inaccessible regions using physics-informed neural networks

A difficult problem concerns the determination of magnetic field components within an experimentally inaccessible region when direct field measurements are not feasible. In this paper, we propose a new method of accessing magnetic field components using non-disruptive magnetic field measurements on a surface enclosing the experimental region. Magnetic field components in the experimental region are predicted by solving a set of partial differential equations (Ampere’s law and Gauss’ law for magnetism) numerically with the aid of physics-informed neural networks (PINNs). Prediction errors due to noisy magnetic field measurements and small number of magnetic field measurements are regularized by the physics information term in the loss function. We benchmark our model by comparing it with an older method. The new method we present will be of broad interest to experiments requiring precise determination of magnetic field components, such as searches for the neutron electric dipole moment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands

Abstract The accurate modeling of water and heat transport in soils is crucial for both geo-environmental and geothermal engineering. Traditional modeling methods are problematic because they require well-defined boundaries and initial conditions. Recently, physics-informed neural networks (PINNs), which incorporate partial differential equations (PDEs) to solve forward and inverse problems, have attracted increasing attention in machine learning research. In this study, we applied PINNs to tackle hydraulic and thermal transport coupling forward problems in silty sands. A fully connected deep neural network was utilized for training. This neural network model leverages automatic differentiation to apply the governing equations as constraints, based on the mathematical approximations established by the neural network itself. We conducted forward problems and compared the solutions derived from PINNs with those from Finite Element Method (FEM) simulations. The forward problem results demonstrate the PINNs model’s capability in predicting hydraulic transport, heat transport, and thermal–hydraulic coupling in silty sands under various boundary conditions. The PINNs exhibited great performance in simulating the thermal–hydraulic coupling problem. The accuracy of the PINNs solutions shows its potential for simulation in geotechnical engineering.

Feng, Yuan↗
DOE OSTI2022

Physics-informed neural networks (PINNs) for fluid mechanics: a review

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). Here, we demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.

42 ENGINEERING↗
DOE OSTI2024

Learning Constitutive Relations From Soil Moisture Data via Physically Constrained Neural Networks

Abstract The constitutive relations of the Richardson‐Richards equation encode the macroscopic properties of soil water retention and conductivity. These soil hydraulic functions are commonly represented by models with a handful of parameters. The limited degrees of freedom of such soil hydraulic models constrain our ability to extract soil hydraulic properties from soil moisture data via inverse modeling. We present a new free‐form approach to learning the constitutive relations using physically constrained neural networks. We implemented the inverse modeling framework in a differentiable modeling framework, JAX, to ensure scalability and extensibility. For efficient gradient computations, we implemented implicit differentiation through a nonlinear solver for the Richardson‐Richards equation. We tested the framework against synthetic noisy data and demonstrated its robustness against varying magnitudes of noise and degrees of freedom of the neural networks. We applied the framework to soil moisture data from an upward infiltration experiment and demonstrated that the neural network‐based approach was better fitted to the experimental data than a parametric model and that the framework can learn the constitutive relations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

The Feasibility of Incorporating a 3D Velocity Model Into Earthquake Location Around Salt Lake City, UT Using a Physics Informed Neural Network

Earthquake location algorithms typically require travel time calculation. Doing this calculation in 3D, despite advances in algorithm efficiency and computational power, can still be prohibitively expensive in terms of resources and storage. Implementation of high-resolution 3D models in routine earthquake location would be a significant step forward in most of the world. Machine learning algorithms have potential to act as substitutes for travel time calculation algorithms or stored travel time tables. We investigate EikoNet - a physics informed neural network machine learning model that estimates travel times very quickly and comes with negligible memory-overhead. Specifically, we apply EikoNet to the Wasatch Fault Community Velocity Model (WFCVM), a highly detailed and complex 3D velocity model of the Salt Lake City, UT region. While routine locations in the area and studies of the 2020 Magna, UT earthquake sequence used a 1D velocity model, a 3D model may help better our understanding the structure of the major fault in the region. Our primary goal was to test the speed, memory requirements, and accuracy of EikoNet compared to a reference eikonal solver. We find that while the EikoNet is exceedingly fast and requires little memory overhead, achieving acceptable accuracy in estimated travel times is difficult and requires extensive computational resources.

58 GEOSCIENCES↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Calibrating constitutive models with full‐field data via physics informed neural networks

Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.

Hamel, Craig M.↗