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Results for “physics informed deep learning”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
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

Micropolar deep material network

This study extends the Deep Material Network (DMN), a physics-informed machine learning framework, to predict the homogenized mechanical response of composite materials with micropolar (Cosserat-type) constitutive behavior. This extension incorporates microstructure-dependent size effects, enabling accurate, efficient, and size-aware predictions for composites with complex internal architectures. While traditional, direct numerical simulation micropolar models effectively capture size effects by introducing extra local degrees of freedom, they bring significant computational challenges, particularly for multiscale analyses relevant to engineering applications. The micropolar DMN developed in this paper achieves high accuracy while significantly reducing computation time compared to micropolar direct numerical simulations. This advancement enables multiscale analyses and parameter studies that were previously impractical, such as high-cycle fatigue simulations and comprehensive investigations of internal length scale effects notably in size-dependent plastic response and the optimization of lattice structures. By uniting microstructure-sensitive modeling, physics-driven learning, and scalable surrogate modeling, the micropolar DMN paves the way for accelerated material design, large-scale parametric studies, and the reliable incorporation of size-dependent effects across a wide range of engineering applications, including optimization and next-generation composite design.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A physics-informed operator regression framework for extracting data-driven continuum models

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a characterization of differential operators while providing structure which may be used to impose biases related to symmetry, isotropy, and conservation form. Here, we demonstrate the effectiveness of our framework for a variety of physics, including local and nonlocal diffusion processes and single and multiphase flows. For the flow physics we demonstrate this approach leads to a learned operator that generalizes to system characteristics not included in the training sets, such as variable particle sizes, densities, and concentration.

42 ENGINEERING↗
DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A physics-constrained deep learning treatment of runaway electron dynamics

An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint problem is solved, its solution can be used to project the RE density forward in time for an arbitrary initial momentum space distribution of REs. Furthermore, by employing a PINN, a parametric solution to the adjoint problem can be learned. Thus, once trained, this adjoint-deep learning framework is able to efficiently project the RE density forward in time across various plasma conditions while still including a fully kinetic description of RE dynamics. As an example application, the temporal evolution of the density of primary electrons is studied, with particular emphasis on evaluating the decay of a RE population when below threshold. Predictions from the adjoint-deep learning framework are found to be in good agreement with a traditional relativistic electron Fokker–Planck solver, for several distinct initial conditions, and across an array of physics parameters. Once trained, the PINN thus provides a means of generating RE density time histories with exceptionally low online execution time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Exploring Causal Physical Mechanisms via Non-Gaussian Linear Models and Deep Kernel Learning: Applications for Ferroelectric Domain Structures

Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. Overall, this analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

MULTISTEP AND CONTINUOUS PHYSICS-INFORMED NEURAL NETWORK METHODS FOR LEARNING GOVERNING EQUATIONS AND CONSTITUTIVE RELATIONS

In this work, we investigate the applicability and relative merit of discrete and continuous versions of physics-informed neural network (PINN) methods for learning unknown governing equations or constitutive relations in a nonlinear dynamical system. In the case of unknown dynamics, entire right-hand-side (RHS) equations of the ordinary differential equations are unknown. In the case of unknown constitutive relations, however, the RHS equations are known up to the specification of constitutive relations (that may depend on the state of the system). We use a deep neural network to model unknown governing equations or constitutive relations. The discrete PINN approach combines classical multistep discretization methods for dynamical systems with neural-network-based machine learning methods. On the other hand, the continuous versions utilize deep neural networks to minimize the residual function for the continuous governing equations. We use the case of a fedbatch bioreactor system to study the effectiveness of these approaches and discuss conditions for their applicability. Our results indicate that the accuracy of the trained neural network models is much higher for the cases where we only have to learn a constitutive relation instead of all dynamics. This finding corroborates the well-known fact from scientific computing that building as much structural information as is available into an algorithm can enhance its efficiency and/or accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Building thermal load prediction through shallow machine learning and deep learning

Building thermal load prediction informs the optimization of cooling plant and thermal energy storage. Physics-based prediction models of building thermal load are constrained by the model and input complexity. In this study, we developed 12 data-driven models (7 shallow learning, 2 deep learning, and 3 heuristic methods) to predict building thermal load and compared shallow machine learning and deep learning. The 12 prediction models were compared with the measured cooling demand. It was found XGBoost (Extreme Gradient Boost) and LSTM (Long Short Term Memory) provided the most accurate load prediction in the shallow and deep learning category, and both outperformed the best baseline model, which uses the previous day's data for prediction. Then, we discussed how the prediction horizon and input uncertainty would influence the load prediction accuracy. Major conclusions are twofold: first, LSTM performs well in short-term prediction (1 h ahead) but not in long term prediction (24 h ahead), because the sequential information becomes less relevant and accordingly not so useful when the prediction horizon is long. Second, the presence of weather forecast uncertainty deteriorates XGBoost's accuracy and favors LSTM, because the sequential information makes the model more robust to input uncertainty. Training the model with the uncertain rather than accurate weather data could enhance the model's robustness. Finally, our findings have two implications for practice. First, LSTM is recommended for short-term load prediction given that weather forecast uncertainty is unavoidable. Second, XGBoost is recommended for long term prediction, and the model should be trained with the presence of input uncertainty.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems

Here, we propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Correspondingly, we prove two new universal approximation theorems that demonstrate that SympNets can approximate arbitrary symplectic maps based on appropriate activation functions. We then perform several experiments including the pendulum, double pendulum and three-body problems to investigate the expressivity and the generalization ability of SympNets. The simulation results show that even very small size SympNets can generalize well, and are able to handle both separable and non-separable Hamiltonian systems with data points resulting from short or long time steps. In all the test cases, SympNets outperform the baseline models, and are much faster in training and prediction. We also develop an extended version of SympNets to learn the dynamics from irregularly sampled data. This extended version of SympNets can be thought of as a universal model representing the solution to an arbitrary Hamiltonian system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Physics constrained unsupervised deep learning for rapid, high resolution scanning coherent diffraction reconstruction

By circumventing the resolution limitations of optics, coherent diffractive imaging (CDI) and ptychography are making their way into scientific fields ranging from X-ray imaging to astronomy. Yet, the need for time consuming iterative phase recovery hampers real-time imaging. While supervised deep learning strategies have increased reconstruction speed, they sacrifice image quality. Furthermore, these methods’ demand for extensive labeled training data is experimentally burdensome. Here, we propose an unsupervised physics-informed neural network reconstruction method, PtychoPINN, that retains the factor of 100-to-1000 speedup of deep learning-based reconstruction while improving reconstruction quality by combining the diffraction forward map with real-space constraints from overlapping measurements. In particular, PtychoPINN gains a factor of 4 in linear resolution and an 8 dB improvement in PSNR while also accruing improvements in generalizability and robustness. This blend of performance and computational efficiency offers exciting prospects for high-resolution real-time imaging in high-throughput environments such as X-ray free electron lasers (XFELs) and diffraction-limited light sources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Machine learning for deep elastic strain engineering of semiconductor electronic band structure and effective mass

Abstract The controlled introduction of elastic strains is an appealing strategy for modulating the physical properties of semiconductor materials. With the recent discovery of large elastic deformation in nanoscale specimens as diverse as silicon and diamond, employing this strategy to improve device performance necessitates first-principles computations of the fundamental electronic band structure and target figures-of-merit, through the design of an optimal straining pathway. Such simulations, however, call for approaches that combine deep learning algorithms and physics of deformation with band structure calculations to custom-design electronic and optical properties. Motivated by this challenge, we present here details of a machine learning framework involving convolutional neural networks to represent the topology and curvature of band structures in k -space. These calculations enable us to identify ways in which the physical properties can be altered through “deep” elastic strain engineering up to a large fraction of the ideal strain. Algorithms capable of active learning and informed by the underlying physics were presented here for predicting the bandgap and the band structure. By training a surrogate model with ab initio computational data, our method can identify the most efficient strain energy pathway to realize physical property changes. The power of this method is further demonstrated with results from the prediction of strain states that influence the effective electron mass. We illustrate the applications of the method with specific results for diamonds, although the general deep learning technique presented here is potentially useful for optimizing the physical properties of a wide variety of semiconductor materials.

Tsymbalov, Evgenii↗
DOE OSTI2023

Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes

Abstract Predicting failure in solids has broad applications including earthquake prediction which remains an unattainable goal. However, recent machine learning work shows that laboratory earthquakes can be predicted using micro-failure events and temporal evolution of fault zone elastic properties. Remarkably, these results come from purely data-driven models trained with large datasets. Such data are equivalent to centuries of fault motion rendering application to tectonic faulting unclear. In addition, the underlying physics of such predictions is poorly understood. Here, we address scalability using a novel Physics-Informed Neural Network (PINN). Our model encodes fault physics in the deep learning loss function using time-lapse ultrasonic data. PINN models outperform data-driven models and significantly improve transfer learning for small training datasets and conditions outside those used in training. Our work suggests that PINN offers a promising path for machine learning-based failure prediction and, ultimately for improving our understanding of earthquake physics and prediction.

42 ENGINEERING↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

State predictive information bottleneck

We report the ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations.

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

Physics informed machine learning for chemistry tabulation

Modeling of turbulent combustion system requires modeling the underlying chemistry and the turbulent transport. Solving both systems simultaneously is computationally prohibitive. Instead, given the difference in scales at which the two sub-systems evolve, the two sub-systems are typically (re)solved separately. Popular approaches such as the Flamelet Generated Manifolds (FGM) use a two-step strategy where the governing reaction kinetics are pre-computed and mapped to a low-dimensional manifold, characterized by a few reaction progress variables (model reduction) and the manifold is then “looked-up” during the run-time to estimate the high-dimensional system state by the turbulent transport system. While existing works have focused on these two steps independently, in this work we show that joint learning of the progress variables and the look-up model, can yield more accurate results. Here, we build on the base formulation and implementation to include the dynamically generated Thermochemical State Variables (Lower Dimensional Dynamic Source Terms). We discuss the challenges in the implementation of this deep neural network architecture and experimentally demonstrate its superior performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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

Accelerating charge estimation in molecular dynamics simulations using physics-informed neural networks: corrosion applications

Molecular Dynamics (MD) simulations are used to understand the effects of corrosion on metallic materials in salt brine. Reactive force fields in classical MD enable accurate modeling of bond formation and breakage in the aqueous medium and at the metal-electrolyte interface, while also facilitating dynamic partial charge equilibration. However, MD simulations are computationally intensive and unsuitable for modeling the long time scales characteristic of corrosive phenomena. To address this, we develop reduced-order machine learning models that provide accurate and efficient predictions of charge density in corrosive environments. Specifically, we use Long Short-Term Memory (LSTM) networks to forecast charge density evolution based on atomic environments represented by Smooth Overlap of Atomic Positions (SOAP) descriptors. A physics-informed loss function enforces charge neutrality and electronegativity equivalence. The atomic charges predicted by the deep learning model trained on this work were obtained two orders of magnitude faster than those from molecular dynamics (MD) simulations, with an error of less than 3% compared to the MD-obtained charges, even in extrapolative scenarios, while adhering to physical constraints. This demonstrates the excellent accuracy, computational efficiency, and validity of the developed model. Lastly, even though developed for corrosion, these protocols are formulated in a phenomenon-agnostic manner, allowing application to various variable-charge interatomic potentials and related fields.

Atomistic models↗
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↗