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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Predicting Open Quantum Dynamics with Data-Informed Quantum-Classical Dynamics

We introduce a data-informed quantum-classical dynamics (DIQCD) approach for predicting the evolution of an open quantum system. The equation of motion in DIQCD is a Lindblad equation with a flexible, time-dependent Hamiltonian that can be optimized to fit sparse and noisy data from local observations of an extensive open quantum system. We demonstrate the accuracy and efficiency of DIQCD for both experimental and simulated quantum devices. We show that DIQCD can predict entanglement dynamics of ultracold molecules (calcium fluoride) in optical tweezer arrays. DIQCD also successfully predicts carrier mobility in organic semiconductors (rubrene) with accuracy comparable to nearly exact numerical methods.

Lindblad equation↗
DOE OSTI2020

Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

Xie, Xuping↗
DOE OSTI2020

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Impact of classical statistics on thermal conductivity predictions of BAs and diamond using machine learning molecular dynamics

Machine learning interatomic potentials (MLIPs) have greatly enhanced molecular dynamics (MD) simulations, achieving near-first-principles accuracy in thermal conductivity studies. In this work, we reveal that this accuracy, observed in BAs and diamond at sub-Debye temperatures, stems from an accidental error cancelation: classical statistics overestimates specific heat while underestimating phonon lifetimes, balancing out in thermal conductivity predictions. However, this balance is disrupted when isotopes are introduced, leading MLIP-based MD to significantly underpredict thermal conductivity compared to experiments and quantum statistics-based Boltzmann transport equation. This discrepancy arises not from classical statistics affecting phonon–isotope scattering rates but from its impact on the interplay between phonon–isotope and phonon–phonon scattering in the normal scattering-dominated BAs and diamond. In conclusion, this work underscores the limitations of MLIP-based MD for thermal conductivity studies at sub-Debye temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

Here, in this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two weak formulations. For the strong formulation, the solution is directly parameterized with a neural network and optimized by minimizing the PDE residual. It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the $L^1$ sense. The weak formulations are derived following (Brenier in Examples of hidden convexity in nonlinear PDEs, 2020) which characterizes the very weak solutions of QPME. Specifically speaking, the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations. Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions. This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods, which we hope can provide some useful experience for future investigations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

In this paper, we present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available and allows for training DNNs when no direct measurements of the functions of interest are available. We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods. For the non-linear diffusion PDE model with a fully unknown constitutive relationship (i.e., no measurements of constitutive relationship are available), the physics informed DNN method can accurately estimate the non-linear constitutive relationship based on state measurements only. Finally, we demonstrate that the proposed method remains accurate in the presence of measurement noise.

42 ENGINEERING↗
DOE OSTI2020

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗
DOE OSTI2022

Operator inference for non-intrusive model reduction with quadratic manifolds

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.

42 ENGINEERING↗
DOE OSTI2025

Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material properties, equation of state (EOS), opacities, and initial conditions. Typically, however, these parameters are not directly observable. What is observed instead is a time sequence of radiographic projections using X-rays. In this work, we define a set of sparse hydrodynamic features derived from the outgoing shock profile and outer material edge, which can be obtained from radiographic measurements, to directly infer such parameters. Our machine learning (ML)-based methodology involves a pipeline of two architectures, a radiograph-to-features network (R2FNet) and a features-to-parameters network (F2PNet), that are trained independently and later combined to approximate a posterior distribution for the parameters from radiographs. We show that the machine learning architectures are able to accurately infer initial conditions and EOS parameters, and that the estimated parameters can be used in a hydrodynamics code to obtain density fields, shocks, and material interfaces that satisfy thermodynamic and hydrodynamic consistency. Finally, we demonstrate that features resulting from an unknown EOS model can be successfully mapped onto parameters of a chosen analytical EOS model, implying that network predictions are learning physics, with a degree of invariance to the underlying choice of EOS model. To the best of our knowledge, our framework is the first demonstration of recovering both thermodynamic and hydrodynamic consistent density fields from noisy radiographs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

DPFEHM: a differentiable subsurface physics simulator

The Earth’s subsurface is a key resource that provides energy via fossil fuels and geothermal sources, stores drinking water, and is used in the fight against climate change via carbon sequestration. Simulating the physical processes that occur in the Earth’s subsurface with computers enables better use of this resource. DPFEHM is a Julia package that includes computer models with a focus on the Earth’s subsurface, especially fluid flow, which is critical for the aforementioned applications. DPFEHM is able to solve the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation. One of the key features of DPFEHM is that it supports automatic differentiation, so it can be integrated into machine learning workflows using frameworks such as Flux or PyTorch. The automatic differentiation capabilities give it the same performance as adjoint methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗
DOE OSTI2024

Accelerating FEM-Based Corrosion Predictions Using Machine Learning

Atmospheric corrosion of metallic parts is a widespread materials degradation phenomena that is challenging to predict given its dependence on many factors (e.g. environmental, physiochemical, and part geometry). For materials with long expected service lives, accurately predicting the degree to which corrosion will degrade part performance is especially difficult due to the stochastic nature of corrosion damage spread across years or decades of service. The Finite Element Method (FEM) is a computational technique capable of providing accurate estimates of corrosion rate by numerically solving complex differential Eqs. characterizing this phenomena. Nevertheless, given the iterative nature of FEM and the computational expense required to solve these complex equations, FEM is ill-equipped for an efficient exploration of the design space to identify factors that accelerate or deter corrosion, despite its accuracy. In this work, a machine learning based surrogate model capable of providing accurate predictions of corrosion with significant computational savings is introduced. Specifically, this work leverages AdaBoosted Decision trees to provide an accurate estimate of corrosion current per width given different values of temperature, water layer thickness, molarity of the solution, and the length of the cathode for a galvanic couple of aluminum and stainless steel.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Machine Learning an Ab-Initio Based Bond-Order Potential for Bismuthene

Bismuthene is a heavy 2D material whose strong spin–orbit coupling and recently observed single-element ferroelectricity have intensified interest in its structural, vibrational, and transport properties. Accurate modeling of these behaviors requires a short-range interatomic potential that can reproduce the underlying bonding physics at a fraction of the computational cost of first-principles methods. However, such a potential is currently unavailable. Here, in this work, we construct a Tersoff bond-order potential for β-bismuthene using a reinforcement-learning framework that integrates a continuous Monte Carlo Tree Search with a simplex-based local optimizer. The optimized parameter sets reproduce first-principles lattice constants, cohesive energy, the equation of state, elastic constants, and phonon dispersion. We validate the models by performing thermal-conductivity calculations and uniaxial fracture simulations our findings confirm the reliability of the resulting models across multiple thermomechanical regimes. Comparison of the three best solutions reveals how differences in pairwise interactions, angular terms, and bond-order behavior govern phonon features and mechanical responses. We demonstrate an interpretable and computationally efficient potential for bismuthene and demonstrate a general reinforcement-learning strategy for developing bond-order models in emerging 2D materials.

deformation↗
DOE OSTI2024

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. Additionally, we identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Adaptively Learned Modeling for a Digital Twin of Hydropower Turbines with Application to a Pilot Testing System

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using the recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using real-time data from a hydropower turbine testing system. This led to semi-physical modeling, in which first principles and data-driven modeling are integrated to produce dynamic models for DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained.

13 HYDRO ENERGY↗
DOE OSTI2023

Probing reaction channels via reinforcement learning

Abstract Chemical reactions are dynamical processes involving the correlated reorganization of atomic configurations, driving the conversion of an initial reactant into a result product. By virtue of the metastability of both the reactants and products, chemical reactions are rare events, proceeding fleetingly. Reaction pathways can be modelled probabilistically by using the notion of reactive density in the phase space of the molecular system. Such density is related to a function known as the committor function, which describes the likelihood of a configuration evolving to one of the nearby metastable regions. In theory, the committor function can be obtained by solving the backward Kolmogorov equation (BKE), which is a partial differential equation (PDE) defined in the full dimensional phase space. However, using traditional methods to solve this problem is not practical for high dimensional systems. In this work, we propose a reinforcement learning based method to identify important configurations that connect reactant and product states along chemical reaction paths. By shooting multiple trajectories from these configurations, we can generate an ensemble of states that concentrate on the transition path ensemble. This configuration ensemble can be effectively employed in a neural network-based PDE solver to obtain an approximation solution of a restricted BKE, even when the dimension of the problem is very high. The resulting solution provides an approximation for the committor function that encodes mechanistic information for the reaction, paving a new way for understanding of complex chemical reactions and evaluation of reaction rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗