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DOE OSTI2023

Physics guided machine learning for multi-material decomposition of tissues from dual-energy CT scans of simulated breast models with calcifications

We introduce a physics guided data-driven method for image-based multi-material decomposition for dual-energy computed tomography (CT) scans. The method is demonstrated for CT scans of virtual human phantoms containing more than two types of tissues. The method is a physics-driven supervised learning technique. We take advantage of the mass attenuation coefficient of dense materials compared to that of muscle tissues to perform a preliminary extraction of the dense material from the images using unsupervised methods. We then perform supervised deep learning on the images processed by the extracted dense material to obtain the final multi-material tissue map. The method is demonstrated on simulated breast models with calcifications as the dense material placed amongst the muscle tissues. The physics-guided machine learning method accurately decomposes the various tissues from input images, achieving a normalized root-mean-squared error of 2.75%.

Gopalakrishnan Meena, Murali↗

DOE OSTI2024

A physics-informed deep learning description of Knudsen layer reactivity reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Physics-guided machine learning for improved accuracy of the National Solar Radiation Database

The National Solar Radiation Database (NSRDB) provides high-resolution spatiotemporal solar irradiance data for the entire globe. The NSRDB uses a two-step Physical Solar Model (PSM) to compute the effects of clouds and other atmospheric variables on the solar radiation reaching the surface of the Earth. Physical and optical cloud properties are fundamental inputs to the PSM and are derived from the National Oceanic and Atmospheric Administration's Geostationary Operational Environmental Satellites. This paper describes recent improvements to the NSRDB driven by physics-guided machine learning methods for cloud property retrieval. The impacts of these new methods on the NSRDB irradiance data are validated using an extensive set of ground measurement sites, showing significant improvement for all sites. We report on average, the mean absolute percentage error for global horizontal irradiance and direct normal irradiance show reductions of 2.16 and 3.95 percentage points respectively for all daylight conditions, 5.92 and 17.39 percentage points respectively for cloudy conditions, and 9.00 and 22.59 percentage points respectively for gap-filled cloudy conditions. These new methods will help improve the quality and accuracy of the irradiance and cloud data in the NSRDB.

14 SOLAR ENERGY↗

DOE OSTI2023

Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials

Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

Sarkar, Sulagna↗

DOE OSTI2024

A Physics-Informed Deep Learning Description of Knudsen Layer Reactivity Reduction

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Improving River Routing Using a Differentiable Muskingum‐Cunge Model and Physics‐Informed Machine Learning

Recently, rainfall-runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics-NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method (δMC-Juniata-hydroDL2) that mimics the classical Muskingum-Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness (n) and channel geometries from raw reach-scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real-world data, the trained differentiable routing model produced more accurate long-term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national-scale hydrologic flood simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Mechanics↗

DOE OSTI2023

The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment

As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models based on daily hydrograph metrics (Nash–Sutcliffe model efficiency coefficient, etc.) and predicted decadal streamflow trends. For prediction in ungauged basins (PUB; randomly sampled ungauged basins representing spatial interpolation), δ models either approached or surpassed the performance of LSTM in daily hydrograph metrics, depending on the meteorological forcing data used. They presented a comparable trend performance to LSTM for annual mean flow and high flow but worse trends for low flow. For prediction in ungauged regions (PUR; regional holdout test representing spatial extrapolation in a highly data-sparse scenario), δ models surpassed LSTM in daily hydrograph metrics, and their advantages in mean and high flow trends became prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. The δ models' deep-network-based parameterization pipeline produced parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, the δ models are strong candidates for regional and global-scale hydrologic simulations and climate change impact assessment.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Deep Learning Parameterization of Vertical Wind Velocity Variability via Constrained Adversarial Training

Atmospheric models with typical resolution in the tenths of kilometers cannot resolve the dynamics of air parcel ascent, which varies on scales ranging from tens to hundreds of meters. Small-scale wind fluctuations are thus characterized by a subgrid distribution of vertical wind velocity W with standard deviation σ W . The parameterization of σ W is fundamental to the representation of aerosol–cloud interactions, yet it is poorly constrained. Using a novel deep learning technique, this work develops a new parameterization for σ W merging data from global storm-resolving model simulations, high-frequency retrievals of W , and climate reanalysis products. The parameterization reproduces the observed statistics of σ W and leverages learned physical relations from the model simulations to guide extrapolation beyond the observed domain. Incorporating observational data during the training phase was found to be critical for its performance. The parameterization can be applied online within large-scale atmospheric models, or offline using output from weather forecasting and reanalysis products.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management

Abstract Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO $$_2$$ 2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. The heterogeneity typically requires high-fidelity physics-based models to make predictions on CO $$_2$$ 2 fate. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both, heterogeneity and uncertainty, makes this a computationally-intensive problem challenging for current reservoir simulators. To tackle this, we use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization at critical reservoir locations. We use DPFEHM framework, which has trustworthy physics based on the standard two-point flux finite volume discretization and is also automatically differentiable like machine learning models. Our physics-informed machine learning framework uses convolutional neural networks to learn an appropriate extraction rate based on the permeability field. We also perform a hyperparameter search to improve the model’s accuracy. Training and testing scenarios are executed to evaluate the feasibility of using physics-informed machine learning to manage reservoir pressures. We constructed and tested a sufficiently accurate simulator that is 400 000 times faster than the underlying physics-based simulator, allowing for near real-time analysis and robust uncertainty quantification.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Physics-informed machine learning analysis for nanoscale grain mapping by synchrotron Laue microdiffraction

Understanding the grain morphology, orientation distribution and crystal structure of nanocrystals is essential for optimizing the mechanical and physical properties of functional materials. Synchrotron X-ray Laue microdiffraction is a powerful technique for characterizing crystal structures and orientation mapping using focused X-rays. However, when the grain sizes are smaller than the beam size, mixed peaks in the Laue pattern from neighboring grains limit the resolution of grain morphology mapping. We propose a physics-informed machine learning (PIML) approach that combines a convolutional neural network feature extractor with a physics-informed filtering algorithm to overcome the spatial resolution limits of X-rays, achieving nanoscale resolution for grain mapping. Our PIML method successfully resolves the grain size, orientation distribution and morphology of Au nanocrystals through synchrotron microdiffraction scans, showing good agreement with electron backscatter diffraction results. This PIML-assisted synchrotron microdiffraction analysis can be generalized to other diffraction-based probes, enabling the characterization of nanosized structures with micrometre-sized probes.

X-ray crystallography↗

DOE OSTI2020

Physics-Informed Machine Learning for Epidemiological Models

One challenge of using compartmental SEIR models for public health planning is the difficulty in manually tuning parameters to capture behavior reflected in the real-world data. This team conducted initial, exploratory analysis of a novel technique to use physics-informed machine learning tools to rapidly develop data-driven models for physical systems. This machine learning approach may be used to perform data assimilation of compartment models which account for unknown interactions between geospatial domains (i.e. diffusion processes coupling across neighborhoods/counties/states/etc.). Results presented here are early, proof-of-concept ideas that demonstrate initial success in using a physically informed neural network (PINN) model to assimilate data in a compartmental epidemiology model. The results demonstrate initial success and warrant further research and development.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Xanthos-Lake Model Source Code

This repository contains the source code for Xanthos-Lake, a lake-modeling extension of the Xanthos framework that introduces a coupled lake component comprising the Xanthos-Lake Snow and Ice Model (xLSIM) and the Xanthos-Lake Water Balance Model (xLWBM). xLSIM is a basin-aware machine-learning model for lake snow, ice, and thermal conditions. It predicts monthly lake ice thickness, snow depth, snow-cover fraction, mixing-layer temperature, and lake ice fraction from meteorological forcing and lake surface-area information. It uses sequence-based deep-learning architectures, including Transformer and hybrid Long Short-Term Memory–Transformer (LSTM–Transformer) models, together with seasonal encoding, multi-lake learning, physical masking, and basin-level cryospheric and non-cryospheric classification. The training workflow uses Ray for scalable execution and includes optional Ray Tune hyperparameter optimization. Model predictions, observations, diagnostics, and feature-importance outputs are written in NetCDF. xLWBM is the water-balance component of the new lake framework. It simulates monthly lake storage, surface area, evaporation, inflow, outflow, and lake–groundwater exchange. It combines physical water-balance equations with calibrated bathymetric relationships, weir-based outlet flow, modified Penman open-water evaporation, groundwater head relaxation, Penman–Monteith snow and ice sublimation, and snow, ice, and thermal conditions supplied by xLSIM. The model calibrates lake parameters against satellite-derived surface-area data, using evaporation-based calibration where surface-area data are unavailable, and supports small, medium, and large lake classes. For large lakes, xLWBM is integrated with the managed-routing workflow so that lake storage and outflow interact directly with downstream river routing and reservoir operations. Together, xLSIM and xLWBM provide Xanthos with a coupled lake-modeling capability. xLSIM supplies the snow, ice, and thermal conditions that affect lake evaporation and snow- and ice-related water exchanges, while xLWBM translates those conditions into dynamic lake storage, surface area, evaporation, and discharge. In return, xLWBM supplies evolving lake surface area to xLSIM. This coupling enables Xanthos to represent lakes as active hydrologic components within basin-scale water-availability and routing simulations.

Machine Learning↗

DOE OSTI2022

Explainable machine learning of the underlying physics of high-energy particle collisions

We present an implementation of an explainable and physics-aware machine learning model capable of inferring the underlying physics of high-energy particle collisions using the information encoded in the energy-momentum four-vectors of the final state particles. We demonstrate the proof-of-concept of our White Box AI approach using a Generative Adversarial Network (GAN) which learns from a DGLAP-based parton shower Monte Carlo event generator. The constrained generator network architecture mimics the structure of a parton shower exhibiting similarities with Recurrent Neural Networks (RNNs). We show, for the first time, that our approach leads to a network that is able to learn not only the final distribution of particles, but also the underlying parton branching mechanism, i.e. the Altarelli-Parisi splitting function, the ordering variable of the shower, and the scaling behavior. While the current work is focused on perturbative physics of the parton shower, we foresee a broad range of applications of our framework to areas that are currently difficult to address from first principles in QCD. Examples include nonperturbative and collective effects, factorization breaking and the modification of the parton shower in heavy-ion, and electron-nucleus collisions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Comparing storm resolving models and climates via unsupervised machine learning

Global storm-resolving models (GSRMs) have gained widespread interest because of the unprecedented detail with which they resolve the global climate. However, it remains difficult to quantify objective differences in how GSRMs resolve complex atmospheric formations. This lack of comprehensive tools for comparing model similarities is a problem in many disparate fields that involve simulation tools for complex data. To address this challenge we develop methods to estimate distributional distances based on both nonlinear dimensionality reduction and vector quantization. Our approach automatically learns physically meaningful notions of similarity from low-dimensional latent data representations that the different models produce. This enables an intercomparison of nine GSRMs based on their high-dimensional simulation data (2D vertical velocity snapshots) and reveals that only six are similar in their representation of atmospheric dynamics. Furthermore, we uncover signatures of the convective response to global warming in a fully unsupervised way. Our study provides a path toward evaluating future high-resolution simulation data more objectively.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Bayesian Physics Informed Spatio-Temporal Network for Streamflow Data Imputation

Reliable reconstruction of incomplete streamflow records is critical for improving hydrological forecasting, flood preparedness, and water resource management. However, large observational gaps and uncertainties in governing physical parameters limit the accuracy of traditional statistical and machinelearning imputation frameworks. To address these challenges, we develop a Bayesian Physics-Informed Spatio-Temporal Network (BPI-STNet) that jointly captures spatial and temporal dependencies while enforcing hydrologic consistency through embedded physical constraints. The framework integrates a GraphSAGE-LSTM architecture to model spatial connectivity across gauges and temporal flow dynamics, coupled with a Bayesian update mechanism to estimate uncertain parameters in a simplified water-balance framework. Unlike conventional physics-informed networks that rely on sampling-based posterior estimation, BPI-STNet derives an analytic solution to the inverse problem, allowing closed-form Bayesian updates of uncertain parameters Λ={α,β,k} using Gaussian priors and likelihoods. Applied to daily observations from the Susquehanna River Basin (1980-2022), BPI-STNet achieves substantial improvements over a purely data-driven RGNN baseline, which reduced RMSE by 23 % and MAE by 9 %, and achieving an average NSE values up to 0.96. The results demonstrate that coupling Bayesian inference with physics-informed learning yields physically consistent, uncertainty-aware reconstructions that preserve the temporal persistence and statistical distribution of observed flows. The proposed framework establishes a generalizable paradigm for data-sparse hydrologic systems where both data fidelity and physical interpretability are essential.

Krishnan Kutty Ambika, Anukesh [ORNL] (ORCID:00000↗