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DOE OSTI2025

Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak

The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.

Compressional↗

DOE OSTI2021

First coupled GENE–XGC microturbulence simulations

Covering the core and the edge region of a tokamak, respectively, the two gyrokinetic turbulence codes Gyrokinetic Electromagnetic Numerical Experiment (GENE) and X-point Gyrokinetic Code (XGC) have been successfully coupled by exchanging three-dimensional charge density data needed to solve the gyrokinetic Poisson equation over the entire spatial domain. Certain challenges for the coupling procedure arise from the fact that the two codes employ completely different numerical methods. This includes, in particular, the necessity to introduce mapping procedures for the transfer of data between the unstructured triangular mesh of XGC and the logically rectangular grid (in a combination of real and Fourier space) used by GENE. Constraints on the coupling scheme are also imposed by the use of different time integrators. First, coupled simulations are presented. We have considered collisionless ion temperature gradient turbulence, in both circular and fully shaped plasmas. Coupled simulations successfully reproduce both GENE and XGC reference results, confirming the validity of the code coupling approach toward a whole device model. Here, many lessons learned in the present context, in particular, the need for a coupling procedure as flexible as possible, should be valuable to our and other efforts to couple different kinds of codes in pursuit of a more comprehensive description of complex real-world systems and will drive our further developments of a whole device model for fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

A Statistician’s Overview of Physics-Informed Neural Networks for Spatio-Temporal Data

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian↗

DOE OSTI2025

Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2022

Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

Abstract. Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by 4 orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIEADA (Artificial Intelligence Emulator-Assisted Data Assimilation).

58 GEOSCIENCES↗

DOE OSTI2023

Operation Optimization Using Reinforcement Learning with Integrated Artificial Reasoning Framework

In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.

Kim, Junyung↗

DOE OSTI2024

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

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

25 ENERGY STORAGE↗

DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Developing and testing capabilities for simulating cases with heterogeneous land/water surfaces in a novel atmospheric large eddy simulation code

Large eddy simulations (LES) are the primary computational tool used to simulate high Reynolds number three-dimensional turbulent flows. In the context of earth system sciences, particularly atmospheric science, LES are uniquely able to resolve the scales of atmospheric motion that are key for building process-level understanding of boundary layer turbulence, atmosphere-surface interaction, clouds, and cloud-aerosol-chemistry interaction, and are a core limited-area modeling capability. Increasing demands are being placed on LES code bases as growing high performance computing resources allow LES to address a wider range of scientific problems. In addition, LES are emerging as a source of high-quality machine learning training data. These demands necessitate an agile and extensible code base that allows the model to quickly adapt to emergent needs. However, LES have largely relied on legacy Fortran code bases that lack flexibility. A new, Python-based LES capability called Predicting INteractions of Aerosol and Clouds in Large Eddy Simulation (PINACLES) has been developed as part of the Department of Energy’s Earth System Model Development (ESMD) program area’s Enabling Aerosol-cloud interactions at Global convection-permitting scalES (EAGLES) project. PINACLES was developed from the ground up with a philosophy of maximizing scientific throughput, by attempting to optimize for both model throughput and software extensibility. The initial development of PINACLES delivered a state-of-the-art idealized LES capability solving the non-hydrostatic anelastic equations of motion with doubly periodic boundary conditions and idealized homogenous surface boundary conditions. Here we provide a final report on the outcomes of a fiscal year 2021 Seed Laboratory Directed Research Project that extended PINACLES in two key ways. First, PINACLES was coupled to a state-of-the-art land surface model enabling it to simulate spatially inhomogeneous land-atmosphere interactions that are known to control key atmospheric processes. Second, the dynamical core of PINACLES was modified to permit non-periodic boundary conditions. This model enhancement enables simulation of realistic cases with boundary conditions prescribed from atmospheric reanalysis and enables nested simulations conducted on a hierarchy of computational domains with increasing resolution. Together, these extensions to PINACLES make it a formidable modeling capability and expand its potential application to diverse components of DOE’s atmospheric science portfolio.

42 ENGINEERING↗

DOE OSTI2025

PAH101: A GW+BSE Dataset of 101 Polycyclic Aromatic Hydrocarbon (PAH) Molecular Crystals

Abstract The excited-state properties of molecular crystals are important for applications in organic electronic devices. TheGWapproximation and Bethe-Salpeter equation (GW+BSE) is the state-of-the-art method for calculating the excited-state properties of crystalline solids with periodic boundary conditions. We present the PAH101 dataset ofGW+BSE calculations for 101 molecular crystals of polycyclic aromatic hydrocarbons (PAHs) with up to ~500 atoms in the unit cell. To the best of our knowledge, this is the firstGW+BSE dataset for molecular crystals. The data records include theGWquasiparticle band structure, the fundamental band gap, the static dielectric constant, the first singlet exciton energy (optical gap), the first triplet exciton energy, the dielectric function, and optical absorption spectra for light polarized along the three lattice vectors. The dataset can be used to (i) discover materials with desired electronic/optical properties, (ii) identify correlations between DFT andGW+BSE quantities, and (iii) train machine learned models to help in materials discovery efforts.

Science & Technology - Other Topics↗

DOE OSTI2022

PythonFOAM: In-situ data analyses with OpenFOAM and Python

Here, we outline the development of a general-purpose Python-based data analysis tool for OpenFOAM. Our implementation relies on the construction of OpenFOAM applications that have bindings to data analysis libraries in Python. Double precision data in OpenFOAM is cast to a NumPy array using the NumPy C-API and Python modules may then be used for arbitrary data analysis and manipulation on flow-field information. We highlight how the proposed wrapper may be used for an in-situ online singular value decomposition (SVD) implemented in Python and accessed from the OpenFOAM solver PimpleFOAM. Here, 'in-situ' refers to a programming paradigm that allows for a concurrent computation of the data analysis on the same computational resources utilized for the partial differential equation solver. In addition, to demonstrate parallel deployments, we deploy a distributed SVD, which collects snapshot data across the ranks of a distributed simulation to compute the global left singular vectors. Crucially, both OpenFOAM and Python share the same message passing interface (MPI) communicator for this deployment which allows Python objects and functions to exchange NumPy arrays across ranks. Subsequently, we provide scaling assessments of this distributed SVD on multiple nodes of Intel Broadwell and KNL architectures for canonical test cases such as the large eddy simulations of a backward facing step and a channel flow at friction Reynolds number of 395. Finally, we demonstrate the deployment of a deep neural network for compressing the flow-field information using an autoencoder to demonstrate an ability to use state-of-the-art machine learning tools in the Python ecosystem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A Hydro-particle-mesh Code for Efficient and Rapid Simulations of the Intracluster Medium

We introduce the cosmological HYPER code based on an innovative hydro-particle-mesh (HPM) algorithm for efficient and rapid simulations of gas and dark matter. For the HPM algorithm, we update the approach of Gnedin & Hui to expand the scope of its application from the lower-density intergalactic medium (IGM) to the higher-density intracluster medium (ICM). While the original algorithm tracks only one effective particle species, the updated version separately tracks the gas and dark matter particles, as they do not exactly trace each other on small scales. For the approximate hydrodynamics solver, the pressure term in the gas equations of motion is calculated using robust physical models. In particular, we use a dark matter halo model, ICM pressure profile, and IGM temperature–density relation, all of which can be systematically varied for parameter-space studies. We show that the HYPER simulation results are in good agreement with the halo model expectations for the density, temperature, and pressure radial profiles. Simulated galaxy cluster scaling relations for Sunyaev–Zel’dovich (SZ) and X-ray observables are also in good agreement with mean predictions, with scatter comparable to that found in hydrodynamic simulations. HYPER also produces lightcone catalogs of dark matter halos and full-sky tomographic maps of the lensing convergence, SZ effect, and X-ray emission. These simulation products are useful for testing data analysis pipelines, generating training data for machine learning, understanding selection and systematic effects, and for interpreting astrophysical and cosmological constraints.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

How Does Feedback Affect the Star Formation Histories of Galaxies?

Star formation in galaxies is regulated by the interplay of a range of processes that shape the multiphase gas in the interstellar and circumgalactic media. Using the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) suite of cosmological simulations, we study the effects of varying feedback and cosmology on the average star formation histories (SFHs) of galaxies at z ∼ 0 across the IllustrisTNG, SIMBA, and ASTRID galaxy formation models. We find that galaxy SFHs in all three models are sensitive to changes in stellar feedback, which affect the efficiency of baryon cycling and the rates at which central black holes grow, whereas the effects of varying active galactic nucleus (AGN) feedback depend on model-specific implementations of black hole seeding, accretion, and feedback. We also find strong interaction terms that couple stellar and AGN feedback, usually by regulating the amount of gas available for the central black hole to accrete. Using a double power law to describe the average SFHs, we derive a general set of equations relating the shape of the SFHs to physical quantities like baryon fraction and black hole mass across all three models. We find that a single set of equations (albeit with different coefficients) can describe the SFHs across all three CAMELS models, with cosmology dominating the SFH at early times, followed by halo accretion, and feedback and baryon cycling at late times. Galaxy SFHs provide a novel, complementary probe to constrain cosmology and feedback, and can connect the observational constraints from current and upcoming galaxy surveys with the physical mechanisms responsible for regulating galaxy growth and quenching.

Iyer, Kartheik G. [Columbia Univ., New York, NY (U↗

DOE OSTI2022

Characterizing soil water content variability across spatial scales from optimized high-resolution distributed temperature sensing technique

Fiber-optic Distributed Temperature Sensing, when combined with the Single-probe Heat-pulse technique can measure soil moisture (θ) across spatial scales. The key limitation of this system is in obtaining the relationship between soil thermal conductivity (λ) and θ for a specific field. Using the Department of Energy Atmospheric Radiation Measurement (ARM) site, this study tested a new methodology to account for the spatial variability in the λ-θ relationship using a Gaussian processes model. The resulting accurate θ measurements (RMSE = 0.03 m 3 m –3 ) were used to characterize the spatial variability of θ across scales and to develop an empirical equation that can correct for the changes in the θ spatial variability observed at different spatial resolutions. In addition, the number of required samples to accurately characterize θ and its variability over scales ranging from 5 m and 350 m were estimated. Finally, these findings provide key information to scale soil moisture from centimeters to hundreds of meters for process understanding.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Tensorized Interior Radiative Heat Transfer for a Scalable and Calibrated Building Energy Simulator

Building energy simulation is a critical tool for developing and testing advanced control strategies, such as Reinforcement Learning (RL), to provide demand flexibility and affordable energy costs. The recently introduced Smart Buildings Control Suite (sbsim) provides a lightweight, scalable, and data-calibrated simulation environment based on a 2D finite-difference model. However, the initial model primarily focused on conductive and convective heat transfer, neglecting the significant impact of long-wave radiative heat exchange between interior surfaces. This paper presents a significant extension to the sbsim framework by incorporating a physically-grounded model for interior radiative heat transfer. Our primary contribution is the development and integration of a fully tensorized radiative heat transfer module, which preserves the computational efficiency and scalability of the original simulator. This was achieved by developing a pipeline for view factor calculation, including an algorithm to identify directly seeing surfaces within complex floor plans, and formulating the net radiation equations for efficient execution on modern hardware accelerators. We validate the numerical accuracy of our tensorized implementation by comparing its results against a traditional iterative approach, demonstrating identical outcomes. This enhancement increases the physical fidelity of sbsim, enabling more accurate training of RL agents for building energy optimization.

Ham, Sang woo↗

DOE OSTI2022

Accurate parameterization of the kinetic energy functional

The absence of a reliable formulation of kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions which have been proposed in the literature and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals - a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since, the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H 2 , LiH, LiF and a one-dimensional chain of 8 hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures. For the ease of reproduction, codes used to generate the models are provided in the supporting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Multi-fidelity equations of state and transport coefficient datasets for pulsed-power applications

Reliably simulating experiments relevant to the National Nuclear Security Administration (NNSA) requires a detailed description of material properties across a wide range of conditions. Such properties include the equations of state, charged-particle transport coefficients, and optical properties like the opacity. Together, these properties make up the material models used in radiation-magnetohydrodynamic simulations of nuclear fusion experiments. Many of these models do not incorporate uncertainties in the data used to produce them. It is unknown whether these uncertainties significantly impact the interpretation of simulation results and diagnostics. The purpose of this work is to quantify how such uncertainties impact simulations of pulsed-power experiments. We accomplished this task by first assessing discrepancies between approaches used to generate the data. This included bringing together members of the high-energy-density community spanning the three NNSA laboratories and multiple universities. Then, using these data, we developed a general framework that systematically incorporates physical uncertainties within the material models suitable for uncertainty quantification analyses. The framework utilizes machine learning, Bayesian inference, and incorporates multi-fidelity datasets. We demonstrated the framework by quantifying the impact that material model uncertainties have on simulations of pulsed-power experiments underway on Z at Sandia National Laboratories. As a result of this work, we discovered that modest uncertainties in material models (roughly 20%) correspond to significant uncertainties in the outputs from simulations. Our framework has enabled rapid construction of material models through an automated procedure and allows for the generation of material models of interest to the NNSA.

36 MATERIALS SCIENCE↗