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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗
DOE OSTI2022

The 3D magnetic topology and plasma dynamics in open stochastic magnetic field lines

We report the thermal quench triggered by locked modes is known to be mainly due to open stochastic magnetic field lines connected to the wall boundary. It is essential to understand the 3D structure of open stochastic field lines since it determines the overall plasma dynamics in the system. In this study, we analyze the 3D magnetic topology for two key concepts, the connection length L c and the effective magnetic mirror ratio M eff , and present a comprehensive picture of electron and ion dynamics related to the magnetic topology. The connection length determines the 3D structure of the ambipolar potential, and a sharp potential drop across distinct L c regions induces the E × B transport and mixing across the field line. The confinement of electrons and ions along the field line is determined by the ambipolar potential and [Formula: see text] configuration. Electron and ion temperatures in magnetic hills (M eff < 1) are lower than in magnetic wells (M eff > 1) because particles in magnetic hills are more likely to escape toward the wall boundary along the field line. The mixing between the magnetic wells and hills by E × B and magnetic drift motions results in collisionless detrapping of electrons and ions, which reduces their temperature efficiently. Numerical simulations of two different magnetic configurations demonstrate the importance of the collisionless detrapping mechanism, which could be the main cause of plasma temperature drop during the thermal quench.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Surrogate modeling of Monte Carlo radiation transport with convolutional neural networks for shielding optimization

Here, we present a machine learning (ML)-based surrogate model using convolutional neural networks (CNN) designed to emulate the attenuation of neutron fields as they pass through various shielding materials. This model can compute the outgoing neutron flux almost instantaneously and achieves reasonable accuracy compared to traditional Monte Carlo (MC)-based codes, which are computationally intensive. This emulator alleviates the complexity of neutron radiation transport through shielding materials by reducing the dimensionality and enables shielding optimization for a known radiation environment. This optimization process, which would have taken an unrealistic timeline due to several complex radiation transport simulations, can now be achieved in minutes, thus increasing computational capabilities in radiation shielding assessment. We demonstrate the applications of this emulator in computing effective dose rates and optimizing shielding solutions for a heavy-ion accelerator facility, such as the Facility for Rare Isotope Beams, where secondary neutrons produced via beam interactions dominate the radiation environment.

accelerator shielding↗
DOE OSTI2020

Self-sustaining sound in collisionless, high- β plasma

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $δn/n_0≳2/β$ (where $β\gg1$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $δn/n_0≳2/β$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Sensitivity analysis, surrogate modeling, and optimization of pebble-bed reactors considering normal and accident conditions

This research provides a valuable tool that streamlines the optimization process while significantly increasing its accuracy. This study creates a robust framework for reactor design optimization by incorporating comprehensive modeling using the Comprehensive Reactor Analysis Bundle, or BlueCRAB, within the Multiphysics Object-Oriented Simulation Environment (MOOSE). BlueCRAB is the United States Nuclear Regulatory Commission's code suite for non-light water reactor analysis and includes the Griffin, Pronghorn, and Bison applications. This not only improves the efficiency of the optimization process but also enhances the reliability of the results. Such a tool is essential for advancing the state-of-the-art in pebble-bed reactor technology and is critical for achieving the goals of Generation IV reactors, which aim for safe, sustainable, and economically viable nuclear energy solutions. This work presents and applies this workflow on pebble-bed reactors while considering both normal and off-normal conditions. A representative gas-cooled pebble-bed reactor at equilibrium core conditions serves as the nominal design specification for normal operation and is based on previous research. The depressurized loss-of-forced-cooling accident is deployed for off-normal conditions in this work. After defining design-related parameters and quantities of interest regarding reactor safety and performance, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of surrogate models. Subsequently, the dataset and surrogate models are employed in two optimization studies aimed at maximizing fuel utilization and economic profit while adhering to safety and operational constraints. Performing the optimization process with fuel utilization as the metric leads to an improvement of approximately 10%, compared to engineering-judgment-based nominal conditions. The optimization on economic profit leads to an estimated increase of ~300 million USD over the lifetime of the reactor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

On Transfer Learning Of Neural Networks Using Bi-Fidelity Data For Uncertainty Propagation

Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantification applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high- and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity-weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data are then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Conservation laws and effective hadronization models

Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting hadronization as a conditioned stochastic diffusion process provides a precise mathematical resolution to this tension. In particular, this language reveals explicitly that constraints stemming from conservation laws induce non-Markovian correlations between otherwise independent fragmentation steps, and that these correlations can be absorbed exactly into a renormalization of the local dynamics through a Doob $h$-transform. We develop this formalism for a $q\bar{q}$ string in the chiral limit, where the longitudinal-transverse factorization of the Lund kernel becomes exact, enabling systematic power counting and clean ultraviolet (UV)/infrared (IR) separation. The dynamics organize naturally into a tower of effective theories distinguished by the remaining string mass, spanning a UV fixed point with scale-invariant transport coefficients, an intermediate regime where transverse phase space induces controlled running, and an IR boundary layer where non-local effects enter at leading order. The tower exhibits genuine Wilsonian structure, including $β$-functions, anomalous dimensions, and systematic matching conditions. The resulting framework achieves a clean factorization of universal microscopic fragmentation dynamics from infrared constraint effects, and opens new directions for both the theoretical analysis and practical simulation of hadronization.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗
DOE OSTI2021

Windowed multipole representation of R -matrix cross sections

Nuclear cross sections are basic inputs to any nuclear computation. Campaigns of experiments are fitted with the parametric R-matrix model of quantum nuclear interactions, and the resulting cross sections are documented—both pointwise and as resonance parameters (with uncertainties)—in standard evaluated nuclear data libraries (ENDF, JEFF, BROND, JENDL, CENDL, TENDL): these constitute our common knowledge of fundamental low-energy nuclear cross sections. In the past decade, a collaborative effort has been deployed to establish a new nuclear cross-section library format—the Windowed Multipole Library—with the goal of considerably reducing the computational cost of cross-section calculations in nuclear transport simulations. This work lays the theoretical foundations underpinning these efforts. From general R-matrix scattering theory, we derive the windowed multipole representation of nuclear cross sections. Though physically and mathematically equivalent to R-matrix cross sections, the windowed multipole representation is particularly well suited for subsequent temperature treatment of angle-integrated cross sections, in particular Doppler broadening, which is the averaging of cross sections over the thermal motion of the target atoms. Doppler broadening is of critical importance in neutron transport applications, as it ensures the stability of many nuclear reactors (negative thermal reactivity). Yet, Doppler broadening of nuclear cross sections has been a considerable bottleneck for nuclear transport computations, often requiring memory-costly pretabulations. We show that the windowed multipole representation can perform accurate Doppler broadening analytically (up to the first reaction threshold), from which we derive cross-section temperature derivatives to any order—all computable on the fly (without precalculations stored in memory). Furthermore, we here establish a way of converting the R-matrix resonance parameters uncertainty (covariance matrices) into windowed multipole parameters uncertainty. We show that generating stochastic nuclear cross sections by sampling from the resulting windowed multipole covariance matrix can reproduce the cross-section uncertainty in the original nuclear data file. The windowed multipole representation is therefore a novel nuclear physics formalism able to generate Doppler broadened stochastic nuclear cross sections on the fly, unlocking breakthrough computational gains for nuclear computations. Through this foundational paper, we hope to make the windowed multipole representation accessible, reproducible, and usable for the nuclear physics community, as well as provide the theoretical basis for future research on expanding its capabilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Uncertainty quantification and propagation in lithium-ion battery electrodes using bayesian convolutional neural networks

The complex nature of manufacturing processes stipulates electrodes to possess high variability with increased heterogeneity during production. X-ray computed tomography imaging has proved to be critical in visualizing the complicated stochastic particle distribution of as-manufactured electrodes in lithium-ion batteries. However, accurate prediction of their electrochemical performance necessitates precise evaluation of kinetic and transport properties from real electrodes. Image segmentation that characterizes voxels to particle/pore phase is often meticulous and fraught with subjectivity owing to a myriad of unconstrained choices and filter algorithms. Here we utilize a Bayesian convolutional neural network to tackle segmentation subjectivity and quantify its pertinent uncertainties. Otsu inter-variance and Blind/Referenceless Imaging Spatial Quality Evaluator are used to assess the relative image quality of grayscale tomograms, thus evaluating the uncertainty in the derived microstructural attributes. We analyze how image uncertainty is correlated with the uncertainties and magnitude of kinetic and transport properties of an electrode, further identifying pathways of uncertainty propagation within microstructural attributes. The coupled effect of spatial heterogeneity and microstructural anisotropy on the uncertainty quantification of transport parameters is also understood. This work demonstrates a novel methodology to extract microstructural descriptors from real electrode images through quantification of associated uncertainties and discerning the relative strength of their propagation, thus facilitating feedback to manufacturing processes from accurate image based electrochemical simulations.

25 ENERGY STORAGE↗
DOE OSTI2021

A domain wall-magnetic tunnel junction artificial synapse with notched geometry for accurate and efficient training of deep neural networks

Inspired by the parallelism and efficiency of the brain, several candidates for artificial synapse devices have been developed for neuromorphic computing, yet a nonlinear and asymmetric synaptic response curve precludes their use for backpropagation, the foundation of modern supervised learning. Spintronic devices—which benefit from high endurance, low power consumption, low latency, and CMOS compatibility—are a promising technology for memory, and domain-wall magnetic tunnel junction (DW-MTJ) devices have been shown to implement synaptic functions such as long-term potentiation and spike-timing dependent plasticity. In this work, we propose a notched DW-MTJ synapse as a candidate for supervised learning. Using micromagnetic simulations at room temperature, we show that notched synapses ensure the non-volatility of the synaptic weight and allow for highly linear, symmetric, and reproducible weight updates using either spin transfer torque (STT) or spin–orbit torque (SOT) mechanisms of DW propagation. We use lookup tables constructed from micromagnetics simulations to model the training of neural networks built with DW-MTJ synapses on both the MNIST and Fashion-MNIST image classification tasks. Accounting for thermal noise and realistic process variations, the DW-MTJ devices achieve classification accuracy close to ideal floating-point updates using both STT and SOT devices at room temperature and at 400 K. Our work establishes the basis for a magnetic artificial synapse that can eventually lead to hardware neural networks with fully spintronic matrix operations implementing machine learning.

42 ENGINEERING↗
DOE OSTI2021

Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion

In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.

Maldonado, BryanP. [Oak Ridge National Lab. (ORNL)↗
DOE OSTI2020

Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis

In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Core Design of the Holos-Quad Microreactor

The Holos-Quad micro-reactor concept, developed by HolosGen LLC, is equipped with a 22 MWt (Mega-Watt thermal) core and an integral power conversion system converting the core thermal energy into approximately 10 MWe (Mega-Watt electric). This design can be configured to support a wide range of applications. It is a very innovative high-temperature gas-cooled reactor concept using TRI-structural ISOtropic particle fuel (TRISO) distributed in graphite hexagonal blocks, cooled with helium in a direct Brayton cycle independently executed by four Subcritical Power Modules (SPMs) fitted into a hardened 40-foot container whose dimensions are in compliance with ISO shipping containers requirements. In FY2019 HolosGen LLC was awarded by the Department of Energy Advanced Research Project Agency-Energy (DOE ARPA-E) under the MEITNER funding program. As part of the MEITNER award, the Argonne National Laboratory (ANL) contributed expertise through two specialized teams: The “Design Team” and the “Resource Team”. The Design Team was dedicated to validate feasibility of the Holos-Quad core and to optimize its core design through neutronics analyses. The Resource Team was dedicated to feasibility verification via high-fidelity codes of Holos-Quad thermal-hydraulic, heat transfer, shielding, and structural aspects. This report summarizes the activities conducted by ANL Design Team. A rigorous design approach based on multi-criteria optimization and code-to-code comparison involving stochastic and high-fidelity deterministic solutions was developed and employed at several evolutionary stages of the Holos-Quad design. Several generations of the Holos-Quad core were designed within this project before converging to the current full-scale Gen 2+ design that is detailed in this report. Figure EA-1 illustrates a cross-sectional view of Gen 2+ Holos-Quad core configuration, and Figure EA-2 provides a simplified perspective view of 1-of-4 SPMs. The Holos-Quad uses four thermal-hydraulically independent SPMs locked into stationary positions during power operation, surrounded by BeO reflector and structural component fully comprised within the dimensional constraints represented by traditional ISO containers. One of the benefits of this approach is to enable transportation of each SPM promptly after irradiation in shielded containers. The core is designed to operate for approximately 8 full-power years while the reactivity controls and power conversion system enable load-following operations. The reactivity controls are represented by independent, diversified, and redundant reactivity control systems based on control drums and redundant sets of shutdown rods. The high-fidelity simulation tools were used to assess detailed power and flux distributions of the three-dimensional full-core or quarter-core of the Gen 2+ configuration. Single-physics and multi-physics simulations of the neutronics code PROTEUS and the thermal-hydraulic code System Analysis Module (SAM) were performed to analyze the Holos design configurations with detailed high-fidelity solutions. The design work performed confirmed feasibility of the Holos-Quad concept, provided realistic design description for detailed design of the operational system, and identified several core design improvements to be further considered for future reactor development activities.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Exploring strain rate effects upon 3D materials using high speed in situ X-ray tomoscopy

Cellular materials are ubiquitous in our modern society. They may be stochastic gas-blown foams (e.g., polyurethane), foamed starches (e.g., cereals), or, in this case, 3D printed microlattices. Failure in these materials is often driven by surface or sub-surface defects, which may be nucleated at a surface roughness, an interior void, or inclusion interfaces that may not be typically observable. Obfuscating our understanding further, bulk materials are known to exhibit strain-rate-dependent mechanical response, making a subsurface understanding of damage even more critical. For the first time, an in situ uniaxial mechanical loading stage that simultaneously rotates specimens up to 18 Hz was fielded at a synchrotron for 3D tomographic imaging. This capability opens a plethora of materials science opportunities to explore strain rate effects in materials and examining deformation, fracture, and delamination’s (in composites) for a complete 3D picture (movie) of material response. We demonstrate the deformation of 3D printed polymer lattice structures, of three different material types, at 0.25, 1.1, and 2.2 s −1 strain rates. We successfully imaged the 3D deformation of these materials and can directly compare the same printed structure to the three material types at three strain rates, all in 3D. Material point method simulations were applied to one of the materials to better understand the role of voids on the 3D printed structure’s performance.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Dynamical structure factors of warm dense matter from time-dependent orbital-free and mixed-stochastic-deterministic density functional theory

Abstract We present the first calculations of the inelastic part of the dynamical structure factor (DSF) for warm dense matter (WDM) using time-dependent orbital-free density functional theory (TD-OF-DFT) and mixed-stochastic-deterministic (mixed) Kohn Sham TD-DFT (KS TD-DFT). WDM is an intermediate phase of matter found in planetary cores and laser-driven experiments, where the accurate calculation of the DSF is critical for interpreting x-ray Thomson scattering measurements. Traditional TD-DFT methods, while highly accurate, are computationally expensive, motivating the exploration of TD-OF-DFT and mixed TD-KS-DFT as more efficient alternatives. We applied these methods to experimentally measured WDM systems, including solid-density aluminum and beryllium, compressed beryllium, and carbon–hydrogen mixtures. Our results show that TD-OF-DFT requires a dynamical kinetic energy potential in order to qualitatively capture the plasmon response. Additionally, it struggles with capturing bound electron contributions. In contrast, mixed TD-KS-DFT offers greater accuracy in distinguishing bound and free electron effects, aligning well with experimental data, though at a higher computational cost. This study highlights the trade-offs between computational efficiency and accuracy, demonstrating that TD-OF-DFT remains a valuable tool for rapid scans of parameter space, while mixed TD-KS-DFT should be preferred for high-fidelity simulations. Our findings provide insight into the future development of DFT methods for WDM and suggest potential improvements for TD-OF-DFT.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Parameter estimation with maximal updated densities

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of “true” parameter values under the assumption that such uncertainties should be reduced as more data are incorporated into the problem, i.e., the uncertainty is considered epistemic. A major contribution of this work is the formulation and solution of such a parameter identification problem (PIP) within the measure-theoretic framework developed for the SIP. The approach is novel in that it utilizes a solution to a stochastic forward problem (SFP) to update an initial density only in the parameter directions informed by the model output data. In other words, this method performs “selective regularization” only in the parameter directions not informed by data. Further, the solution is defined by a maximal updated density (MUD) point where the updated density defines the measure-theoretic solution to the PIP. Another significant contribution of this work is the full theory of existence and uniqueness of MUD points for linear maps with Gaussian distributions. Data-constructed Quantity of Interest (QoI) maps are also presented and analyzed for solving the PIP within this measure-theoretic framework as a means of reducing uncertainties in the MUD estimate. We conclude with a demonstration of the general applicability of the method on two problems involving either spatial or temporal data for estimating uncertain model parameters. The first problem utilizes spatial data from a stationary partial differential equation to produce a MUD estimate of an uncertain boundary condition. The second problem utilizes temporal data obtained from the state-of-the-art ADvanced CIRCulation (ADCIRC) model to obtain a MUD estimate of uncertain wind drag coefficients for a simulated extreme weather event near the Shinnecock Inlet located in the Outer Barrier of Long Island, NY, USA.

42 ENGINEERING↗