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DOE OSTI2023

A Review of Physics-Informed Machine Learning in Fluid Mechanics

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

42 ENGINEERING↗

DOE OSTI2026

Best practices in software development for robust and reproducible geoscientific models based on insights from the Global Carbon Budget's dynamic vegetation models

Computational models play an increasingly vital role in scientific research by enabling the numerical simulation of complex processes. Such models are also fundamental in geosciences. For instance, they offer critical insights into the impacts of global change on the Earth system today and in the future. Beyond their value as research tools, models are also software products and should therefore adhere to certain established software engineering standards. However, scientists are rarely trained as software developers, which can lead to potential deficiencies in software quality like unreadable, inefficient, or erroneous code. The complexity of models, coupled with their integration into broader workflows, also often makes it challenging to reproduce results, evaluate processes, and build upon them. In this paper, we review the state and current practices of the development processes of the state-of-the-art land surface models used by the Global Carbon Budget. We combine the experience of modelers from the respective research groups with the expertise of software engineers from tech companies to outline key principles and tools for improving software quality in research. We explore four main areas: (1) model testing and validation, (2) scientific, technical, and user documentation, (3) version control, continuous integration, and code review, and (4) the portability and reproducibility of workflows. Our review reveals that while modeling communities are incorporating many best practices, significant room for improvement remains in areas such as automated testing, automated documentation, and reproducibility. Therefore, we here identify and promote essential software engineering practices, including numerous examples of practices from within the community that can serve as guidelines for other models and could help streamline processes across the entire community. We conclude with an open-source example implementation of these principles, demonstrating portable and reproducible data flows, a continuous integration setup, and web-based visualizations. This example may serve as a practical resource for model developers, users, and all scientists engaged in scientific programming.

Gregor, Konstantin [Technical Univ. of Munich (Ger↗

DOE OSTI2025

CaptureFOAM

CaptureFOAM provides utilities for fast and accurate direct air capture (DAC) contactor simulations, based on the OpenFOAM framework. At the core, CaptureFOAM is a suite of mass transfer and chemistry models built upon the OpenFOAM thin film model, which allows coarser mesh resolution and less constrictive time step requirements when compared to a traditional volume of fluid approach. This allows CaptureFOAM to conduct device-scale simulations for complex geometries including commercial packing materials and novel contactor shapes, matching experimental results in a wide variety of applications.

Kincaid, Kellis [Oak Ridge National Laboratory (OR↗

DOE OSTI2026

On the Statistical Uncertainty of Monte Carlo-Calculated Scattering Sensitivities

Sensitivity coefficients calculated with Monte Carlo codes are widely used for nuclear data uncertainty quantification in the modeling and simulation of complex 3D reactor systems. This study systematically compares sensitivity coefficients and associated statistical uncertainties for the multiplication factor and fuel temperature reactivity across multiple Monte Carlo codes (SCALE/KENO, SCALE/Shift, MCNP, and Serpent) using simple models representing light-water reactors and advanced reactor concepts. For multiplication factor sensitivities, statistical uncertainties are generally acceptable, although scattering sensitivities show significantly larger statistical uncertainties than, for example, fission and capture reactions. Fuel temperature reactivity sensitivities show significantly larger statistical uncertainties across all reactions. Elastic scattering sensitivities are the most problematic: all Monte Carlo codes fail to resolve energy-dependent coefficients, and they produce dramatically different energy-collapsed values. Critically, the use of these sensitivity coefficients in nuclear data uncertainty propagation leads to reduced statistical uncertainties in individual uncertainty contributions. This can lead to the masking of unusable sensitivity coefficients and producing misleading uncertainty results. The findings of this study show that new or enhanced methods are needed to improve Monte Carlo elastic scattering sensitivity calculations. Additionally, this study shows the relevance of verifying sensitivity coefficients through direct perturbation calculations for individual nuclide reactions, instead of only for total cross sections as commonly done.

Bostelmann, Rike [ORNL] (ORCID:0000000165968088)↗

DOE OSTI2025

HIGH-FIDELITY SIMULATION OF SOOT FORMATION AND THERMAL RADIATION IN A LABORATORY-SCALE RICH-QUENCH-LEAN BURNER

High-fidelity simulations of a swirl-stabilized turbulent spray flame in a laboratory-scale aero-combustor have been performed to evaluate the predictability of state-of-the-art models in capturing soot formation. The simulations employ a complex chemical mechanism developed for Jet-A with PAH chemistry, coupled with the Hybrid Method of Moments (HMOM) soot model, and a Lagrangian dilute spray model for the fuel injection. Two simulations are performed to compare the results when thermal radiation is neglected or included in the solution with a mean spectral model. Modeling closures for the soot differential diffusion effects in mixture fraction space, as well as turbulence-radiation interaction are also evaluated using the data generated by the simulations. Given the degree of complexity of the simulation, the results showed good agreement with experimental measurements of the spatial distribution of the soot volume fraction ensemble average. A closer agreement with the experiment is observed when thermal radiation is included in the solution. Thermal radiation is observed to reduce the flame temperature and increase the flame intermittency, denoted by the increase in the temperature standard deviation in mixture fraction space. The reduction in temperature also leads to a reduction in PAH production and soot volume fraction. Turbulence is observed to have different effects on radiative emission depending on the mixture fraction. Turbulent scalar fluctuations significantly enhance radiative emission in fuel lean mixtures and can also play a role for fuel rich conditions. The statistical description of the turbulence-radiation interaction, previously proposed in the literature, was observed to correctly reproduce the high-fidelity results. Model coefficients were provided for swirl-stabilized flames. The soot differential diffusion model, previously proposed in the literature, based on the residual between the exact term and its model approximation, was also evaluated. The residual correction term further improved the agreement with exact differential diffusion term evaluated with the high-fidelity simulation data in mixture fraction space. The results suggest that the effective turbulent Lewis number can be equal to unity in simulations of turbulent non-premixed recirculating flames.

Soriano, Bruno [Sandia National Laboratories (SNL)↗

DOE OSTI2021

Evaluating Terrain as a Turbulence Generation Method

When driving microscale large-eddy simulations with mesoscale model solutions, turbulence will take space to develop, known as fetch, on the microscale domain. To reduce fetch, it is common to add perturbations near the boundaries to speed up turbulence development. However, when simulating domains over complex terrain, it is possible that the terrain itself can quickly generate turbulence within the boundary layer. It is shown here that rugged terrain is able to generate turbulence without the assistance of a perturbation strategy; however, the levels of turbulence generated are improved when adding perturbations at the inlet. Flow over smoothed, but not flat, terrain fails to generate adequate turbulence throughout the boundary layer in all tests conducted herein. Sensitivities to the strength of the mean wind speed and boundary layer height are investigated and show that higher wind speeds produce turbulence over terrain features that slower wind speeds do not. Further, by increasing the height of the capping inversion, the effectiveness of topography alone to generate turbulence throughout the depth of the boundary is diminished. In all cases, the inclusion of a perturbation strategy improved simulation performance with respect to turbulence development.

17 WIND ENERGY↗

DOE OSTI2022

Uncertainty Analysis in Multi‐Sector Systems: Considerations for Risk Analysis, Projection, and Planning for Complex Systems

Abstract Simulation models of multi‐sector systems are increasingly used to understand societal resilience to climate and economic shocks and change. However, multi‐sector systems are also subject to numerous uncertainties that prevent the direct application of simulation models for prediction and planning, particularly when extrapolating past behavior to a nonstationary future. Recent studies have developed a combination of methods to characterize, attribute, and quantify these uncertainties for both single‐ and multi‐sector systems. Here, we review challenges and complications to the idealized goal of fully quantifying all uncertainties in a multi‐sector model and their interactions with policy design as they emerge at different stages of analysis: (a) inference and model calibration; (b) projecting future outcomes; and (c) scenario discovery and identification of risk regimes. We also identify potential methods and research opportunities to help navigate the tradeoffs inherent in uncertainty analyses for complex systems. During this discussion, we provide a classification of uncertainty types and discuss model coupling frameworks to support interdisciplinary collaboration on multi‐sector dynamics (MSD) research. Finally, we conclude with recommendations for best practices to ensure that MSD research can be properly contextualized with respect to the underlying uncertainties.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Ground state property calculations of LiH n complexes using IBM Qiskit’s quantum simulator

In this study, the variational quantum eigensolver (VQE) on a quantum simulator is used in calculating ground state electronic structure properties of the LiH n , n = 1–3, complexes including their singly charged ions. Results calculated using classical electronic structure algorithms are also included. We investigate the use of the unitary coupled cluster with singles and doubles (UCCSD) Ansatz using VQE within Qiskit and compare results to full configuration interaction (FCI) calculations. Computed ground state energies, electron affinities, ionization potentials, and dipole moments are considered. We report the first-of-its-kind simulated quantum computing results of selected LiH n species and use the parity orbital to qubit mapping scheme. We find that VQE/UCCSD results are comparable to classical coupled clusters with singles and doubles for all considered systems with respect to FCI. A VQE calculation cost evaluation is included in which we evaluate performance using both Jordan–Wigner and parity orbital to qubit mapping schemes. We also discuss some of the current limitations of utilizing VQE for the study of chemical systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Understanding Complex Magnetic Spin Textures with Simulation-Assisted Lorentz Transmission Electron Microscopy

There is an increased interest in topologically nontrivial magnetic spin textures such as skyrmions and chiral domain-wall solitons, both from a point of fundamental physics understanding as well as potential technological interest in low-power memory applications. In order to control their behavior, it is necessary to understand their complex spin texture at the nanoscale. Lorentz transmission electron microscopy (LTEM) is a suitable technique for studying these systems due to its high spatial resolution and capability to simultaneously characterize magnetic texture and microstructure. In this work, we present the application of PyLorentz, an open-source software suite that we have developed, for quantitative image analysis of Neel-type skyrmions in thin-film heterostructures. PyLorentz enhances LTEM capabilities by enabling reconstruction of magnetic induction maps from experimental images, as well as simulating LTEM images using micromagnetic simulation data. We demonstrate this for simulated Neel skyrmions as well as experimental data from [Pt/Co/W] multilayer heterostructures. Finally, we also show how simulation-assisted LTEM analysis is crucial for understanding these complex magnetic spin textures, in which the reconstructed magnetic induction map (seen in the LTEM images) differs significantly from the magnetization configuration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Composable Programming of Hybrid Workflows for Quantum Simulation

We present a composable design scheme for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. Our object-oriented approach is based on constructing an expressive set of common data structures and methods that enable programming of a broad variety of complex hybrid quantum simulation applications. The abstract core of our scheme is distilled from the analysis of the current quantum simulation algorithms. Subsequently, it allows a synthesis of new hybrid algorithms and workflows via the extension, specialization, and dynamic customization of the abstract core classes defined by our design. We implement our design scheme using the hardware-agnostic programming language QCOR into the QuaSiMo library. To validate our implementation, we test and show its utility on commercial quantum processors from IBM, running some prototypical quantum simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Associative memories using complex-valued Hopfield networks based on spin-torque oscillator arrays

Abstract Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting the oscillatory output of the oscillators. Pseudo-inverse training suffices to store at least 12 images in a set of 192 oscillators, representing 16 × 12 pixel images. The energy required to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 5% root mean square deviations from the ideal image require approximately 5 μ s and consume roughly 130 nJ. Simulations show that the network functions well when the resonant frequency of the oscillators can be tuned to have a fractional spread less than 10 −3 , depending on the strength of the feedback.

Prasad, Nitin (ORCID:0000000180880164)↗

DOE OSTI2021

Assembly and Analysis of Cell-Scale Membrane Envelopes

The march toward exascale computing will enable routine molecular simulation of larger and more complex systems, for example, simulation of entire viral particles, on the scale of approximately billions of atoms-a simulation size commensurate with a small bacterial cell. Anticipating the future hardware capabilities that will enable this type of research and paralleling advances in experimental structural biology, efforts are currently underway to develop software tools, procedures, and workflows for constructing cell-scale structures. Herein, we describe our efforts in developing and implementing an efficient and robust workflow for construction of cell-scale membrane envelopes and embedding membrane proteins into them. A new approach for construction of massive membrane structures that are stable during the simulations is built on implementing a subtractive assembly technique coupled with the development of a structure concatenation tool (fastmerge), which eliminates overlapping elements based on volumetric criteria rather than adding successive molecules to the simulation system. Using this approach, we have constructed two "protocells" consisting of MARTINI coarse-grained beads to represent cellular membranes, one the size of a cellular organelle and another the size of a small bacterial cell. The membrane envelopes constructed here remain whole during the molecular dynamics simulations performed and exhibit water flux only through specific proteins, demonstrating the success of our methodology in creating tight cell-like membrane compartments. Extended simulations of these cell-scale structures highlight the propensity for nonspecific interactions between adjacent membrane proteins leading to the formation of protein microclusters on the cell surface, an insight uniquely enabled by the scale of the simulations. We anticipate that the experiences and best practices presented here will form the basis for the next generation of cell-scale models, which will begin to address the addition of soluble proteins, nucleic acids, and small molecules essential to the function of a cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Artificial Intelligence for imaging Cherenkov detectors at the EIC

Abstract Imaging Cherenkov detectors form the backbone of particle identification (PID) at the future Electron Ion Collider (EIC). Currently all the designs for the first EIC detector proposal use a dual Ring Imaging CHerenkov (dRICH) detector in the hadron endcap, a Detector for Internally Reflected Cherenkov (DIRC) light in the barrel, and a modular RICH (mRICH) in the electron endcap. These detectors involve optical processes with many photons that need to be tracked through complex surfaces at the simulation level, while for reconstruction they rely on pattern recognition of ring images. This proceeding summarizes ongoing efforts and possible applications of AI for imaging Cherenkov detectors at EIC. In particular we will provide the example of the dRICH for the AI-assisted design and of the DIRC for simulation and particle identification from complex patterns and discuss possible advantages of using AI.

Instruments & Instrumentation↗

DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of the Monte Carlo N-Particle radiation transport simulation tool, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) confirm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results assessment methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exemplified through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of the Monte Carlo N-Particle radiation transport simulation tool, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) con firm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results assessment methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exempli fied through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than "building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers. In this paradigm, reduced complexity computational and analytical models still have an important purpose. The explicit form of an analytic solution is arguably the best way to understand the qualitative properties of simple models. In contrast to "building up" a complex problem through understanding simpler problems, results from detailed computational scenarios can be better explained by "building down" the complex model through simple models rooted in the fundamental or essential phenomenology. Simplified analytic and computational models can be used to 1) increase a user's confidence in the computational solution of a complex model, 2) confirm there are no user input errors, and 3) ensure essential assumptions of the simulation tool are preserved. This process of using analytic models to develop a more valuable analysis of simulation results is named the results analysis methodology. The utility of the results assessment methodology and a complimentary sensitivity analysis is exemplified through the analysis of the neutron flux in a dry used fuel storage cask. This application was chosen due to current scientific interest in used nuclear fuel storage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Exploring model complexity in machine learned potentials for simulated properties

Abstract Machine learning (ML) enables the development of interatomic potentials with the accuracy of first principles methods while retaining the speed and parallel efficiency of empirical potentials. While ML potentials traditionally use atom-centered descriptors as inputs, different models such as linear regression and neural networks map descriptors to atomic energies and forces. This begs the question: what is the improvement in accuracy due to model complexity irrespective of descriptors? We curate three datasets to investigate this question in terms of ab initio energy and force errors: (1) solid and liquid silicon, (2) gallium nitride, and (3) the superionic conductor Li $$_{10}$$ 10 Ge(PS $$_{6}$$ 6 ) $$_{2}$$ 2 (LGPS). We further investigate how these errors affect simulated properties and verify if the improvement in fitting errors corresponds to measurable improvement in property prediction. By assessing different models, we observe correlations between fitting quantity (e.g. atomic force) error and simulated property error with respect to ab initio values. Graphical abstract

Rohskopf, A. (ORCID:0000000227128296)↗

DOE OSTI2022

Voronoi Meshing to Accurately Capture Geological Structure in Subsurface Simulations

Mesh generation lies at the interface of geological modeling and reservoir simulation. Highly skewed or very small grid cells may be necessary to accurately capture the geometry of geological features, but the resulting poorly scaled or small grid cells can have a substantial negative impact on simulator accuracy and speed. One way to minimize numerical errors caused by gridding complex structures is to simulate on high-quality Voronoi meshes, which reduce grid orientation effects in fluid flow. This work presents a complete methodology to create Voronoi simulation grids, model fluid flow in complex geological systems, and visualize the results. A recently developed Voronoi meshing method that can automatically generate provably good unstructured meshes that conform to input surfaces creating closed volumes is used. Initially an analytical benchmark simulation is presented to validate the quality of the meshes and simulation results and demonstrate the superiority of simulation results using Voronoi meshes over flexed-hexahedral meshes on a domain with internal features. Next, meshes are created for test structures representing four of the most common geological features in the subsurface: layering, pinch-out, an interior lens that tapers to zero thickness on all sides and a fault with offset. Two benchmark flow simulations are run for each test structure. Finally, a realistic geological example for CO 2 injection into an anticline is simulated. Three realizations of the Voronoi mesh at the same resolution are generated for the simulations. Each mesh is highly refined near the injection wells and coarse in areas of less interest. These three meshes are used to model the CO 2 plume in the subsurface as it migrates to the top of the structure and then fills downward. Simulations on the meshes with randomly generated elements inside the input volumes each give slightly different fingering patterns for the viscous-unstable buoyant gas flow. The results presented in this work show a promising step towards utilizing fully automated Voronoi meshing for subsurface flow simulations in complex geology.

58 GEOSCIENCES↗