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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Measuring thermal profiles in high explosives using neural networks

We present a new method for calculating the temperature profile of high explosive (HE) material using a Convolutional Neural Network (CNN). To train/test the CNN, we have developed a hybrid experiment/simulation method for collecting acoustic and temperature data. We experimentally heat cylindrical containers of HE material until detonation/deflagration, where we continuously measure the acoustic bursts through the HE using multiple acoustic transducers lined around the exterior container circumference. However, measuring the temperature profile in the HE in an experiment would require inserting a large number of thermal probes, which would disrupt the heating process. Thus, we use two thermal probes, one at the HE center and one at the wall. We then use numerical simulation of the heating process to calculate the temperature distribution and correct the simulated temperatures based on the experimental center and wall temperatures. We calculate temperature errors on the order of 15 °C, which is ∼12% of the range of temperatures in the experiment. We also investigate how the algorithm’s accuracy is affected by the number of acoustic receivers used to collect each measurement and the resolution of the temperature prediction. This work provides a means of assessing the safety status of HE material, which cannot be achieved using existing temperature measurement methods. In addition, it has implications for a range of other applications where internal temperature profile measurements would provide critical information. These applications include detecting chemical reactions, observing thermodynamic processes such as combustion, monitoring metal or plastic casting, determining the energy density in thermal storage capsules, and identifying abnormal battery operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Identifying Climate Patterns Using Clustering Autoencoder Techniques

Abstract The complexity of growing spatiotemporal resolution of climate simulations produces a variety of climate patterns under different projection scenarios. This paper proposes a new data-driven climate classification workflow via an unsupervised deep learning technique that can dimensionally reduce the vast volume of spatiotemporal numerical climate projection data into a compact representation. We aim to identify distinct zones that capture multiple climate variables as well as their future changes under different climate change scenarios. Our approach leverages convolutional autoencoders combined with k -means clustering (standard autoencoder) and online clustering based on the Sinkhorn–Knopp algorithm (clustering autoencoder) across the conterminous United States (CONUS) to capture unique climate patterns in a data-driven fashion from the Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G). The developed approach compresses 70 years of GFDL-ESM2G simulation at 0.125° spatial resolution across the CONUS under multiple warming scenarios to a lower-dimensional space by a factor of 660 000 and then tested on 150 years of GFDL-ESM2G simulation data. The results show that five climate clusters capture physically reasonable and spatially stable climatological patterns matched to known climate classes defined by human experts. Results also show that using a clustering autoencoder can reduce the computational time for clustering by up to 9.2 times when compared to using a standard autoencoder. Our five unique climate patterns resulting from the deep learning–based clustering of the lower-dimensional space thereby enable us to provide insights on hydrometeorology and its spatial heterogeneity across the conterminous United States immediately without downloading large climate datasets. Significance Statement This paper presents a data-driven climate classification approach using unsupervised deep learning to dimensionally reduce climate model outputs and to identify distinct climate regions for their future changes. Our approach compresses climate information for 70 years of Geophysical Fluid Dynamics Laboratory Earth System Model data across the conterminous United States (CONUS) at 0.125° spatial resolution. The results reveal that five climate clusters capture reasonable and stable climatological patterns matched to known climate patterns. The embedded clustering process in deep learning provides ×9.2 times faster execution than the k -means clustering technique. These results give us insight about climate spatial patterns and heterogeneity of hydrological patterns across the conterminous United States without downloading large climate datasets.

Kurihana, Takuya↗
DOE OSTI2024

Measuring thermal profiles in high explosives using neural networks

We present a new method for calculating the temperature profile of high explosive (HE) material using a Convolutional Neural Network (CNN). To train/test the CNN, we have developed a hybrid experiment/simulation method for collecting acoustic and temperature data. We experimentally heat cylindrical containers of HE material until detonation/deflagration, where we continuously measure the acoustic bursts through the HE using multiple acoustic transducers lined around the exterior container circumference. However, measuring the temperature profile in the HE in an experiment would require inserting a large number of thermal probes, which would disrupt the heating process. Thus, we use two thermal probes, one at the HE center and one at the wall. We then use numerical simulation of the heating process to calculate the temperature distribution and correct the simulated temperatures based on the experimental center and wall temperatures. We calculate temperature errors on the order of 15 °C, which is ~12% of the range of temperatures in the experiment. We also investigate how the algorithm’s accuracy is affected by the number of acoustic receivers used to collect each measurement and the resolution of the temperature prediction. This work provides a means of assessing the safety status of HE material, which cannot be achieved using existing temperature measurement methods. In addition, it has implications for a range of other applications where internal temperature profile measurements would provide critical information. These applications include detecting chemical reactions, observing thermodynamic processes such as combustion, monitoring metal or plastic casting, determining the energy density in thermal storage capsules, and identifying abnormal battery operations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

An Extension of the Athena++ Code Framework for Radiation-magnetohydrodynamics in General Relativity Using a Finite-solid-angle Discretization

We extend the general-relativistic magnetohydrodynamics (GRMHD) capabilities of Athena++ to incorporate radiation. The intensity field in each finite-volume cell is discretized in angle, with explicit transport in both space and angle properly accounting for the effects of gravity on null geodesics, and with matter and radiation coupled in a locally implicit fashion. Here we describe the numerical procedure in detail, verifying its correctness with a suite of tests. Motivated in particular by black hole accretion in the high-accretion-rate, thin-disk regime, we demonstrate the application of the method to this problem. With excellent scaling on flagship computing clusters, the port of the algorithm to the GPU-enabled AthenaK code now allows the simulation of many previously intractable radiation-GRMHD systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling

Plug-and-play priors (PnP) is an image reconstruction framework that utilizes an image denoiser as an imaging prior. Unlike traditional regularized inversion, PnP does not require the prior to be expressible in the form of a regularization function. This flexibility enables PnP algorithms to exploit the most effective image denoisers, leading to their state-of-the-art performance in various imaging tasks. However, many powerful denoisers, such as the ones based on convolutional neural networks (CNNs), do not have tunable parameters that would allow controlling their influence within PnP. To address this issue, in this paper, we introduce a scaling parameter that adjusts the magnitude of the denoiser input and output. We theoretical justify the denoiser scaling from the perspectives of proximal optimization, statistical estimation, and consensus equilibrium. Finally, we provide numerical experiments demonstrating the ability of denoiser scaling to systematically improve the performance of PnP for denoising CNN priors that do not have explicitly tunable parameters.

Boosting↗
DOE OSTI2020

Stability Analysis of Interface Conditions for Ocean-Atmosphere Coupling

In this paper, we analyze the stability of different coupling strategies for multidomain PDEs that arise in general circulation models used in climate simulations. We focus on fully coupled ocean–atmosphere models that are needed to represent and understand the complicated interactions of these two systems, becoming increasingly important in climate change assessment in recent years. Numerical stability issues typically arise because of different time-stepping strategies applied to the coupled PDE system. In particular, the contributing factors include using large time steps, lack of accurate interface flux, and single-iteration coupling. We investigate the stability of the coupled ocean–atmosphere models for various interface conditions such as the Dirichlet–Neumann condition and the bulk interface condition, which is unique to climate modeling. By analyzing a simplified model, we demonstrate here how the parameterization of the bulk condition and other numerical and physical parameters affect the coupling stability and establish stability conditions for different coupling strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dendrite-resolved, full-melt-pool phase-field simulations to reveal non-steady-state effects and to test an approximate model

In this report we study the epitaxial, columnar growth of (multiply oriented) dendrites/cells for a spot melt in a polycrystalline Al–Cu substrate using two-dimensional, phase-field, direct numerical simulations (DNS) at the full-melt-pool scale. Our main objective is to compare the expensive DNS model to a much cheaper but approximate “line” model in which a single-crystal phase-field simulation is confined to a narrow rectangular geometry. To perform this comparison, we develop algorithms that automatically extract quantities of interest (QoIs) from both DNS and line models. These QoIs allow us to quantitatively assess the assumptions in the line model and help us analyze its discrepancy with the DNS model. We consider four sets of heat source parameters, mimicking welding and additive manufacturing conditions, that create a combination shallow and deep melt pools. Our largest DNS simulation used 16K x 14K grid points in space. Our main findings can be summarized as follows. Under AM conditions, the QoIs of line models are in excellent agreement with the full DNS results for both shallow and deep melt pools. Under welding conditions, the primary spacing of the DNS model is smaller than the prediction of line model. We identify a geometric crowding effect that accounts for the discrepancies between the DNS and line models. We propose two potential mechanisms that determine the response of the microstructure to geometric crowding.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Recent advances in computational mathematics and applications

We are honored to bring you this special issue dedicated to recent advances in computational mathematics and applications in science and engineering. The papers in this special issue were presented in ”Conference on Computational Mathematics and Applications (CCMA)” held at the University of Nevada Las Vegas (UNLV) during October 25–27, 2019. The conference has attracted about 90 attendees from six countries. The 15 papers in the special issue comprise a diverse collection of theoretical numerical analysis as well as applications in various subjects. Topics cover optimal control of PDEs, discontinuous Galerkin methods, fluid flow in porous media, turbulence flow, static and moving interface problems, complex fluids composed by the mixture of Newtonian fluid and nematic (liquid crystal) flows, modeling of ocean–atmosphere system, image segmentation algorithm, uncertainty quantification problems for turbulence model and Maxwell’s equations, iterative solver for systems resulting from mixed methods, and novel methods for solving systems of nonlinear equations. As the Guest Editors we would like to thank Dr. Leland Jameson at NSF (National Science Foundation) for kindly supporting our conference proposal which made this conference possible. We would also like to thank Darren Sugrue from Elsevier who provided partial support for our conference, and Thennarasu Gunasekaran and his production team from Elsevier who produced this nice special issue. We are grateful to many people (Dr. Zhijian Wu, Lori Ornelas, Elsa Juarez, and many Ph.D. students) at the Department of Mathematical Sciences of UNLV who provided tremendous support for the conference. Finally, we very much appreciate all authors who contributed their precious results to this special issue.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast calculation of diffraction patterns from an ensemble of aligned molecules

We report an algorithm to calculate electron diffraction patterns for molecules with anisotropic angular distribution, which is significantly faster than existing methods. The algorithm uses a transform to convert the molecular orientation distribution, which is a function of three Euler angles, to the atom-pair distribution functions which depend on the polar and azimuthal angles. The diffraction signal can then be calculated from the atom-pair distributions. We demonstrate the computation method numerically by calculating electron diffraction patterns for a symmetric top molecule (trifluoroiodomethane) and an asymmetric top molecule (formaldehyde) and show that it reduces the calculation time by approximately two orders of magnitude compared to the standard brute-force method. Here, the method can also be applied to the calculation of x-ray diffraction patterns.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast

This paper presents a novel bidding curve design algorithm tailored for hybrid power plants (HPPs) to participate in the wholesale electricity market. Utilizing forecasts for photovoltaic (PV) generation and available battery power, our algorithm strategically computes the bidding curve to maximize HPP profit while adeptly managing the inherent uncertainty associated with PV power generation. In addition, the introduction of the penalty cost in HPP bidding curves provides the system operator a tool to effectively manage the system-level uncertainty that caused by HPPs. Numerical analysis through Monte Carlo simulations confirms that our bidding curve methodology outperforms the benchmark across various scenarios.

bidding curve↗
DOE OSTI2024

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast: Preprint

This paper presents a novel bidding curve design algorithm tailored for hybrid power plants (HPPs) to participate in the wholesale electricity market. Utilizing forecasts for photovoltaic (PV) generation and available battery power, our algorithm strategically computes the bidding curve to maximize HPP profit while adeptly managing the inherent uncertainty associated with PV power generation. In addition, the introduction of the penalty cost in HPP bidding curves provides the system operator a tool to effectively manage the system-level uncertainty that caused by HPPs. Numerical analysis through Monte Carlo simulations confirms that our bidding curve methodology outperforms the benchmark across various scenarios.

bidding curve↗
DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A cancellation problem in hybrid particle-in-cell schemes due to finite particle size

The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the different spatial discretizations of ions as finite-spatial-size particles and electrons as a grid-based fluid can lead to significant numerical wave dispersion errors in the long wavelength limit (kd i «1, where k is the wavenumber and di is the ion skin-depth). The problem occurs when high-order particle-grid interpolations, or grid-based smoothing, spreads the electric field experienced by the ions across multiple spatial cells and leads to inexact cancellation of electric field terms in the total (ion + electron) momentum equation. Practical requirements on the mesh spacing Δx/d i are suggested to bound these errors from above. The accuracy impact of not respecting these resolution constraints is shown for a non-linear shock problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Fast neural Poincaré maps for toroidal magnetic fields

Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. Furthermore, this structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Perturbative second-order optical susceptibility of bulk materials: a symmetry-enforced return to non-orthogonal localized basis sets

The second-order optical susceptibility of semiconductors $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier (i.e. localized) orbitals, making a comeback onto frameworks based on localized basis sets. Here, in this work, we present an approach for calculating $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ reliant on numerical pseudo-atomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of ‘Slater–Koster-like’ two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well.

Huamán, Angiolo [Univ. of Arkansas, Fayetteville, ↗
DOE OSTI2024

SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world’s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger “outer-loop” time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.

97 MATHEMATICS AND COMPUTING↗