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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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DOE OSTI2022

Multiscale analysis in solids with unseparated scales: fine-scale recovery, error estimation, and coarse-scale adaptivity

There are several engineering applications in which the assumptions of homogenization and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. Here, we investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.

42 ENGINEERING↗
DOE OSTI2024

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest 𝜂′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous 𝜂′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted 𝜂′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the 𝜂′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions.

Lattice field theory↗
DOE OSTI2023

Multimode theory of electron hole transverse instability

We present Vlasov–Poisson three-dimensional linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel to $B$ ) is expanded in eigenfunctions of the adiabatic Poisson operator, generalizing the prior assumption of a rigid shift of the equilibrium. We show that the shiftmode is then modified by a second discrete mode plus an integral over a continuum of wave-like modes. A rigorous treatment shows that the continuum can be approximated effectively by a single mode that satisfies the external wave dispersion relation, thus making the perturbation a weighted sum of three modes. We find numerically the solution for the complex instability frequency, and the corresponding three mode amplitudes determining the perturbation eigenmode. This multimode analysis refines the accuracy of the prior single-mode results, giving slightly higher growth rates at most parameters, as expected from the extra mode shape freedom. Oscillating modes near stability boundaries have larger mode distortions which help explain particle-in-cell simulations that observe instability up to ${\sim }20$ % beyond the prior shiftmode thresholds, and narrowing of the perturbation. At high magnetic field, the multimode analysis predicts a reduction of the already small growth rate.

Physics↗
DOE OSTI2022

Optimal Control of Biomass Feedstock Processing System Under Uncertainty in Biomass Quality

Planning of biorefinery operations is complicated by the stochastic nature of physical and chemical characteristics of biomass feedstock, such as, moisture level and carbohydrate content. Biomass characteristics affect the performance of the equipment which feed the reactor and the efficiency of the conversion process in a biorefinery. We propose a stochastic optimization model to identify a blend of feedstocks, inventory levels, and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor while meeting the requirements of the biochemical conversion process. We propose a sample average approximation (SAA) of the model, and develop an efficient algorithm to solve the SAA model. A feedstock preprocessing process consists of two-stage grinding and pelleting is used to develop a case study. Extensive numerical analysis are conducted which lead to a number of observations. Our main observation is that sequencing bales based on moisture level and carbohydrate content leads to robust solutions that improve processing time and processing rate of the reactor. We provide a number of managerial insights that facilitate the implementation of the model proposed. Note to Practitioners—This paper is motivated by the challenges faced in the bioenergy industry. The focus of this paper is on plants which use the biochemical conversion process to generate liquid fuels. It has been observed that variations in biomass characteristics, such as moisture content, cause variations in feeding of the system which lead to under-utilization of equipment. A requirement of biochemical conversion process is to maintain the carbohydrate content of biomass processed by the reactor, larger than a threshold. We propose a model that identifies the inventory levels and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor. The goal is to improve equipment utilization while satisfying the requirements of the conversion process. The model is tested using real-life data. We found out that by sequencing bales based on moisture level and carbohydrate content, a plant can reduce variability in the system leading to improved system reliability, higher processing rates of the reactor, and higher throughput.

09 BIOMASS FUELS↗
DOE OSTI2026

The Dark Energy Survey supernova program: a reanalysis of cosmology results and evidence for evolving dark energy with an updated Type Ia supernova calibration

We present improved cosmological constraints from a re-analysis of the Dark Energy Survey (DES) 5-year sample of Type Ia supernovae (DES-SN5YR). This re-analysis includes an improved photometric cross-calibration, recent white dwarf observations to cross-calibrate between DES and low-redshift surveys, retraining the salt3 light-curve model and fixing a numerical approximation in the host-galaxy colour law. Our fully recalibrated sample, which we call DES-Dovekie, comprises ~1600 likely Type Ia SNe from DES and ~200 low-redshift SNe from other surveys. With DES-Dovekie, we obtain Ω m = 0.330 ± 0.015 in flat Lambda-cold dark matter (⁠ΛCDM) which changes Ω m by –0.022 compared to DES-SN5YR. Combining DES-Dovekie with cosmic microwave background data from Planck, Atacama Cosmology Telescope, and South Pole Telescope and the DESI DR2 measurements in a flat CDM cosmology, we find ω 0 = –0.803 ± 0.054 and ω a = –0.72 ± 0.21⁠. Our results hold a significance of 3.2σ, reduced from 4.2σ for DES-SN5YR, to reject the null hypothesis that the data are compatible with the cosmological constant. This significance is equivalent to a Bayesian model preference odds of approximately 5:1 in favour of the flat ω 0 ω a CDM model. Using generally accepted thresholds for model preference, our updated data exhibits only a weak preference for evolving dark energy.

dark energy↗
DOE OSTI2023

A unified and constructive framework for the universality of neural networks

Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is as follows: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)≡xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2.

Leon, Christopher↗
DOE OSTI2023

Learning to Predict Arbitrary Quantum Processes

We present an efficient machine-learning (ML) algorithm for predicting any unknown quantum process ℰ over 𝑛 qubits. For a wide range of distributions 𝒟 on arbitrary 𝑛-qubit states, we show that this ML algorithm can learn to predict any local property of the output from the unknown process ℰ, with a small average error over input states drawn from 𝒟. The ML algorithm is computationally efficient even when the unknown process is a quantum circuit with exponentially many gates. Our algorithm combines efficient procedures for learning properties of an unknown state and for learning a low-degree approximation to an unknown observable. The analysis hinges on proving new norm inequalities, including a quantum analogue of the classical Bohnenblust-Hille inequality, which we derive by giving an improved algorithm for optimizing local Hamiltonians. Numerical experiments on predicting quantum dynamics with evolution time up to 10 6 and system size up to 50 qubits corroborate our proof. Overall, our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.

quantum computation↗
DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

GeN-ROM—An OpenFOAM®-based multiphysics reduced-order modeling framework for the analysis of Molten Salt Reactors

This work presents a projection-based multiphysics Model Order Reduction (MOR) framework for the analysis of nuclear systems and its application to parametric simulations of Molten Salt Reactors (MSR). The framework, named GeN-ROM, is developed using OpenFOAM® and employs a Proper Orthogonal Decomposition aided Reduced-Basis technique (POD-RB). It can be used to reduce steady-state and transient multiphysics problems involving parametric fluid dynamics, heat exchange, and neutronics phenomena. For the treatment of structural elements in the hydraulic systems, a porous medium approach has been adopted. The reduction process is data-driven and snapshot information is extracted via POD to learn the solution manifold and to build global spatial basis functions. At the data collection phase, GeN-ROM makes use of the solvers available in GeN-Foam, a similarly OpenFOAM®-based multiphysics framework developed for the analysis of nuclear reactors. The global bases are used both to approximate the solution fields and to project the full-order equations onto lower-dimensional subspaces, thus considerably reducing the number of unknowns in a numerical system. This reduction leads to significant computational speedups, which is ideal for multi-query applications such as uncertainty quantification or design optimization. The developed tool has been tested using a 2D multiphysics model of the Molten Salt Fast Reactor (MSFR) with steady-state and transient scenarios, with speedups on the order of 10 – 10 5 .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Selected 3D Flash-X Checkpoints for the Long-Time Evolution of a 9.6 Solar-Mass Core-Collapse Supernova Model

This dataset contains selected 3D Flash-X checkpoint files from the long-time evolution of a low-energy core-collapse supernova explosion of a 9.6 Msun zero-metallicity, low-mass iron-core progenitor. The checkpoints span the shock-breakout phase through the young-remnant phase, ending at approximately 3 yr after core bounce. The dataset is intended for follow-up analysis and post-processing, especially radiation-transport calculations using the hydrodynamic and compositional structure of the ejecta. For a full description of the numerical setup, physical assumptions, limitations, and interpretation of the simulation, users should refer to the associated paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity

Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [C. Rodrigo et al., Comput. Methods App. Mech. Engrg, 341 (2018), pp. 467--484]; we show here why this is a difficult task and, as a result, we modify the discretization in [Rodrigo et al.] through the use of a reduced-quadrature approximation, yielding a more “solver-friendly” discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess--Sarazin relaxation. Further, numerical results are presented to validate the local Fourier analysis predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework

A theoretical framework which unifies the conventional Mori--Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori--Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reduced-order dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that, similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori--Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz `96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori--Zwanzig analysis. The nontrivial generalized fluctuation-dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. Here we present numerical evidence that the generalized Langevin equation, a key construct in the Mori--Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU⁡(2⁢N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2025

Efficient analysis of small-angle scattering curves for large biomolecular assemblies using Monte Carlo methods

Structure elucidation from small-angle scattering curves of large biomolecular assemblies is notoriously challenging. This is because the simulation of high-resolution features in the structure of large macromolecular assemblies, such as de novo protein assemblies, is computationally demanding when it needs to cover a broad range of length scales. Conventional methods, such as the numerical approximation to the Debye equation or the use of spherical harmonics, do not scale well as the size of the assembly increases, which limits their application to small structures (e.g. individual proteins). This work explores the effectiveness of a Monte Carlo method to simulate and fit scattering curves for large biomolecular assemblies spanning over ranges covering atomic and molecular detail (e.g. spacing and orientation of proteins in an assembly) as well as large-scale (hundreds of nanometres) features. Owing to its speed and scalability, it can be combined with a fitting algorithm to extract structural features from experimental small-angle scattering curves in biomolecular assemblies that are otherwise intractable for interpretation. This work first demonstrates the effectiveness of the tool using experimental small-angle X-ray scattering (SAXS) data from tile-like proteins that assemble into 1D tube-like macromolecular structures. Here, the diameter distribution of tubes is extracted from SAXS fits, and this is quantitatively compared with distributions from electron microscopy. SAXS data are also obtained from 2D sheet-like protein assemblies, and the proposed method is used to quantify structural features such as the separation distance between protein building blocks and the flexing of the sheet. An open-source implementation of the methodology is provided for use in a broad range of biological systems involving multi-scale scattering analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗