Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “mathematical physics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Preparing Underrepresented Minorities for STEM Careers in Energy

The purpose of the grant was to increase the participation of underrepresented minorities and women in STEM disciplines that are critical for the energy industry. The grant was implemented by the Fort Valley State University’s (FVSU) Cooperative Developmental Energy Program (CDEP). FVSU-CDEP enrolled two cohorts of six academically talented freshmen students into its accelerated five-year 3+2 dual degree STEM program. In the 3+2 dual degree format, students enroll at FVSU for three years and earn bachelor’s degrees in biology, chemistry, or mathematics and transfer to a partnering university for two years to earn second bachelor’s degrees in engineering, geology/geophysics, or health physics. FVSU-CDEP partnering universities consist of Georgia Tech, Grand Valley State University, Penn State University, University of Alabama, University of Arkansas, University of Nevada-Las Vegas, and the University of Texas-Austin. Cohort I enrolled at FVSU fall semester of 2017 and cohort II enrolled fall semester of 2020. All six of the students in cohort I earned bachelor’s STEM degrees at FVSU and transferred to a partnering university. Five of the six who transferred to a partnering university earned the second bachelor’s degree. One student transferred from a partnering university to a non-partner university to continue pursuit of the second degree. All students in cohort I had internships, attended professional meetings, and made presentations. Cohort II enrolled the fall-semester of 2020 in the midst of COVID epidemic. Cohort II was only funded for one year, 2020/2021. The DOE Office of Economic Impact and Diversity informed the PI that there would not be any funding for the fifth and final year (2021/2022) of the project. All six of the students in cohort II earned bachelor’s STEM degrees from FVSU and transferred to one of CDEP’s partnering universities. One of the students in cohort II graduate with an MS degree spring of 2023. Currently, four are pursuing graduate degrees at partnering universities and one withdrew from a partnering school because health reasons. Students in cohort II opportunities to participate in internship were negatively impact by the COVID epidemic (2020-2022). Of the 12 scholarship participants, 8 were females. Fifty percent of the males pursued second degrees in Engineering while only twenty-five percent of the females chose Engineering as their second degree.

42 ENGINEERING↗
DOE OSTI2020

DPM: A deep learning PDE augmentation method with application to large-eddy simulation

A framework is introduced that leverages known physics to reduce overfitting in machine learning for scientific applications. The partial differential equation (PDE) that expresses the physics is augmented with a neural network that uses available data to learn a description of the corresponding unknown or unrepresented physics. Training within this combined system corrects for missing, unknown, or erroneously represented physics, including discretization errors associated with the PDE's numerical solution. For optimization of the network within the PDE, an adjoint PDE is solved to provide high-dimensional gradients, and a stochastic adjoint method (SAM) further accelerates training. Additionally, the approach is demonstrated for large-eddy simulation (LES) of turbulence. High-fidelity direct numerical simulations (DNS) of decaying isotropic turbulence provide the training data used to learn sub-filter-scale closures for the filtered Navier–Stokes equations. Out-of-sample comparisons show that the deep learning PDE method outperforms widely-used models, even for filter sizes so large that they become qualitatively incorrect. It also significantly outperforms the same neural network when a priori trained based on simple data mismatch, not accounting for the full PDE. Measures of discretization errors, which are well-known to be consequential in LES, point to the importance of the unified training formulation's design, which without modification corrects for them. For comparable accuracy, simulation runtime is significantly reduced. A relaxation of the typical discrete enforcement of the divergence-free constraint in the solver is also successful, instead allowing the DPM to approximately enforce incompressibility physics. Since the training loss function is not restricted to correspond directly to the closure to be learned, training can incorporate diverse data, including experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Observing leptogenesis in action with gravitational waves

Leptogenesis is arguably the best motivated theory of baryogenesis given the discovery of finite neutrino masses, yet its experimental test is elusive given its high energy scale. We discuss gravitational waves (GWs) produced via graviton bremsstrahlung in right-handed neutrino decays during leptogenesis. The presence of right-handed neutrinos in the early universe can lead to a period of early matter domination. In this context, the resultant GW spectrum scales quadratically with the right-handed neutrino mass, while its peak frequency scales inversely with the Yukawa coupling. Detecting such a spectrum would provide strong evidence for leptogenesis and the existence of heavy right-handed neutrinos. We also discuss how the GW spectrum emitted from the thermal plasma is altered by an era of early matter domination. We show that it can mimic the effects of additional relativistic degrees of freedom and a higher reheating temperature, and that information from the graviton bremsstrahlung GW spectrum can break this degeneracy.

baryon asymmetry↗
DOE OSTI2021

Request for Information: Access to Quantum Systems

Quantum science and technology is a focal point of research at Lawrence Livermore National Laboratory (LLNL). Quantum-coherent devices offer the potential for unprecedented precision in sensing and the ability to directly simulate complex quantum phenomena that have no known efficient classical algorithms. Thus, development and implementation of quantum technologies is expected to have a significant impact on our ability to address some of the most complex national security problems. LLNL maintains projects involving a broad spectrum of Quantum Information Science (QIS) research activities including investigating sources of decoherence, the 3DQ microscope, studies into quantum interconnects, 3-D printed ion traps, fusion energy and nuclear physics simulations, modeling for data-starved environments, and quantum sensing, including accelerometry and timing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies (0.15 < z < 0.65) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle θ, of the galaxy density contrast δ g and the weak lensing convergence κ, in the vicinity of these identified troughs and peaks, referred to as ‘void’ and ‘cluster’ superstructures. The ratio of the profiles depend mildly on θ, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta )$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta )$ using a suite of N-body (‘Gower Street’) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit Planck cosmology. Similar values with ∼0.1σ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 3 × 2-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

cosmology: observations↗
DOE OSTI2024

Feasibility of Formulating Ecosystem Biogeochemical Models From Established Physical Rules

Abstract To improve the predictive capability of ecosystem biogeochemical models (EBMs), we discuss the feasibility of formulating biogeochemical processes using physical rules that have underpinned the many successes in computational physics and chemistry. We argue that the currently popular empirically based approaches, such as multiplicative empirical response functions and the law of the minimum, will not lead to EBM formulations that can be continuously refined to incorporate improved mechanistic understanding and empirical observations of biogeochemical processes. Instead, we propose that EBM parameterizations, as a lossy data compression problem, can be better formulated using established physical rules widely used in computational physics and chemistry, and different biogeochemical processes can be more robustly integrated within a reactive‐transport framework. Through several examples, we demonstrate how mathematical representations derived from physical rules can improve understanding of relevant biogeochemical processes and enable more effective communication between modelers, observationalists, and experimentalists regarding essential questions, such as what measurements are needed to meaningfully inform models and how can models generate new process‐level hypotheses to test in empirical studies. Finally, while empirical models with more parameters are often less robust, physical rules‐based models can be more robust and show lower predictive equifinality, stemming from their enhanced consistency in representations of processes, interactions and spatial scaling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Direct neutrino-mass measurement based on 259 days of KATRIN data

That neutrinos carry a nonvanishing rest mass is evidence of physics beyond the Standard Model of elementary particles. Their absolute mass holds relevance in fields from particle physics to cosmology. We report on the search for the effective electron antineutrino mass with the KATRIN experiment. KATRIN performs precision spectroscopy of the tritium β-decay close to the kinematic endpoint. On the basis of the first five measurement campaigns, we derived a best-fit value of $m^{2}_{v} = -0.14^{+0.13}_{-0.15}$ eV 2 , resulting in an upper limit of m ν < 0.45 eV at 90% confidence level. Stemming from 36 million electrons collected in 259 measurement days, a substantial reduction of the background level, and improved systematic uncertainties, this result tightens KATRIN’s previous bound by a factor of almost two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A convergent genus expansion for the plateau

We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To understand the origin of this series, we compare to the semiclassical theory of “encounters” in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.

2D Gravity↗
DOE OSTI2020

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. Additionally, the performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity

Production of hydrocarbons and water from subsurface reservoirs are known to cause permanent deformation of the reservoir and seismicity along faults both of which are detrimental to sustainable development of natural resources. Most of the prior studies on understanding fluid flow-induced plasticity and seismicity have focused on one or the other phenomenon due to the numerical difficulty associated with simultaneous modeling of the two failure phenomena because stress and deformation evolve non-linearly in both plasticity and seismicity. However, in reservoirs undergoing long-term production, plastic failure can alter the stress paths of points on a fault such that the onset, location, and magnitude of actual seismic events can no longer be predicted by a poroelastic simulation due to inaccurate stress and deformation history. We present a computational framework for coupled multiphase flow, finite strain poroplastic deformation, and dynamic fault slip and use it to understand the impact of plastic deformation on the onset, location, and magnitude of induced fault slip events. We evaluate the impact of plasticity on reservoir pressure, deformation, induced stress, and fault slip by comparing infinitesimal strain elastic and finite strain poro-elastoplastic models. For real-world applications, we consider different scenarios where the reservoir is either mechanically weaker or stronger than the caprock. We analyze the stress evolution as a function of the change in reservoir pressure to understand the role of contrast in reservoir and caprock elastic moduli on geomechanical stability. The results show that the poroplastic reservoir exhibits larger vertical deformation and delayed slip than the poroelastic reservoir after the same amount of oil production. For the same amount of pressure drop, a reservoir with a smaller modulus than the caprock displays a larger vertical displacement and an earlier onset of both plastic failure and fault slip. For a reservoir with a larger modulus than the caprock, vertical displacement is larger on the reservoir top boundary and smaller on the ground surface, and a higher pressure drop is needed to induce plastic failure and fault slip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Development and assessment of a reactor system prognosis model with physics-guided machine learning

Autonomous control systems provide recommendations to help operators in decision-making during plant operations ranging from normal operation to accident management. An important step of autonomous control is prognosis. In nuclear engineering domain, prognosis is the process of predicting future conditions of a system or equipment based on present signs and symptoms of a fault. The prognosis model allows predicting future reactor states for possible candidate control strategies so that the outcomes can be evaluated to determine the best control strategy. The prognosis model requires representing direct relationships between the symptoms and the predictions. In nuclear engineering, computational simulations are approximate representations of the operation of the real system. However, prognosis with computational simulations requires high computation power and time due to possible large number of scenarios. Necessary computation resources can be reduced with machine learning (ML) approach for fast predictions by building a surrogate function using the simulation data. A critical issue is, ML models are ignorant of physical knowledge, and these models approximate statistical relationships between the system variables. This ignorance can produce results that are inconsistent with physical laws, even if an optimal result is achieved from a mathematical point of view. Physics-guided machine learning (PGML) is an approach to tackle this issue. Here, this work formulates and illustrates a framework to guide development and assessment of the ML-based prognosis model for autonomous control systems. The development of the prognosis model considers the training of a ML model which consists of optimizing many aspects of the ML approach. The assessment of the prognosis model considers training data limitations and uncertainties of the ML approach. Prognosis models with standalone ML and PGML are developed and assessed on the loss-of-flow scenario of Experimental Breeder Reactor II. The results indicate that PGML based prognosis model has the best performance compared to other prognosis models.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Solving the Grad–Shafranov equation using spectral elements for tokamak equilibrium with toroidal rotation

The Grad–Shafranov equation is solved using spectral elements for tokamak equilibrium with toroidal rotation. The Grad–Shafranov solver builds upon and extends the NIMEQ code (Howell and Sovinec, 2014) previously developed for static tokamak equilibria. Both geometric and algebraic convergence are achieved as the polynomial degree of the spectral-element basis increases. A new analytical solution to the Grad–Shafranov equation is obtained for Solov’ev equilibrium in presence of rigid toroidal rotation, in addition to a previously obtained analytical solution for a different set of equilibrium and rotation profiles. The numerical solutions from the extended NIMEQ are benchmarked with the analytical solutions, with good agreements. Besides, the extended NIMEQ code is benchmarked with the FLOW code (Guazzotto et al., 2004). The modification of pressure profile induced by toroidal flow is investigated. The relative change of pressure profile is found significant around the edge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗