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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A novel implicit hybrid machine learning model and its application for reinforcement learning

A novel methodology to develop implicit hybrid models is presented. PyTorch is used to integrate physics-based equations with machine learning models. Automatic differentiation of the hybrid model is leveraged to solve the implicit equations. Iterative solving enables gradient based updates to the machine learning model. The novel methodology is compared to an explicit hybrid approach on a continuously stirred tank reactor (CSTR). The novel method results in a lower modelling error. Both hybrid models effectively train with noisy data. To test the implicit hybrid model, it is employed as a reinforcement learning (RL) training model. The RL algorithm trained on the hybrid model outperforms real time optimization of the CSTR and performs nearly as well as RL trained directly on the CSTR and a traditional gradient based approach. Training RL directly on the CSTR requires over 60,000 system interactions compared to 6000 historical data points for hybrid model development.

42 ENGINEERING↗
DOE OSTI2024

Numerical methods for fractional Fokker–Planck equation with multiplicative Marcus Lévy noises

The Fokker–Planck equation (FPE) is an important deterministic tool for investigating stochastic dynamical systems. In this paper, we consider the space-time fractional FPE driven by multiplicative Marcus Lévy noises. Efficient numerical schemes are presented to solve the equations. Stability and convergence of the methods are also discussed. We give some numerical experiments to validate our schemes, and examine the effects of parameters on solutions. Additionally, we analyze the maximal likely trajectories and the critical time for the change of the most probability location.

Mathematics↗
DOE OSTI2021

Coupling Finite Element and Finite Volume Simulation Within MOOSE

This work focuses on adding capability to couple finite element (FE) variables into finite volume (FV) physics within INL’s Multiphysics Object-Oriented Simulation Environment (MOOSE). This coupling can allow for improvement of multiphysics simulations where one set of physics is best suited for an FE discretization, while another set is best suited for an FV discretization. Electrohydrodynamics, which govern liquid metal reactor concepts and plasma dynamics, is a fitting example where the electromagnetic field equations are solved with FE and the fluid flow is solved with FV. The new FE to FV coupling method can be summarized as taking the element or face average of the FE variable value or gradient and applying that quantity directly in the FV equation objects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Numerically modeling stochastic inflation in slow-roll and beyond

In this work, we present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes. We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations. The stochastic differential equations are solved event by event on a discrete time grid. We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations. Our numerical procedure helps us to easily extend the formalism to ultra slow-roll inflation and study the possibility of primordial black hole formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Implicit and coupled fluid plasma solver with adaptive Cartesian mesh and its applications to non-equilibrium gas discharges

In this work, we present a new fluid plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (nonlinear, implicit) scheme for non-equilibrium gas discharge plasma. The electrons and ions are described using drift-diffusion approximation coupled to Poisson equation for the electric field. The electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperature and could also depend on electron density (important for plasma stratification). The ion and gas temperature are kept constant. The transport equations are discretized using a non-isothermal Scharfetter-Gummel scheme to resolve possible large temperature gradients in the sheaths. We demonstrate the new solver for simulations of direct current (DC) and radiofrequency (RF) discharges. The implicit treatment of the coupled equations allows using large time steps. The full-Newton method (FNM) enables fast nonlinear convergence at each time step, offering significantly improved simulation efficiency. We discuss the selection of time steps for solving different plasma problems. The new solver enables solving several problems we could not solve before with existing software: two- and three-dimensional structures of the entire DC discharges including cathode and anode regions, electric field reversals and double-layer formation, the normal cathode spot and an anode ring, moving striations in diffuse and constricted DC discharges, and standing striations in RF discharges. The developed FNM-ACM technique offers many benefits for tackling the disparity of gas discharge plasma systems' time scales and nonlinearity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Helicity evolution at small x : quark to gluon and gluon to quark transition operators

We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1,2,3]. While such transitions do not affect the large-N c version of the evolution equations for helicity, the large-N c & N f equations are affected. (N c and N f are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-N c & N f equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of α s ln 2 (1/x) with αs the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4,5,6,7]. Similar to the large-Nc helicity evolution in the shock-wave approach [8], our large-N c & N f small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A numerical extension of the spatially-filtered Euler equations for contact discontinuities

Solving the spatially-filtered Euler equations with a kinetic energy-preserving centered discretization is an efficient framework for simulating shock-dominated flows. Here, the present work describes a numerical treatment of the spatially-filtered Euler equations to minimize oscillations when simulating contact discontinuities. To counteract dispersive errors inherent to centered schemes, a WENO-like correction term is applied to the enthalpy transport in the energy equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation

Here, we present a method for solving the linearized Vlasov-Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Divergence of Velocity Fields in Electrochemical Systems

The passage of current through electrochemical systems results in the development of concentration gradients in the electrolytic phase that can be modeled using concentrated solution theory. Application of this theory requires knowledge of three concentration-dependent transport coefficients, which are often taken to be conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity. The governing diffusion equation for molar concentration contains two additional terms - the thermodynamic factor which is related to activity of the electrolytic species and the solvent velocity. The main advance in this paper is the derivation of an expression for the divergence of the solvent velocity. Solving this equation requires knowledge of the partial molar volume of the electrolyte. Analogous expressions are derived for the mass average and molar average velocities. These velocities occur naturally in the diffusion equation if concentration is expressed as weight fraction and mole fraction of the electrolytic species, respectively.

diffusion↗
DOE OSTI2024

Improved Precision Scaling for Simulating Coupled Quantum-Classical Dynamics

In this paper, we present a superpolynomial improvement in the precision scaling of quantum simulations for coupled quantum-classical systems. Such systems are found in, e.g., molecular-dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman–von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a superpolynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density. Published by the American Physical Society 2024

Simon, Sophia (ORCID:0000000332612338)↗
DOE OSTI2021

Integrability and Symmetries of Classical Geometries

This research project had two major objectives: advancement in constructing quantum theory of gravity and analytical understanding of strongly--coupled systems. The project contributed to advancing quantum theory of gravity by studying dynamics of black holes. A comprehensive analysis of excitations of rotating black holes in arbitrary dimensions has been performed, all solutions of Maxwell's equations as well as their generalizations to arbitrary p-forms in such backgrounds have been constructed, and a significant progress towards extension of these results to gravitational waves has been made. The project also advanced theoretical understanding of strongly-coupled theories by analyzing properties of exactly-solvable (integrable) models. A new method for solving dynamical equations for various fields in a large class of backgrounds without isometries has been developed, and this technique was used to extract spectra of supergravity modes in several integrable string theories. The analytical structure of large classes of integrable string theories has also been analyzed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

A Lumped Stochastic Model of Coupled Neutronic Assemblies

The objective of the present work is to apply the Harris ansatz to coupled assemblies in a lumped setting, i.e., ignoring the neutron phase dependence, which hitherto has not been considered. A Master equation for the single-time joint distribution of neutron number in each assembly, accounting for transfer of neutrons from one assembly to another via leakage transition probabilities and intercept or view factors is derived from which equations for the mean and variance in each assembly are developed. Because of the neutronic coupling, it is necessary to additionally compute the correlation function between pairs of assemblies which gives an expanded set of moment equations to solve. The reactivity of each assembly is allowed to vary with time, although a formal mechanism that is responsible for reactivity coupling between assemblies is not considered or proposed. Following Harris, it is then hypothesized that the number distribution in each assembly is a gamma distribution with assembly-specific mean and variance computed exactly from the moment equations. Illustrative numerical results are presented for the moments of a system of four coupled assemblies under various reactivity and neutronic coupling scenarios. The gamma distribution is then used to compute the probability that the neutron population exceeds a threshold value in any assembly. The report concludes with a discussion of recommended further work on this problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A hybrid nodal-staggered pseudo-spectral electromagnetic particle-in-cell method with finite-order centering

Electromagnetic particle-in-cell (PIC) codes are widely used to perform computer simulations of a variety of physical systems, including fusion plasmas, astrophysical plasmas, plasma wakefield particle accelerators, and secondary photon sources driven by ultra-intense lasers. In a PIC code, Maxwell's equations are solved on a grid with a numerical method of choice. This article focuses on pseudo-spectral analytical time-domain (PSATD) algorithms and presents a novel hybrid PSATD PIC scheme that combines the respective advantages of standard nodal and staggered methods. The novelty of the hybrid scheme consists in using finite-order centering of grid quantities between nodal and staggered grids, in order to combine the solution of Maxwell's equations on a staggered grid with the deposition of charges and currents and the gathering of electromagnetic forces on a nodal grid. The correctness and performance of the novel hybrid scheme are assessed by means of numerical tests that employ different classes of PSATD equations in a variety of physical scenarios, ranging from the modeling of electron-positron pair creation in vacuum to the simulation of laser-driven and particle beam-driven plasma wakefield acceleration. It is shown that the novel hybrid scheme offers significant numerical and computational advantages, compared to purely nodal or staggered methods, for all the test cases presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

How machine learning can extend electroanalytical measurements beyond analytical interpretation

Electroanalytical measurements are routinely used to estimate material properties exhibiting current and voltage signatures. Analysis of such measurements relies on analytical expressions of material properties to describe the experiments. The need for analytical expressions limits the experiments that can be used to measure properties as well as the properties that can be estimated from a given experiment. Such analytical relations are essentially solutions of the physics-based differential equations (with properties as coefficients) describing the material behavior under certain specific conditions. In recent years, a new machine learning-based approach has been gaining popularity wherein the differential equations are numerically solved to interpret the electroanalytical experiments in terms of corresponding material properties. Since the physics-based differential equations are solved, one can additionally estimate underlying fields, e.g., concentration profile, using such an approach. To exemplify the characteristics of such a machine learning assisted interpretation of electroanalytical measurements, we use data from the Hebb–Wagner test on a magnesium spinel intercalation host. In conclusion, as compared to the traditional analytical expression-based interpretation, the emerging approach decreases experimental efforts to characterize relevant material properties as well as provides field information that was previously inaccessible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

An investigation of Newton-Sketch and subsampled Newton methods

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.

97 MATHEMATICS AND COMPUTING↗