Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical approximations”

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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin- 1/2 1 / 2 J_1-J_2 J 1 − J 2 Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Measurement and feedback-driven adaptive dynamics in the classical and quantum kicked top

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

Prasad, Mahaveer [Tata Inst.; Singapore U. Tech. D↗
DOE OSTI2024

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

58 GEOSCIENCES↗
DOE OSTI2023

Customizable adaptive regularization techniques for B-spline modeling

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. Further, the proposed method selectively incorporates regularization terms based on first and second derivatives to maintain model accuracy while minimizing numerical artifacts. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations. In addition, a key tuning parameter is highlighted and the effects of this parameter are presented in detail. This paper is an extension of our previous conference paper at the 2022 International Conference on Computational Science (ICCS) (Lenz et al., 2022).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Systematic quark/gluon identification with ratios of likelihoods

Discriminating between quark- and gluon-initiated jets has long been a central focus of jet substructure, leading to the introduction of numerous observables and calculations to high perturbative accuracy. At the same time, there have been many attempts to fully exploit the jet radiation pattern using tools from statistics and machine learning. We propose a new approach that combines a deep analytic understanding of jet substructure with the optimality promised by machine learning and statistics. After specifying an approximation to the full emission phase space, we show how to construct the optimal observable for a given classification task. This procedure is demonstrated for the case of quark and gluons jets, where we show how to systematically capture sub-eikonal corrections in the splitting functions, and prove that linear combinations of weighted multiplicity is the optimal observable. In addition to providing a new and powerful framework for systematically improving jet substructure observables, we demonstrate the performance of several quark versus gluon jet tagging observables in parton-level Monte Carlo simulations, and find that they perform at or near the level of a deep neural network classifier. Combined with the rapid recent progress in the development of higher order parton showers, we believe that our approach provides a basis for systematically exploiting subleading effects in jet substructure analyses at the Large Hadron Collider (LHC) and beyond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Multiscale formulation of frictional contact mechanics at the pore scale

Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

42 ENGINEERING↗
DOE OSTI2022

Stringent σ8 constraints from small-scale galaxy clustering using a hybrid MCMC + emulator framework

ABSTRACT We present a novel simulation-based hybrid emulator approach that maximally derives cosmological and Halo Occupation Distribution (HOD) information from non-linear galaxy clustering, with sufficient precision for DESI Year 1 (Y1) analysis. Our hybrid approach first samples the HOD space on a fixed cosmological simulation grid to constrain the high-likelihood region of cosmology + HOD parameter space, and then constructs the emulator within this constrained region. This approach significantly reduces the parameter volume emulated over, thus achieving much smaller emulator errors with fixed number of training points. We demonstrate that this combined with state-of-the-art simulations result in tight emulator errors comparable to expected DESI Y1 LRG sample variance. We leverage the new abacussummit simulations and apply our hybrid approach to CMASS non-linear galaxy clustering data. We infer constraints on σ8 = 0.762 ± 0.024 and fσ8(zeff = 0.52) = 0.444 ± 0.016, the tightest among contemporary galaxy clustering studies. We also demonstrate that our fσ8 constraint is robust against secondary biases and other HOD model choices, a critical first step towards showcasing the robust cosmology information accessible in non-linear scales. We speculate that the additional statistical power of DESI Y1 should tighten the growth rate constraints by at least another 50–60 ${{\ \rm per\ cent}}$, significantly elucidating any potential tension with Planck. We also address the ‘lensing is low’ tension, which we find to be in the same direction as a potential tension in fσ8. We show that the combined effect of a lower fσ8 and environment-based bias accounts for approximately $50{{\ \rm per\ cent}}$ of the discrepancy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Mixing bispectrum multipoles under geometric distortions

We derive general expressions for how the Alcock–Paczynski distortions affect the power spectrum and the bispectrum of cosmological fields. We compute explicit formulas for the mixing coefficients of bispectrum multipoles in the linear approximation. The leading-order effect for the bispectrum is the uniform dilation of all three wavevectors. The mixing coefficients depend on the shape of the bispectrum triplet. Our results for the bispectrum multipoles are framed in terms of the ‘natural’ basis of the lengths of three wavevectors but can be easily generalized for other bases and reduction schemes. Our validation tests confirm that the linear approximation is extremely accurate for all power spectrum multipoles. The linear approximation is accurate for the bispectrum monopole but results in sub-per cent level inaccuracies for the bispectrum quadrupole and fails for the bispectrum hexadecapole. Our results can be used to simplify the analysis of the bispectrum from galaxy surveys, especially the measurement of the baryon acoustic oscillation peak position. They can be used to replace numeric schemes with exact analytical formulae.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Tree hydrodynamic modelling of the soil–plant–atmosphere continuum using FETCH3

Modelling the water transport along the soil–plant–atmosphere continuum is fundamental to estimating and predicting transpiration fluxes. A Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH3) for the water fluxes across the soil–plant–atmosphere continuum is presented here. The model combines the water transport pathways into one vertical dimension, and assumes that the water flow through the soil, roots, and above-ground xylem can be approximated as flow in porous media. This results in a system of three partial differential equations, resembling the Richardson–Richards equation, describing the transport of water through the plant system and with additional terms representing sinks and sources for the transfer of water from the soil to the roots and from the leaves to the atmosphere. The numerical scheme, developed in Python 3, was tested against exact analytical solutions for steady state and transient conditions using simplified but realistic model parameterizations. The model was also used to simulate a previously published case study, where observed transpiration rates were available, to evaluate model performance. With the same model setup as the published case study, FETCH3 results were in agreement with observations. Through a rigorous coupling of soil, root xylem, and stem xylem, FETCH3 can account for variable water capacitance, while conserving mass and the continuity of the water potential between these three layers. FETCH3 provides a ready-to-use open access numerical model for the simulation of water fluxes across the soil–plant–atmosphere continuum.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Metaplectic geometrical optics for ray-based modeling of caustics: Theory and algorithms

The optimization of radio frequency-wave (RF) systems for fusion experiments is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at caustics such as cutoffs and focal points, erroneously predicting the wave intensity to be infinite. This is a critical shortcoming of GO, since the caustic wave intensity is often the quantity of interest, e.g., RF heating. Full-wave modeling can be used instead, but the computational cost limits the speed at which such optimizations can be performed. Here, we have developed a less expensive alternative called metaplectic geometrical optics (MGO). Instead of evolving waves in the usual x (coordinate) or k (spectral) representation, MGO uses a mixed X$\equiv$Ax+Bk representation. By continuously adjusting the matrix coefficients A and B along the rays, one can ensure that GO remains valid in the X coordinates without caustic singularities. The caustic-free result is then mapped back onto the original x space using metaplectic transforms. Here, we overview the MGO theory and review algorithms that will aid the development of an MGO-based ray-tracing code. We show how using orthosymplectic transformations leads to considerable simplifications compared to previously published MGO formulas. We also prove explicitly that MGO exactly reproduces standard GO when evaluated far from caustics (an important property that until now has only been inferred from numerical simulations), and we relate MGO to other semiclassical caustic-removal schemes published in the literature. Finally this discussion is then augmented by an explicit comparison of the computed spectrum for a wave bounded between two cutoffs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Data-scarce surrogate modeling of shock-induced pore collapse process

Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. Here, in this work, we study the use of a data-driven reduced-order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 s on CPU. In contrast, training a generative adversarial network model takes 8 h on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3 to 5% in the interpolatory cases and 8 to 9% in extrapolatory cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Exact time-dependent density-functional theory for nonperturbative dynamics of the helium atom

By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist for real three-dimensional systems. We demonstrate that the Kohn-Sham and true current-densities differ by a rotational component. The results have direct implications for approximate TDDFT calculations of atoms and molecules in strong fields, emphasizing the need to go beyond the adiabatic approximation, and highlighting caution in quantitative use of the Kohn-Sham current.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Learning Forecasts of Rare Stratospheric Transitions from Short Simulations

Abstract Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, sudden stratospheric warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These optimal forecasts concretely measure the event’s progress. Direct numerical simulation can estimate them in principle but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are short compared to the time scale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in time scales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

Finkel, Justin↗
DOE OSTI2022

Koopman Model Predictive Control for Eco-Driving of Automated Vehicles

In this paper, we develop a data-driven process for building a model predictive control (MPC) for eco-driving of automated vehicles. The process involves performing system identification in which the non-linear vehicle dynamics model is approximated by the Koopman operator, a linear predictor of higher state-dimension, in a data-driven framework. This approach allows us to formulate the eco-driving problem in a constrained quadratic program that leads to a computationally fast MPC. The MPC is then implemented as a closed-loop control of an electric vehicle in numerical simulations for demonstration.

autonomous vehicle↗
DOE OSTI2021

thornado-hydro: A Discontinuous Galerkin Method for Supernova Hydrodynamics with Nuclear Equations of State

This paper describes algorithms for non-relativistic hydrodynamics in the toolkit for high-order neutrino radiation hydrodynamics (thornado), which is being developed for multiphysics simulations of core-collapse supernovae (CCSNe) and related problems with Runge–Kutta discontinuous Galerkin (RKDG) methods. More specifically, thornado employs a spectral type nodal collocation approximation, and we have extended limiters — a slope limiter to prevent non-physical oscillations and a bound-enforcing limiter to prevent non-physical states — from the standard RKDG framework to be able to accommodate a tabulated nuclear equation of state (EoS). To demonstrate the efficacy of the algorithms with a nuclear EoS, we first present numerical results from basic test problems in idealized settings in one and two spatial dimensions, employing Cartesian, spherical-polar, and cylindrical coordinates. Then, we apply the RKDG method to the problem of adiabatic collapse, shock formation, and shock propagation in spherical symmetry, initiated with a 15 M ⊙ progenitor. Herein, we find that the extended limiters improve the fidelity and robustness of the RKDG method in idealized settings. The bound-enforcing limiter improves robustness of the RKDG method in the adiabatic collapse application, while we find that slope limiting in characteristic fields is vulnerable to structures in the EoS — more specifically, in the phase transition from nuclei and nucleons to bulk nuclear matter. The success of these applications marks an important step toward applying RKDG methods to more realistic CCSN simulations with thornado in the future.

Nuclear astrophysics (1129)↗
DOE OSTI2020

IGA-MPM: The Isogeometric Material Point Method

In this work, we propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous representation of the strain rate, and, as a result, prevents jumps in the stress and other history variables as the material points cross the element boundaries. Furthermore, NURBS can exactly represent all conic sections and the corresponding symmetries in the solution, which may be important in some applications. Several numerical examples of increasing complexity are presented, and show the ability of IGA-MPM to eliminate the well known cell-crossing instability of the conventional MPM. In addition, the examples presented demonstrate improved accuracy, convergence, and symmetry preservation of IGA-MPM compared to the conventional MPM, both for rectilinear and curved geometries.

42 ENGINEERING↗