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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Residual Monte Carlo high-order solver for Moment-Based Accelerated Thermal Radiative Transfer equations

In this article we explore the possibility of replacing Standard Monte Carlo (SMC) transport sweeps within a Moment-Based Accelerated Thermal Radiative Transfer (TRT) algorithm with a Residual Monte Carlo (RMC) formulation. Previous Moment-Based Accelerated TRT implementations have encountered trouble when stochastic noise from SMC transport sweeps accumulates over several iterations and pollutes the low-order system. With RMC we hope to significantly lower the build-up of statistical error at a much lower cost. First, we display encouraging results for a zero-dimensional test problem. Then, we demonstrate that we can achieve a lower degree of error in two one-dimensional test problems by employing an RMC transport sweep with multiple orders of magnitude fewer particles per sweep. We find that by reformulating the high-order problem, we can compute more accurate solutions at a fraction of the cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Variance-based sensitivity indices for stochastic models with correlated inputs

The goal of this article is the formulation of the principles of one of the possible strategies in implementing correlation between input random variables so as to be usable for algorithm development and the evaluation of Sobol’s sensitivity analysis. With regard to the types of stochastic computational models, which are commonly found in structural mechanics, an algorithm was designed for effective use in conjunction with Monte Carlo methods. Sensitivity indices are evaluated for all possible permutations of the decorrelation procedures for input parameters. The evaluation of Sobol’s sensitivity coefficients is illustrated on an example in which a computational model was used for the analysis of the resistance of a steel bar in tension with statistically dependent input geometric characteristics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Fast cooling for a system of stochastic oscillators

We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired steady state corresponding to reduced thermal noise. Among the feedback controls achieving the desired asymptotic transfer, we find that the most efficient one from an energy point of view is characterized by time-reversibility. We also extend the theory of Schrödinger bridges to this model, thereby steering the system in finite time and with minimum effort to a target steady-state distribution. The system can then be maintained in this state through the optimal steady-state feedback control. The solution, in the finite-horizon case, involves a space-time harmonic function φ, and −logφ plays the role of an artificial, time-varying potential in which the desired evolution occurs. This framework appears extremely general and flexible and can be viewed as a considerable generalization of existing active control strategies such as macromolecular cooling. In the case of a quadratic potential, the results assume a form particularly attractive from the algorithmic viewpoint as the optimal control can be computed via deterministic matricial differential equations. An example involving inertial particles illustrates both transient and steady state optimal feedback control.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Efficient gradient estimation using finite differencing and likelihood ratios for kinetic Monte Carlo simulations

While many optimization and control methods for stochastic processes require gradient information from the process of interest, obtaining gradient information from experiments is prohibitively expensive and time-consuming. As a result, such information is often obtained from stochastic process simulations. Computing gradients efficiently and accurately from stochastic simulations is challenging, especially for simulations involving computationally expensive models with significant inherent noise. In this work, we analyze and characterize the applicability of two gradient estimation methods for kinetic Monte Carlo simulations: finite differencing and likelihood ratio. We developed a systematic method for choosing an optimal perturbation size for finite differencing and discuss, for both methods, important implementation issues such as scaling with respect to the number of elements in the gradient vector. Through a series of numerical experiments, the methods were compared across different time and size regimes to characterize the precision and accuracy associated with each method. We determined that the likelihood ratio method is appropriate for estimating gradients at short (transient) times or for systems with small population sizes, whereas finite differencing is better-suited for gradient estimation at long times (steady state) or for systems with large population sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion

Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Monitored Fluctuating Hydrodynamics

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

classical statistical mechanics↗
DOE OSTI2015

Hybrid discrete/continuum algorithms for stochastic reaction networks

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker–Planck equation. The Fokker–Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by switching to explicit stabilized stochastic methods and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of MLMC methods, the computational cost for stiff systems is significantly reduced, while keeping the computational algorithm fully explicit and easy to implement. Numerical experiments on linear and nonlinear stochastic differential equations and on a stochastic partial differential equation illustrate the performance of the stabilized MLMC method and corroborate our theoretical findings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A multilevel stochastic collocation method for SPDEs

We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model

The multiscale FENE model is applied to a 3D square-square contraction flow problem. For this purpose, the stochastic Brownian configuration field method (BCF) has been coupled with our fully parallelized three-dimensional Navier-Stokes solver NaSt3DGPF. The robustness of the BCF method enables the numerical simulation of high Deborah number flows for which most macroscopic methods suffer from stability issues. The results of our simulations are compared with that of experimental measurements from literature and show a very good agreement. In particular, flow phenomena such as a strong vortex enhancement, streamline divergence and a flow inversion for highly elastic flows are reproduced. Due to their computational complexity, our simulations require massively parallel computations. Using a domain decomposition approach with MPI, the implementation achieves excellent scale-up results for up to 128 processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

2–stage stochastic Runge–Kutta for stochastic delay differential equations

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale

The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. Here, we present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.

Nguyen, Thien↗
DOE OSTI2020

Non-Hermitian approach for quantum plasmonics

Herein, we examine the limits of applicability of a simple non-Hermitian model for exciton/plasmon interactions in the presence of dissipation and dephasing. The model can be used as an alternative to the more complete Lindblad density matrix approach and is computationally and conceptually simpler. We find that optical spectra in the linear regime can be adequately described by this approach. The model can fail, however, under continuous optical driving in some circumstances. In the case of two quantum dots or excitons interacting with a plasmon, the model can also describe coherences and entanglement qualitatively when both dissipation and dephasing are present and quantitatively in the limit with no dephasing. The approach, within a single excitation manifold, is also applied to assess the role of disorder for 50 quantum dots interacting with a plasmon, where we find that, on average, large enough disorder can help stabilize the ensemble average of the open quantum system toward a dark quasi-steady-state much faster than without disorder. Furthermore, while such single excitation manifold calculations in this size limit can readily be done with either the non-Hermitian or Lindblad forms, as one goes to larger Hilbert space sizes, the computational and storage advantages of the non-Hermitian approach can become more useful. Published under license by AIP Publishing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Theory of magnetic field line random walk in noisy reduced magnetohydrodynamic turbulence

When a magnetic field consists of a mean part and fluctuations, the stochastic wandering of its field lines is often treated as a diffusive process. Under suitable conditions, a stable value is found for the mean square transverse displacement per unit parallel displacement relative to the mean field. Here, we compute the associated field line diffusion coefficient for a highly anisotropic 'noisy' reduced magnetohydrodynamic model of the magnetic field, which is useful in describing low frequency turbulence in the presence of a strong applied DC mean magnetic field, as may be found, for example, in the solar corona, or in certain laboratory devices. Our approach is nonperturbative, based on Corrsin's independence hypothesis, and makes use of recent advances in understanding factors that control decorrelation over a range of parameters described by the Kubo number. Both Bohm and quasilinear regimes are identified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Comparing (stochastic-selection) ab initio multiple spawning with trajectory surface hopping for the photodynamics of cyclopropanone, fulvene, and dithiane

Ab Initio Multiple Spawning (AIMS) simulates the excited-state dynamics of molecular systems by representing nuclear wavepackets in a basis of coupled traveling Gaussian functions, called trajectory basis functions (TBFs). New TBFs are spawned when nuclear wavepackets enter regions of strong nonadiabaticity, permitting the description of non-Born–Oppenheimer processes. The spawning algorithm is simultaneously the blessing and the curse of the AIMS method: it allows for an accurate description of the transfer of nuclear amplitude between different electronic states, but it also dramatically increases the computational cost of the AIMS dynamics as all TBFs are coupled. Recently, a strategy coined stochastic-selection AIMS (SSAIMS) was devised to limit the ever-growing number of TBFs and tested on simple molecules. In this work, we use the photodynamics of three different molecules—cyclopropanone, fulvene, and 1,2-dithiane—to investigate (i) the potential of SSAIMS to reproduce reference AIMS results for challenging nonadiabatic dynamics, (ii) the compromise achieved by SSAIMS in obtaining accurate results while using the smallest average number of TBFs as possible, and (iii) the performance of SSAIMS in comparison to the mixed quantum/classical method trajectory surface hopping (TSH)—both in terms of its accuracy and computational cost. We show that SSAIMS can accurately reproduce the AIMS results for the three molecules considered at a much cheaper computational cost, often close to that of TSH. We deduce from these tests that an overlap-based criterion for the stochastic-selection process leads to the best agreement with the reference AIMS dynamics for the smallest average number of TBFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗