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Results for “Monte Carlo ensemble methods”

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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Continuous integration data-driven platform of industrial-scale subsurface storage for real-time analytics

This project helped address the growing need for efficient and scalable models to support geological carbon and energy storage, which are crucial for achieving net-zero emissions. Traditionally accurate high-fidelity numerical models have been used to simulate relevant storage processes under a handful of processes, however such models are computationally demanding, making uncertainty quantification impractical. Consequently, we first developed a machine learning framework, based on Graph Neural Operators (GNOs), to improving the accuracy of model predictions for a fixed computational budget. We then developed an Ensemble of Improved Neural Operators (ENO), which uses bagging and Monte Carlo dropout techniques, to further improve prediction accuracy. Lastly, we developed the way to explain progressive transfer learning methods to reduce the amount of training data and computational cost of training (i.e., reduce trainable parameters) when using our models for multiple storage sites. Our numerical investigation, which used real-world case studies, demonstrated that our framework can significantly improve the safety and efficiency of geological storage operations, with potential applications in other domains such as geothermal reservoirs and climate modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Reducing the complexity of finite-temperature auxiliary-field quantum Monte Carlo

The auxiliary-field quantum Monte Carlo (AFMC) method is a powerful and widely used technique for ground-state and finite-temperature simulations of quantum many-body systems. Here we introduce several algorithmic improvements for finite-temperature AFMC calculations of dilute fermionic systems that reduce the computational complexity of most parts of the algorithm. This is principally achieved by reducing the number of single-particle states that contribute at each configuration of the auxiliary fields to a number that is of the order of the number of fermions. Our methods are applicable for both the canonical and grand-canonical ensembles. We demonstrate the reduced computational complexity of the methods for the homogeneous unitary Fermi gas.

67.85.Lm↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO 2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. Here we applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO 2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

58 GEOSCIENCES↗
DOE OSTI2020

Ab Initio Nuclear Thermodynamics

Here, we propose a new Monte Carlo method called the pinhole trace algorithm for ab initio calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first ab initio study of the density and temperature dependence of nuclear clustering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Bridging confined phase behavior of CH 4 -CO 2 binary systems across scales

Phase behavior of confined fluids may deviate significantly from that of the bulk fluid due to the fluid-wall interactions being a significant portion of all intermolecular interactions under confinement. Despite recent advancements in understanding confined phase behavior of pure fluids, confined phase behavior of mixtures remains an understudied topic. In this work, we examine the confined phase behavior of a CH 4 -CO 2 binary system by combining Monte Carlo (MC) simulations, a cubic equation of state (EoS), and the lattice Boltzmann method (LBM). First, the effects of confinement on density and phase distribution in nano-size pores are established using Gibbs Ensemble MC calculations, which produce precise results of liquid and vapor confined pressures and account for the modification of the phase change location. By comparing the phase envelopes of bulk and confined mixtures at a fixed temperature, here it is observed that the phase envelopes shrink with reductions in pore size. Based on this observation, we extend a modified Peng-Robinson EoS, which was originally developed for pure fluids under confinement, to mixtures via van-der-Waals-type mixing rules and by accounting for shifts in the critical properties of confined CH 4 -CO 2 . The resulting phase envelopes are in good agreement with the MC data. In addition, a local density model is used in combination with the confined EoS to calculate adsorption isotherms of CH 4 -CO 2 mixtures and to characterize the behavior of confined matter in nanopores. Finally, we incorporate this EoS in a multicomponent multiphase LBM that uses a pseudopotential model to represent intermolecular forces. This workflow utilizes multiscale simulation techniques to bridge the behavior of multicomponent systems across scales and to shed light on the confined phase behavior of CH 4 -CO 2 binary systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Reweighting Monte Carlo predictions and automated fragmentation variations in Pythia 8

This work reports on a method for uncertainty estimation in simulated collider-event predictions. The method is based on a Monte Carlo-veto algorithm, and extends previous work on uncertainty estimates in parton showers by including uncertainty estimates for the Lund string-fragmentation model. This method is advantageous from the perspective of simulation costs: a single ensemble of generated events can be reinterpreted as though it was obtained using a different set of input parameters, where each event now is accompanied with a corresponding weight. This allows for a robust exploration of the uncertainties arising from the choice of input model parameters, without the need to rerun full simulation pipelines for each input parameter choice. Such explorations are important when determining the sensitivities of precision physics measurements. Accompanying code is available at https://gitlab.com/uchep/mlhad-weights-validation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗
DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Stochastic equilibrium Raman spectroscopy (STERS)

In this manuscript, we propose a new method for cavity- and surface-enhanced Raman spectroscopy (SERS) with improved temporal resolution in the measurement of stochastic Raman spectral fluctuations. Our approach combines Fourier spectroscopy and photon correlation to decouple the integration time from the temporal resolution. Using statistical optics Monte Carlo simulations, we establish the relationship between time resolution and Raman signal strength, revealing that typical Raman spectral fluctuations, commensurate with molecular conformational dynamics, can theoretically be resolved on micro- to millisecond timescales. The method can further extract average single-molecule dynamics from small sub-ensembles, thereby potentially mitigating challenges in achieving strictly single-molecule isolation on SERS substrates.

Cobb-Bruno, Colburn [University of California, Ber↗
DOE OSTI2022

Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

In this work, we propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there is an associated average energy. The sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates of the circuit itself. Observables calculated under the canonical ensemble from these samples of circuits are extrapolated from higher energies to the ground state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Ensemble Monte Carlo calculations with five novel moves

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007), walk moves by Goodman and Weare (2010) and quadratic moves by Militzer (2023). Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Abstract Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Automated calculation and convergence of defect transport tensors

Defect diffusion is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant end-user intervention. These two bottlenecks prevent high-throughput implementations essential to propagate model-form uncertainty from interatomic interactions to predictive simulations. In order to address these issues, we extend a massively parallel accelerated sampling scheme, autonomously controlled by Bayesian estimators of statewide sampling completeness, to build atomistic kinetic Monte Carlo models on a state-space irreducible under exchange and space group symmetries. Focusing on isolated defects, we derive analytic expressions for drift and diffusion coefficients, providing a convergence metric by calculating the Kullback–Leibler divergence across the ensemble of diffusion processes consistent with the sampling uncertainty. The autonomy and efficacy of the method is demonstrated on surface trimers in tungsten and Hexa-interstitials in magnesium oxide, both of which exhibit complex, correlated migration mechanisms.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Visual HPC Workflows for the Analysis of System Dynamics Models

Visual analytics supported by high performance computing (HPC) accelerates and enhances the discovery, exploration, and analysis of causal patterns in complex system dynamics (SD) models. We present a suite of visualization-assisted ensemble-based techniques for hypothesis generation and testing, and for sensitivity analysis. By employing HPC to provide parallel, on-demand simulation of SD models, one can “steer” an ensemble of simulated scenarios in real time as one first formulates and then informally tests those hypotheses: this provides rapid feedback for analysts to refine their understanding of the causal relationships emergent from a model. Such understandings can be followed and augmented by rigorous application of statistical methods, namely global variance-based sensitivity analysis, Monte-Carlo filtering, adaptive regional sensitivity analysis, and self-organized maps: here timely computation relies on HPC, while effective presentation emphasizes high-dimensional multivariate data visualization. Immersive visualization in virtual 3D environments provides an excellent adjunct to the traditional 2D graphics typically used for SD models, as it generates an embodied understanding of model behavior and facilitates an active, collaborative critique of model structure and output. Finally, we summarize prospects for HPC-enabled visual analytics applied to SD modeling.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.

54 ENVIRONMENTAL SCIENCES↗