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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Kalai-Smorodinsky solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the R package GPGame available on CRAN at https://cran.r-project.org/package=GPGame.

Game theory↗
DOE OSTI2022

m-CUBES An efficient and portable implementation of multi-dimensional integration for gpus

The task of multi-dimensional numerical integration is frequently encountered in physics and other scientific fields, e.g., in modeling the effects of systematic uncertainties in physical systems and in Bayesian parameter estimation. Multi-dimensional integration is often time-prohibitive on CPUs. Efficient implementation on many-core architectures is challenging as the workload across the integration space cannot be predicted a priori. We propose m-Cubes, a novel implementation of the well-known Vegas algorithm for execution on GPUs. Vegas transforms integration variables followed by calculation of a Monte Carlo integral estimate using adaptive partitioning of the resulting space. m-Cubes improves performance on GPUs by maintaining relatively uniform workload across the processors. As a result, our optimized Cuda implementation for Nvidia GPUs outperforms parallelization approaches proposed in past literature. We further demonstrate the efficiency of m-Cubes by evaluating a six-dimensional integral from a cosmology application, achieving significant speedup and greater precision than the CUBA library's CPU implementation of VEGAS. We also evaluate m-Cubes on a standard integrand test suite. m-Cubes outperforms the serial implementations of the Cuba and GSL libraries by orders of magnitude speedup while maintaining comparable accuracy. Our approach yields a speedup of at least 10 when compared against publicly available Monte Carlo based GPU implementations. In summary, m-Cubes can solve integrals that are prohibitively expensive using standard libraries and custom implementations. A modern C++ interface header-only implementation makes m-Cubes portable, allowing its utilization in complicated pipelines with easy to define stateful integrals. Compatibility with non-Nvidia GPUs is achieved with our initial implementation of m-Cubes using the Kokkos framework.

Sakiotis, Ioannis↗
DOE OSTI2022

Controls Optimization Final Report, Controls Algorithms Report, Control Optimization - SPA II: Heaving Buoy Test Results [Three reports]

The over-arching project objective is to fully develop and validate optimal controls frameworks that can subsequently be applied widely to different WEC devices and concepts. Optimal controls of WEC devices represent a fundamental building block for WEC designers that must be considered as an integral part of every stage of device development. Using a building-blocks approach to optimal controls development, this effort will result in the full development of a feed-forward and feed-back control approach and a wave prediction system. Phase I focused primarily on numerical offline optimization and validation using wave tank testing of three industry partners’ WEC devices, including; CalWave, Ocean Energy, and Resolute Marine Energy. These industry partnerships allowed us to identify optimal control strategies for these different WEC topologies at different maturity levels. Phase II focused on demonstrating an integrated control system on an at-sea prototype that is to be custom-built and maturing the HW and SW required to successfully run our advanced controls code frameworks on at-sea systems. A secondary focus during phase II is to adapt our systems identification, controls and wave-prediction frameworks to become more robust and comprehensive in respect to RT capability, robustness, and reliability.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
DOE OSTI2020

Extreme Compression for Large Scale Data Store

For the last 5 years Accelogic pioneered and perfected a radically new theory of numerical computing codenamed “Compressive Computing”, which has an extremely profound impact on real-world computer science [1]. At the core of this new theory is the discovery of one of its fundamental theorems which states that, under very general conditions, the vast majority (typically between 70% and 80%) of the bits used in modern large-scale numerical computations are absolutely irrelevant for the accuracy of the end result. This theory of Compressive Computing provides mechanisms able to identify (with high intelligence and surgical accuracy) the number of bits (i.e., the precision) that can be used to represent numbers without affecting the substance of the end results, as they are computed and vary in real time. The bottom line outcome would be to provide a state-of-the-art compression algorithm that surpasses those currently available in the ROOT framework, with the purpose of enabling substantial economic and operational gains (including speedup) for High Energy and Nuclear Physics data storage/analysis. In our initial studies, a factor of nearly x4 (3.9) compression was achieved with RHIC/STAR data where ROOT compression managed only x1.4.In this contribution, we will present our concepts of “functionally lossless compression”, have a glance at examples and achievements in other communities, present the results and outcome of our current, ongoing R&D, as well as present a high-level view of our plan to move forward with a ROOT implementation that would deliver a basic solution readily integrated into HENP applications. As a collaboration of experimental scientists, private industry, and the ROOT Team, our aim is to capitalize on the substantial success delivered by the initial effort and produce a robust technology properly packaged as an open-source tool that could be used by virtually every experiment around the world as means for improving data management and accessibility.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Progress toward Accelogic compression in ROOT

For the last 7 years, Accelogic pioneered and perfected a radically new theory of numerical computing codenamed “Compressive Computing”, which has an extremely profound impact on real-world computer science [1]. At the core of this new theory is the discovery of one of its fundamental theorems which states that, under very general conditions, the vast majority (typically between 70% and 80%) of the bits used in modern large-scale numerical computations are absolutely irrelevant for the accuracy of the end result. This theory of Compressive Computing provides mechanisms able to identify (with high intelligence and surgical accuracy) the number of bits (i.e., the precision) that can be used to represent numbers without affecting the substance of the end results, as they are computed and vary in real time. The bottom-line outcome will be to provide state-of-the-art compression algorithms --and accompanying software libraries-- able to surpass the performance of the compression engines currently available in the ROOT [7] framework. The resulting technology has the capability to enable substantial economic and operational gains (including speedup) for High Energy and Nuclear Physics data storage/analysis. In our initial studies, a factor of nearly x4 (3.9) compression was achieved with RHIC/STAR data where ROOT compression managed only x1.4 [6].As a collaboration of experimental scientists, private industry, and the ROOT Team, our aim is to capitalize on the substantial success delivered by the initial effort and produce a robust technology properly packaged as an open-source tool that could be used by virtually every experiment around the world as means for improving data management and accessibility.In this contribution, we will present our efforts integrating our concepts of “functionally lossless compression” within the ROOT framework implementation, with the purpose of producing a basic solution readily integrated into HENP applications. We will also present our progress applying this compression through realistic examples of analysis from both the STAR and CMS experiments.

Canal, Ph.↗
DOE OSTI2022

Quantum advantage for noisy channel discrimination

Many quantum mechanical experiments can be viewed as multiround interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum “coherent” access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single-qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between the performance of fully coherent and fully incoherent protocols as a function of noise strength. Moreover, the size of the region of coherent quantum advantage shrinks inverse polynomially in the number of channel uses, and in an intermediate regime an improved strategy is a hybrid of fully coherent and fully incoherent subroutines. The fully coherent protocol is based on quantum signal processing, suggesting a generalizable algorithmic framework for the study of quantum advantage in the presence of realistic noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bayesian Optimization Framework for Imperfect Data or Models

Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Progress with the 5D full-F continuum gyrokinetic code COGENT

COGENT is an Eulerian gyrokinetic code being developed for edge plasma modelling. The code is distinguished by the use of a high-order finite-volume (conservative) discretization combined with mapped multi-block grid technology. Our recent work is focused on the development of a 5D full-F COGENT version.Anumerical algorithm utilizing locally a field-aligned multi-block coordinate system is implemented to facilitate simulations of highly anisotropic microturbulence in the presence of a strong magnetic shear. In this approach, the toroidal direction is divided into blocks such that,within each block, the cells are field-aligned and a non-matching (non-conformal) grid interface is allowed at the block boundaries. In this paper we report on details of the numerical implementation and present preliminary results of verification studies performed for the case of the ion temperature gradient (ITG) instability in a sheared toroidal annulus geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals

We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work (Daubechies et al., Pure Appl. Math. 57(11), 1413–1457, 2004), where the single vector signal can be infinite-dimensional, and (Fornasier and Rauhut, SIAM J. Numer. Anal. 46(2), 577613, 2008), which extends the aforementioned work to the joint sparse recovery of finite number of infinite-dimensional vectors. In our case, to take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty ℓ 2,1 . This paper discusses the computation of the solutions of linear inverse problems with such relaxation by a forward-backward splitting algorithm. However, since the solution matrix possesses infinitely many columns, the arguments of Daubechies et al. (Pure Appl. Math. 57(11), 1413–1457, 2004) no longer apply. As such, we establish new strong convergence results for the algorithm, in particular when the set of jointly sparse vectors is infinite.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Novel usage of deep learning and high-performance computing in long-baseline neutrino oscillation experiments

Mención Internacional en el título de doctorDeep-learning methods are playing a crucial role in numerous scientific and industrialapplications. Over the past two decades, these techniques have helped in the collection,reconstruction, and analysis of large data samples in particle physics experiments. Themain topic of this PhD research is the study of deep-learning techniques in long-baselineneutrino oscillation experiments. Neutrinos are mysterious light elementary particles,and their investigation is essential to shed light on some of the remaining open questionsin physics. The work presented here describes an algorithm based on a convolutionalneural network developed to provide highly accurate and efficient selections of electronneutrino and muon neutrino interactions in the Deep Underground Neutrino Experiment(DUNE). With this algorithm, the electron neutrino (antineutrino) selection efficiencypeaks at 90% (94%) and exceeds 85% (90%) for reconstructed neutrino energies between2-5 GeV. The selection efficiency for muon neutrino (antineutrino) interactions is foundto have a maximum of 96% (97%) and exceeds 90% (95%) efficiency for reconstructedneutrino energies above 2 GeV. When considering all electron neutrino and antineutrinointeractions as signal (both those appearing from oscillations and those intrinsic tothe beam), a selection purity of 90% is achieved. These event selections are criticalto maximise the sensitivity of the experiment to CP-violating effects, key to furtherunderstand the matter-antimatter asymmetry of the Universe.In high-energy physics experiments, deep learning has also been explored for producingfast simulations and physically-motivated manipulations of simulated images. Some ofthose simulations, such as the light production and detection, are very computationallyexpensive and require novel methods to produce the necessary samples while controllingthe varied underlying physics model parameters. To do so, we invented the model-assistedgenerative adversarial network (MAGAN), first validated on simple generic case studiesand then successfully applied to the DUNE photon-detector simulation.Moreover, we also developed graph neural networks for 3D-voxel classification ofambiguities and optical crosstalk for a different particle physics experiment, most preciselyfor the proposed SuperFGD. This novel 3D-granular plastic-scintillator neutrino detectorwill be used to upgrade the near detector of the T2K neutrino oscillation experiment, and our method reports efficiencies and purities of 94-96% per event in the classificationof particle track voxels.Due to the growth and complexity of deep neural networks, researchers have beeninvestigating techniques to train those networks in a more computationally-efficient way.Many efforts have been made by the community to optimise deep-learning models byparallelising or distributing their training computation across multiple devices. In thisthesis, we study an approach based on data locality for those neural networks that cannotbenefit from scaling their computation due to a significant bottleneck in the data I/O.The research also includes a detailed study on the performance of deep neural networkson hardware accelerator boards.Los métodos de aprendizaje profundo son cada vez más utilizados en numerosas aplicacionescientíficas e industriales hoy en día. Durante las dos últimas décadas, estastécnicas se han empleado en la recolección, reconstrucción y análisis de la gran cantidadde datos generados por experimentos de física de partículas. El tema principal de estatesis doctoral es el uso de estos modelos de aprendizaje profundo en experimentos defísica de neutrinos, en concreto en los experimentos de larga distancia DUNE y T2K. Losneutrinos, partículas fundamentales neutras, de las más ligeras del Universo, pueden serclave para explicar algunas de las cuestiones todavía sin resolver en física fundamental.Entre las diferentes contribuciones que esta tesis ha hecho a su estudio, cabe destacar eldesarrollo de un algoritmo basado en una red de neuronas convolucional para seleccionarcon gran eficiencia y precisión las interacciones de neutrinos electrónicos y muónicos enel Deep Underground Neutrino Experiment (DUNE). La eficiencia de selección obtenidapara neutrinos (antineutrinos) electrónicos alcanza un máximo del 90% (94%) y supera el85% (90%) para neutrinos con energías reconstruidas en el rango 2-5 GeV. La selección deneutrinos (antineutrinos) muónicos tiene una eficiencia máxima del 96% (97%) y excedeel 90% (95%) para neutrinos con energías reconstruidas de más de 2 GeV. Considerandocomo señal todas las interacciones de neutrinos y antineutrinos electrónicos (procedentestanto de oscilaciones como intrínsecos en el haz inicial), se logra una pureza en la seleccióndel 90%. Dichas selecciones de eventos son fundamentales para maximizar la sensibilidaddel experimento a los efectos de violació...

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Online Learning and Pricing for Network Revenue Management with Reusable Resources

We consider a price-based network revenue management problem with multiple products and multiple reusable resources. Each randomly arriving customer requests a product (service) that needs to occupy a sequence of reusable resources (servers). We adopt an incomplete information setting where the firm does not know the price-demand function for each product and the goal is to dynamically set prices of all products to maximize the total expected revenue of serving customers. We propose novel batched bandit learning algorithms for finding near-optimal pricing policies, and show that they admit a near-optimal cumulative regret bound of $O(J\sqrt{XT})$, where J, X, and T, are the numbers of products, candidate prices, and service periods, respectively. As part of our regret analysis, we develop the first finite-time mixing time analysis of an open network queueing system (i.e., the celebrated Jackson Network), which could be of independent interest. Our numerical studies show that the proposed approaches perform consistently well.

42 ENGINEERING↗
DOE OSTI2021

Probabilistic Day-Ahead Forecasting Using an Analog Ensemble Approach for Wind Farm Grid Services

Wind resource assessment and wind power forecasting are used in research and industry to anticipate future power output at scales ranging from individual wind turbines to entire wind farms. Probabilistic day-ahead wind forecasting is useful for anticipating how a wind farm could potentially participate in the day-ahead market by providing upper and lower bounds for expected power generation, thus informing grid operators of its uncertainty. Understanding this uncertainty is part of a larger project focused on building a platform that combines efforts in weather forecasting, aerodynamic and economic modeling to create maximum value of a wind plant to better provide services to the grid. This effort is also known as the Atmosphere to Electrons to Grid (A2E2G) project. One method for producing a probabilistic forecast is through the analog ensemble approach (Delle Monache et al., 2011). This method leverages historical forecasts and their corresponding observations as a training data set from which future forecasts can be made. For some future forecast, the most similar historical forecasts (analogs) are identified on a regular time basis such as once per a 3-hour window. The most similar analogs, based on a metric such as root mean square error (RMSE), are recorded and their corresponding verifying observations are used as an ensemble member for this future forecast. Prior work in this area demonstrates improvements over raw Numerical Weather Prediction (NWP) forecasts and shows skill similar to techniques such as logistic regression and machine learning (Delle Monache et al., 2013; Alessandrini et al., 2015). Here, we take the High-Resolution Rapid Refresh model (HRRR) day-ahead forecast (0-36 hours) to create a probabilistic day-ahead forecast using an analog ensemble approach. The HRRR has an hourly temporal resolution, with a spatial resolution of 3 km. The 12 UTC HRRR model run is downloaded every day for one year from August 2019 - July 2020, with the first 11 months serving as a bank of analogs from which the forecasting algorithm can create a probabilistic forecast. Once downloaded, the original HRRR forecast is temporally interpolated to 5-minutes, aligning with both the temporal resolution of the observations as well as the timescale relevant for day-ahead power forecasts. The forecast is validated at the M2 tower at the Flatirons Campus of the National Renewable Energy Laboratory (NREL) at a typical wind turbine height of 80 m. Variables such as wind speed, wind direction, and turbulence intensity are incorporated into the probabilistic forecast model and weighted according to their relative importance to the forecast. Based on metrics such as mean bias error (MBE), mean absolute error (MAE), and root mean square error, the analog ensemble forecast outperforms the raw HRRR forecast during the testing period of July 2020. Figure 1 illustrates an example day-ahead forecast compared against the verifying observations. The general variability and ramps are captured throughout the day, with potential to further improve the analog ensemble model through machine learning techniques.

numerical weather prediction↗
DOE OSTI2022

Learning high-dimensional parametric maps via reduced basis adaptive residual networks

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error estimates. A scalable neural network learning framework is thus to learn the nonlinear compressed reduced basis mapping. Unlike the reduced basis construction, however, neural network constructions are not guaranteed to reduce errors by adding representation power, making it difficult to achieve good practical performance. Inspired by recent approximation theory that connects ResNets to sequential minimizing flows, we present an adaptive ResNet construction algorithm. This algorithm allows for depth-wise enrichment of the neural network approximation, in a manner that can achieve good practical performance by first training a shallow network and then adapting. We prove universal approximation of the associated neural network class for $L^2_v$ functions on compact sets. Our overall framework allows for constructive means to detect appropriate breadth and depth, and related compact parametrizations of neural networks, significantly reducing the need for architectural hyperparameter tuning. Numerical experiments for parametric PDE problems and a 3D CFD wing design optimization parametric map demonstrate that the proposed methodology can achieve remarkably high accuracy for limited training data, and outperformed other neural network strategies we compared against.

42 ENGINEERING↗
DOE OSTI2020

Spatiotemporal parallelization of an analytical heat conduction model for additive manufacturing via a hybrid OpenMP + MPI approach

The ability to do thermal simulations for entire additive manufacturing builds is a key computational problem facing the additive manufacturing community; however, complex numerical models considering multiple physical phenomena currently do not have the capacity for simulations at this scale. To this end, conduction only analytic models offer a viable approach due to the massive drop in computational expense. In this work, we extend an existing implementation which uses a governing equation which can be evaluated at any point in space and time. This implementation already utilizes OpenMP with a spatial decompositions scheme stemming from a melt pool tracking algorithm. Furthermore, we then combine this with a parallel in time (PinT) approach to make the problem highly parallelizable. The new scheme, which uses MPI for internode communication and OpenMP for intranode communication, is shown to scale very well across multiple computational nodes. This approach results in the ability to simulate the 3D solidification conditions for entire layers of additively manufactured parts in minutes making part scale thermal simulations more practical.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods

Abstract The phase-field method is a powerful and versatile computational approach for modeling the evolution of microstructures and associated properties for a wide variety of physical, chemical, and biological systems. However, existing high-fidelity phase-field models are inherently computationally expensive, requiring high-performance computing resources and sophisticated numerical integration schemes to achieve a useful degree of accuracy. In this paper, we present a computationally inexpensive, accurate, data-driven surrogate model that directly learns the microstructural evolution of targeted systems by combining phase-field and history-dependent machine-learning techniques. We integrate a statistically representative, low-dimensional description of the microstructure, obtained directly from phase-field simulations, with either a time-series multivariate adaptive regression splines autoregressive algorithm or a long short-term memory neural network. The neural-network-trained surrogate model shows the best performance and accurately predicts the nonlinear microstructure evolution of a two-phase mixture during spinodal decomposition in seconds, without the need for “on-the-fly” solutions of the phase-field equations of motion. We also show that the predictions from our machine-learned surrogate model can be fed directly as an input into a classical high-fidelity phase-field model in order to accelerate the high-fidelity phase-field simulations by leaping in time. Such machine-learned phase-field framework opens a promising path forward to use accelerated phase-field simulations for discovering, understanding, and predicting processing–microstructure–performance relationships.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems

In this work we develop EPOCH (equilibrium propagator by orthogonal polynomial chain), a computationally efficient method to calculate the time-dependent equilibrium Green's functions, including the anomalous Green's functions of superconductors, to capture the time evolution in large inhomogeneous systems. The EPOCH method generalizes the Chebyshev wave-packet propagation method from quantum chemistry and efficiently incorporates the Fermi-Dirac statistics that is needed for equilibrium quantum condensed matter systems. The computational cost of EPOCH scales only linearly in the system degrees of freedom, generating an extremely efficient algorithm also for very large systems. We demonstrate the power of the EPOCH method by calculating the time evolution of an excitation near a superconductor–normal metal interface in two and three dimensions, capturing transmission as well as normal and Andreev reflections.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗