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DOE OSTI2022

Surrogate Modeling of Nonlinear Dynamic Systems: A Comparative Study

Surrogate models play a vital role in overcoming the computational challenge in designing and analyzing nonlinear dynamic systems, especially in the presence of uncertainty. This paper presents a comparative study of different surrogate modeling techniques for nonlinear dynamic systems. Four surrogate modeling methods, namely, Gaussian process (GP) regression, a long short-term memory (LSTM) network, a convolutional neural network (CNN) with LSTM (CNN-LSTM), and a CNN with bidirectional LSTM (CNN-BLSTM), are studied and compared. All these model types can predict the future behavior of dynamic systems over long periods based on training data from relatively short periods. The multi-dimensional inputs of surrogate models are organized in a nonlinear autoregressive exogenous model (NARX) scheme to enable recursive prediction over long periods, where current predictions replace inputs from the previous time window. Three numerical examples, including one mathematical example and two nonlinear engineering analysis models, are used to compare the performance of the four surrogate modeling techniques. The results show that the GP-NARX surrogate model tends to have more stable performance than the other three deep learning (DL)-based methods for the three particular examples studied. The tuning effort of GP-NARX is also much lower than its deep learning-based counterparts.

42 ENGINEERING↗

DOE OSTI2024

Uncertainty-Aware, Structure-Preserving Machine Learning Approach for Domain Shift Detection From Nonlinear Dynamic Responses of Structural Systems

Complex structural systems deployed for aerospace, civil, or mechanical applications must operate reliably under varying operational conditions. Structural health monitoring (SHM) systems help ensure the reliability of these systems by providing continuous monitoring of the state of the structure. SHM relies on synthesizing measured data with a predictive model to make informed decisions about structural states. However, these models—which may be thought of as a form of a digital twin—need to be updated continuously as structural changes (e.g., due to damage) arise. We propose an uncertainty-aware machine learning model that enforces distance preservation of the original input state space and then encodes a distance-aware mechanism via a Gaussian process (GP) kernel. The proposed approach leverages the spectral-normalized neural GP algorithm to combine the flexibility of neural networks with the advantages of GP, subjected to structure-preserving constraints, to produce an uncertainty-aware model. This model is used to detect domain shift due to structural changes that cannot be observed directly because they may be spatially isolated (e.g., inside a joint or localized damage). This work leverages detection theory to detect domain shift systematically given statistical features of the prediction variance produced by the model. The proposed approach is demonstrated on a nonlinear structure being subjected to damage conditions. In conclusion, it is shown that the proposed approach is able to rely on distances of the transformed input state space to predict increased variance in shifted domains while being robust to normative changes.

Algorithms↗

DOE OSTI2019

Global Sensitivity Analysis for Statistical Model Parameters

Global sensitivity analysis (GSA) is typically used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable reduced or parsimonious modeling and greater predictive capability. Yet, difficulties such as parameter correlation, model stochasticity, multivariate model output, and unknown parameter distributions prohibit a direct application of GSA tools to statistical models. By leveraging a loss function associated with the statistical model, we introduce a novel framework to address these difficulties and enable efficient GSA for statistical model parameters. Theoretical and computational properties are considered and hihglighted on a synthetic example. The framework is applied to a Gaussian process model from the literature, which depends on 95 parameters. Noninfluential parameters are discovered through GSA, and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Landmark-Warped Emulators for Models with Misaligned Functional Response

Many computer models output functional data, and in some cases, these functional data have similar, but misaligned, shape characteristics. In this paper, we introduce a general approach for building emulators for computer models that output misaligned functional data when key values in the functional response (landmarks) can be easily identified. This approach has two main parts: modeling the aligned (using the landmarks) functional data, and modeling the functions that map the misaligned data to the aligned space (warping functions). As the warping functions are required to be monotonic, we give special attention to modeling monotonic functional response data. We discuss how our approach can be easily applied for a variety of typical emulators, such as Gaussian processes, Bayesian multivariate adaptive regression splines, and Bayesian additive regression trees, and how sensitivity analysis can be performed. We demonstrate our approach by building emulators for two applications: (1) a high-energy-density physics computer model used to simulate inertial confinement fusion ignition experiments, where model outputs are highly misaligned, and (2) a multiphysics continuum hydrocode used to simulate high-velocity impact experiments, where model outputs are only slightly misaligned. In case (1) traditional methods cannot be applied, while in (2) they can be applied, but the proposed method performs significantly better.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Discovering the Unknowns: A First Step

This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden changes in the data. We use Gaussian process modeling and a sparse representation of the sudden changes to efficiently estimate the large number of parameters in the proposed statistical model. The method is tested on a realistic dataset generated using a one-dimensional implementation of a Magnetized Liner Inertial Fusion (MagLIF) simulation model, and encouraging results are obtained.

42 ENGINEERING↗

DOE OSTI2020

Comparison of unfolding methods using RooFitUnfold

In this study we describe RooFitUnfold, an extension of the RooFit statistical software package to treat unfolding problems, and which includes most of the unfolding methods that commonly used in particle physics. The package provides a common interface to these algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. In this paper we exploit this common interface of RooFitUnfold to compare the performance of unfolding with the Richardson–Lucy, Iterative Dynamically Stabilized, Tikhonov, Gaussian Process, bin-by-bin and inversion methods on several example problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

WebGIobe - A cloud-based geospatial analysis framework for interacting with climate data

While climate models have evolved over time to produce high fidelity and high resolution climate forecasts, visualization and analysis of the output of the model simulations has been limited, typically constrained to single dimensional charts for visualization and basic aggregate statistics for analytics. Same is true for the large troves of observational data available from meteorological stations all over the world. For richer understanding of climate and the impact of climate change, one needs computational tools that allow researchers, policymakers, and general public, to interact with the climate data. In this paper, we describe, webGlobe, a browser based GIS framework for interacting with climate data, and other datasets available in similar format. webGlobe is a unique resource that allows unprecedented access to climate data through a browser. The framework also allows for deploying machine learning based analytical applications on the climate data without putting computational burden on the client. Instead, webGlobe uses a client-server framework, where the server, deployed on a cloud infrastructure, allows for dynamic allocation of resources for running compute-intensive applications. The capabilities of the framework will be discussed in context of a use case: identifying extreme events from real and simulated climate data using a Gaussian process based change detection algorithm.

Sharma, Arun↗

DOE OSTI2019

Adaptive Learning for Concept Drift in Application Performance Modeling

Supervised learning is a promising approach for modeling the performance of applications running on large HPC systems. A key assumption in supervised learning is that the training and testing data are obtained under the same conditions. However, in production HPC systems these conditions might not hold because the conditions of the platform can change over time as a result of hardware degradation, hardware replacement, software upgrade, and configuration updates. These changes could alter the data distribution in a way that affects the accuracy of the predictive performance models and render them less useful; this phenomenon is referred to as concept drift. Ignoring concept drift can lead to suboptimal resource usage and decreased efficiency when those performance models are deployed for tuning and job scheduling in production systems. To address this issue, we propose a concept-drift-aware predictive modeling approach that comprises two components: (1) an online Bayesian changepoint detection method that can automatically identify the location of events that lead to concept drift in near-real time and (2) a moment-matching transformation inspired by transfer learning that converts the training data collected before the drift to be useful for retraining. We use application input/output performance data collected on Cori, a production supercomputing system at the National Energy Research Scientific Computing Center, to demonstrate the effectiveness of our approach. The results show that concept-drift-aware models obtain significant improvement in accuracy; the median absolute error of the best-performing Gaussian process regression improved by 58.8% when the proposed approaches were used.

adaptive learning↗

DOE OSTI2017

CosmicEmu, Version 2.0

The CosmicEmu implements a Gaussian process emulation scheme to predict the dark matter and dark matter + neutrino power spectra over a range of physical parameters that describe the composition and evolution of the Universe. The procedure can produce thousands of spectra per second, much faster than the complex n-body simulations used to produce the training set, which can take weeks per simulation. The training simulations, their design, and the general scheme is described in Lawrence et al. (2010), Heitmann et al. (2014), Heitmann et al. (2016), and an upcoming paper.

Lawrence, Earl↗

DOE OSTI2018

Emulator Generation Gadget

This software automates the production of standalone emulators for complex computer models. The end result of running the software is a piece of code called an emulator, a statistical approximation which predicts the output of complex computer simulation, but at a much faster speed. The emulator is built using a training set of inputs and outputs from the simulations. The input-output pairs are used in a Bayesian scheme to estimate the parameters of a Gaussian process based regression model that learns the input-output relationship. The estimated parameters are combined with a generic C skeleton to produce a compile-able instantiation of the emulator.

Sweeney, Christine↗

DOE OSTI2019

Quantile Kriging R Package

A re-implementation of Quantile Kriging. Quantile Kriging was described by Matthew Plumlee & Rui Tuo in their 2014 paper "Building Accurate Emulators for Stochastic Simulations via Quantile Kriging." With computational savings when dealing with replication from the recent paper "Practical heteroskedastic Gaussian process modeling for large simulation experiments”, it is now possible to apply Quantile Kriging to a wider class of problems. In addition to fitting the model, other useful tools are provided such as the ability to automatically perform leave-one-out cross validation.

Quinlan, KevinR.↗

DOE OSTI2021

gpCAM v6

gpCAM is tailored to be used by experimentalists who want to steer experiments autonomously. It is based on a Gaussian process (GP). Its strength compared to other software lies in its flexibility, which together with the right training, makes it more powerful than any GP-based software. However, that means, that the software in as-is mode cannot reach its full potential.

Noack, Marcus↗

DOE OSTI2021

fvGP v2.2.0

fvGP is a flexible Gaussian process API that enables gpCAM, a software recently submitted, to do uncertainty quantification and steer data acquisition autonomously. In short, given a bunch of data, fvGP can find the most likely model creating the data and the model's uncertainty.

Noack, Marcus↗

DOE OSTI2021

gp_blendclass_singleband

The code used for the data preprocessing, image simulation, and model training and analysis reported in the paper "Gaussian Process Classification for Galaxy Blend Identification in LSST" (arXiv:2107.09246).

Buchanan, JamesJ.↗

DOE OSTI2021

ZTF_image_classification

This repo demonstrates how to use the LLNL developed Gaussian process hyperparameter estimation method, MuyGPS, for image classification using Zwicky Transient Facility (ZTF) data.

Pruett, Kerianne↗

DOE OSTI2022

Code for paper "Reconstructing an Implosion with Space-Time Smoothing of Velocimetry Traces"

New diagnostics to obtain high-temporal resolution observation of surface velocity provide a rich collection of data from high-explosive (HE) experiments. Using this data to estimate the temporal evolution of an imploding, HE-driven surface is of great interest for validating simulation of the physical system and for design of future experiments. This is the code for a paper in which we propose a method for using a Gaussian process to estimate the surface position over time and provide uncertainty estimates on that reconstruction accounting for measurement error, uncertainty to sparse spatial sampling velocity data, and robustness to outlying observations. In the paper, the code is applied on data from a hemispherical HE implosion experiment. This code is for release with the paper for peer-review, replicating the results and making the figures from the paper.

Grosskopf, Michael↗

DOE OSTI2023

gpde

The R package gpde is an R implementation of a probabilistic differential equation solver. The package has a basic implementation of the Chkrebtii (2013) probabilistic ODE solver and an extension using the connection between Kalman Filtering for SDEs and Gaussian Processes from work by Simo Sarkka. The package also implements the Integrated Wiener covariance function from Schober 2014 to obtain probabilistic ODE solutions with the Runge-Kutta solution as the mean result. This collection of tools has been built into an R package for easy use at LANL and in the probabilistic numerics community.

Grosskopf, Michael↗