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Perron–Frobenius Operator Filter for Stochastic Dynamical Systems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-03-15 Ningxin Liu, Lijian Jiang
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 182-211, March 2024. Abstract.Filtering problems are derived from a sequential minimization of a quadratic function representing a compromise between the model and data. In this paper, we use the Perron–Frobenius operator in a stochastic process to develop a Perron–Frobenius operator filter. The proposed method belongs to Bayesian
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Stacking Designs: Designing Multifidelity Computer Experiments with Target Predictive Accuracy SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-03-11 Chih-Li Sung, Yi (Irene) Ji, Simon Mak, Wenjia Wang, Tao Tang
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 157-181, March 2024. Abstract. In an era where scientific experiments can be very costly, multifidelity emulators provide a useful tool for cost-efficient predictive scientific computing. For scientific applications, the experimenter is often limited by a tight computational budget, and thus wishes to (i) maximize predictive power
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Adaptive Importance Sampling Based on Fault Tree Analysis for Piecewise Deterministic Markov Process SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-03-07 Guillaume Chennetier, Hassane Chraibi, Anne Dutfoy, Josselin Garnier
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 128-156, March 2024. Abstract. Piecewise deterministic Markov processes (PDMPs) can be used to model complex dynamical industrial systems. The counterpart of this modeling capability is their simulation cost, which makes reliability assessment untractable with standard Monte Carlo methods. A significant variance reduction can
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Multifidelity Bayesian Experimental Design to Quantify Rare-Event Statistics SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-02-29 Xianliang Gong, Yulin Pan
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 101-127, March 2024. Abstract. In this work, we develop a multifidelity Bayesian experimental design framework to efficiently quantify the rare-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. The key idea here is to leverage low-fidelity samples whose responses
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Projective Integral Updates for High-Dimensional Variational Inference SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-02-08 Jed A. Duersch
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 69-100, March 2024. Abstract. Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables
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Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-02-02 Daniel Sanz-Alonso, Nathan Waniorek
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 30-68, March 2024. Abstract. This paper analyzes a popular computational framework for solving infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm
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Error Estimate of a Quasi-Monte Carlo Time-Splitting Pseudospectral Method for Nonlinear Schrödinger Equation with Random Potentials SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2024-01-30 Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao
SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 1-29, March 2024. Abstract. In this paper, we consider the numerical solution of a nonlinear Schrödinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combined with the time-splitting pseudospectral discretization is applied and analyzed. The nonlinearity in the equation induces
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Fully Bayesian Inference for Latent Variable Gaussian Process Models SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-12-11 Suraj Yerramilli, Akshay Iyer, Wei Chen, Daniel W. Apley
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1357-1381, December 2023. Abstract. Real engineering and scientific applications often involve one or more qualitative inputs. Standard Gaussian processes (GPs), however, cannot directly accommodate qualitative inputs. The recently introduced latent variable Gaussian process (LVGP) overcomes this issue by first mapping each qualitative
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Space-time Multilevel Quadrature Methods and their Application for Cardiac Electrophysiology SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-12-05 Seif Ben Bader, Helmut Harbrecht, Rolf Krause, Michael D. Multerer, Alessio Quaglino, Marc Schmidlin
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1329-1356, December 2023. Abstract. We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the transmembrane potential inside the cardiac cells, we evaluate the effect of spatially correlated perturbations of the
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Parameter Selection in Gaussian Process Interpolation: An Empirical Study of Selection Criteria SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-12-04 Sébastien J. Petit, Julien Bect, Paul Feliot, Emmanuel Vazquez
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1308-1328, December 2023. Abstract. This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of Bayesian procedures to perform predictions about the unknown
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Theoretical Guarantees for the Statistical Finite Element Method SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-11-30 Yanni Papandreou, Jon Cockayne, Mark Girolami, Andrew Duncan
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1278-1307, December 2023. Abstract. The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesized with the numerical solution of a PDE intended to describe it in a coherent statistical framework, to compensate for model error. This work presents
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Quantification of Errors Generated by Uncertain Data in a Linear Boundary Value Problem Using Neural Networks SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-11-28 Vilho Halonen, Ilkka Pölönen
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1258-1277, December 2023. Abstract. Quantifying errors caused by indeterminacy in data is currently computationally expensive even in relatively simple PDE problems. Efficient methods could prove very useful in, for example, scientific experiments done with simulations. In this paper, we create and test neural networks which quantify
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Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-11-27 Toni Karvonen
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1225-1257, December 2023. Abstract. It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Matérn covariance kernel. The smoothness parameter of a Matérn kernel determines many important properties of the model in the large data limit, including the rate
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An Order-Theoretic Perspective on Modes and Maximum A Posteriori Estimation in Bayesian Inverse Problems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-10-20 Hefin Lambley, T. J. Sullivan
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1195-1224, December 2023. Abstract. It is often desirable to summarize a probability measure on a space [math] in terms of a mode, or MAP estimator, i.e., a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius limit. However, the theory is not entirely straightforward:
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Sensitivity Analysis of Quasi-Stationary Distributions (QSDs) of Mass-Action Systems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-10-20 Yao Li, Yaping Yuan
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1164-1194, December 2023. Abstract. This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous-time Markov chain, a mass-action system can be described by an equation driven by finitely many Poisson processes, which
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Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-10-18 Johannes Milz
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1139-1163, December 2023. Abstract. We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite dimensional control problems. We establish an exponential tail
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Are Minimizers of the Onsager–Machlup Functional Strong Posterior Modes? SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-10-10 Remo Kretschmann
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1105-1138, December 2023. Abstract. In this work we connect two notions: that of the nonparametric mode of a probability measure, defined by asymptotic small ball probabilities, and that of the Onsager–Machlup functional, a generalized density also defined via asymptotic small ball probabilities. We show that in a separable Hilbert
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Bayesian Inference with Projected Densities SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-09-27 Jasper M. Everink, Yiqiu Dong, Martin S. Andersen
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 1025-1043, September 2023. Abstract. Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a constrained prior such that the posterior assigns positive probability
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Fast Calibration for Computer Models with Massive Physical Observations SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-09-27 Shurui Lv, Jun Yu, Yan Wang, Jiang Du
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 1069-1104, September 2023. Abstract. Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation of the calibration parameters is urgently needed. To alleviate the computational burden, we design a two-step algorithm to estimate the calibration
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Dimension Free Nonasymptotic Bounds on the Accuracy of High-Dimensional Laplace Approximation SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-09-27 Vladimir Spokoiny
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 1044-1068, September 2023. Abstract. This paper aims at revisiting the classical results on Laplace approximation in a modern nonasymptotic and dimension-free form. Such an extension is motivated by applications to high-dimensional statistical and optimization problems. The established results provide explicit nonasymptotic bounds
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Towards Practical Large-Scale Randomized Iterative Least Squares Solvers through Uncertainty Quantification SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-08-31 Nathaniel Pritchard, Vivak Patel
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 996-1024, September 2023. Abstract. As the scale of problems and data used for experimental design, signal processing, and data assimilation grow, the oft-occurring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems creates prohibitive memory movement costs for the usual
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Deep Surrogate Accelerated Delayed-Acceptance Hamiltonian Monte Carlo for Bayesian Inference of Spatio-Temporal Heat Fluxes in Rotating Disc Systems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-08-28 Teo Deveney, Eike H. Mueller, Tony Shardlow
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 970-995, September 2023. Abstract. We introduce a deep learning accelerated methodology to solve PDE-based Bayesian inverse problems with guaranteed accuracy. This is motivated by solving the ill-posed problem of inferring a spatio-temporal heat-flux parameter known as the Biot number in a PDE model given temperature data; however
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A Simple, Bias-free Approximation of Covariance Functions by the Multilevel Monte Carlo Method Having Nearly Optimal Complexity SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-08-23 Alexey Chernov, Erik Marc Schetzke
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 941-969, September 2023. Abstract. We develop simple and bias-free Monte Carlo and multilevel Monte Carlo approximations to covariance functions of sufficiently regular random fields in tensor products of Hilbert spaces. We investigate approximating the covariance function by means of full tensor product approximations, and additionally
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Evaluating Forecasts for High-Impact Events Using Transformed Kernel Scores SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-08-17 Sam Allen, David Ginsbourger, Johanna Ziegel
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 906-940, September 2023. Abstract. To account for uncertainties, forecasts for future events are commonly expressed in terms of probability distributions over the set of possible outcomes. To evaluate the quality of such forecasts, it is customary to employ proper scoring rules, which provide an objective framework with which
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Robust Level-Set-Based Topology Optimization Under Uncertainties Using Anchored ANOVA Petrov–Galerkin Method SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-07-25 Christophe Audouze, Aaron Klein, Adrian Butscher, Nigel Morris, Prasanth Nair, Masayuki Yano
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 877-905, September 2023. Abstract. We present a nonintrusive approach to robust structural topology optimization. Specifically, we consider optimization of mean- and variance-based robustness metrics of a linear functional output associated with the linear elasticity equation in the presence of probabilistic uncertainties in the
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Active Learning of Tree Tensor Networks using Optimal Least Squares SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-07-17 Cécile Haberstich, A. Nouy, G. Perrin
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 848-876, September 2023. Abstract. In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that generates a sequence of nested tensor subspaces based
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Quantifying and Managing Uncertainty in Piecewise-Deterministic Markov Processes SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-07-17 Elliot Cartee, Antonio Farah, April Nellis, Jacob Van Hook, Alexander Vladimirsky
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 814-847, September 2023. Abstract. In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the corresponding piecewise-deterministic trajectory up to the
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Large Deviation Theory-based Adaptive Importance Sampling for Rare Events in High Dimensions SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-07-11 Shanyin Tong, Georg Stadler
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 788-813, September 2023. Abstract. We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance sampling. The importance sampler uses a cross-entropy
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Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-07-10 Claudia Schillings, Claudia Totzeck, Philipp Wacker
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 757-787, September 2023. Abstract. We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions from a given ensemble of particles. Pointwise evaluation of some potential V in an ensemble contains implicit information about first- or higher-order
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Reduced-Order Modeling with Time-Dependent Bases for PDEs with Stochastic Boundary Conditions SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-07-10 Prerna Patil, Hessam Babaee
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 3, Page 727-756, September 2023. Abstract. Low-rank approximation using time-dependent bases (TDBs) has proven effective for reduced-order modeling of stochastic partial differential equations (SPDEs). In these techniques, the random field is decomposed to a set of deterministic TDBs and time-dependent stochastic coefficients. When applied
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Scalable Physics-Based Maximum Likelihood Estimation Using Hierarchical Matrices SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-06-05 Yian Chen, Mihai Anitescu
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 682-725, June 2023. Abstract. Physics-based covariance models provide a systematic way to construct covariance models that are consistent with the underlying physical laws in Gaussian process analysis. The unknown parameters in the covariance models can be estimated using maximum likelihood estimation, but direct construction
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A Continuation Method in Bayesian Inference SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-31 Ben Mansour Dia
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 646-681, June 2023. Abstract. We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of transition distributions, by tempering the likelihood function
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On Unbiased Estimation for Discretized Models SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-26 Jeremy Heng, Ajay Jasra, Kody J. H. Law, Alexander Tarakanov
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 616-645, June 2023. Abstract. In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time and/or space in order to practically work with the probability
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Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-25 Tim Jahn
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 591-615, June 2023. Abstract. In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretization
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Wavenumber-Explicit Parametric Holomorphy of Helmholtz Solutions in the Context of Uncertainty Quantification SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-18 E. A. Spence, J. Wunsch
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 567-590, June 2023. Abstract. A crucial role in the theory of uncertainty quantification (UQ) of PDEs is played by the regularity of the solution with respect to the stochastic parameters; indeed, a key property one seeks to establish is that the solution is holomorphic with respect to (the complex extensions of) the parameters
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The Zero Problem: Gaussian Process Emulators for Range-Constrained Computer Models SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-17 Elaine T. Spiller, Robert L. Wolpert, Pablo Tierz, Taylor G. Asher
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 540-566, June 2023. Abstract. We introduce a zero-censored Gaussian process as a systematic, model-based approach to building Gaussian process emulators for range-constrained simulator output. This approach avoids many pitfalls associated with modeling range-constrained data with Gaussian processes. Further, it is flexible enough
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Multifidelity Surrogate Modeling for Time-Series Outputs SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-12 Baptiste Kerleguer
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 514-539, June 2023. Abstract. This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series and two code levels are available: a high-fidelity and expensive code level and a low-fidelity and cheap code level. The goal is to emulate a fast-running approximation
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Convergence Rates for Learning Linear Operators from Noisy Data SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-11 Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, Andrew M. Stuart
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 480-513, June 2023. Abstract. This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known
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Nonparametric Posterior Learning for Emission Tomography SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-05-11 Fedor Goncharov, Éric Barat, Thomas Dautremer
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 452-479, June 2023. Abstract. We continue studies of the uncertainty quantification problem in emission tomographies such as positron emission tomography (PET) or single photon emission computed tomography (SPECT) when additional multimodal data (anatomical magnetic resonance imaging (MRI) images) are available. To solve the aforementioned
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Gaussian Process Regression on Nested Spaces SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-04-25 Christophette Blanchet-Scalliet, Bruno Demory, Thierry Gonon, Céline Helbert
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 426-451, June 2023. Abstract. As computer codes simulate complex physical phenomena, they involve a very large number of variables. To gain time, industrial experts build metamodels on a restricted set of variables, the most influential ones, while the others are fixed. The set of variables is then enlarged progressively to improve
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Robust Kalman and Bayesian Set-Valued Filtering and Model Validation for Linear Stochastic Systems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-04-25 Adrian N. Bishop, Pierre Del Moral
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 2, Page 389-425, June 2023. Abstract. Consider a linear stochastic filtering problem in which the probability measure specifying all randomness is only partially known. The deviation between the real and assumed probability models is constrained by a divergence bound between the respective probability measures under which the models are
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Context-Aware Surrogate Modeling for Balancing Approximation and Sampling Costs in Multifidelity Importance Sampling and Bayesian Inverse Problems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-10 Terrence Alsup, Benjamin Peherstorfer
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 285-319, March 2023. Abstract. Multifidelity methods leverage low-cost surrogate models to speed up computations and make occasional recourse to expensive high-fidelity models to establish accuracy guarantees. Because surrogate and high-fidelity models are used together, poor predictions by surrogate models can be compensated
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Generalized Sparse Bayesian Learning and Application to Image Reconstruction SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-03 Jan Glaubitz, Anne Gelb, Guohui Song
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 262-284, March 2023. Abstract. Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the
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A Fast and Scalable Computational Framework for Large-Scale High-Dimensional Bayesian Optimal Experimental Design SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-03 Keyi Wu, Peng Chen, Omar Ghattas
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 235-261, March 2023. Abstract. We develop a fast and scalable computational framework to solve Bayesian optimal experimental design problems governed by partial differential equations (PDEs) with application to optimal sensor placement by maximizing expected information gain (EIG). Such problems are particularly challenging due
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Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in [math] SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-03 Christoph Schwab, Jakob Zech
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 199-234, March 2023. Abstract. For artificial deep neural networks, we prove expression rates for analytic functions [math] in the norm of [math] where [math]. Here [math] denotes the Gaussian product probability measure on [math]. We consider in particular [math] and [math] activations for integer [math]. For [math], we show
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Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-03 Cédric Travelletti, David Ginsbourger, Niklas Linde
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 168-198, March 2023. Abstract. We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. Here we show that in the context of inverse problems involving integral operators, one faces
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On the Generalized Langevin Equation for Simulated Annealing SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-03 Martin Chak, Nikolas Kantas, Grigorios A. Pavliotis
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 139-167, March 2023. Abstract. In this paper, we consider the generalized (higher order) Langevin equation for the purpose of simulated annealing and optimization of nonconvex functions. Our approach modifies the underdamped Langevin equation by replacing the Brownian noise with an appropriate Ornstein–Uhlenbeck process to account
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Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-03-03 Juan P. Madrigal-Cianci, Fabio Nobile, Raúl Tempone
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 91-138, March 2023. Abstract. In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis–Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving a complex differential model, which is then
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On the Deep Active-Subspace Method SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-02-02 Wouter Edeling
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 62-90, March 2023. Abstract. The deep active-subspace method is a neural-network based tool for the propagation of uncertainty through computational models with high-dimensional input spaces. Unlike the original active-subspace method, it does not require access to the gradient of the model. It relies on an orthogonal projection
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Uncertainty Quantification of Inclusion Boundaries in the Context of X-Ray Tomography SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-01-25 Babak Maboudi Afkham, Yiqiu Dong, Per Christian Hansen
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 31-61, March 2023. Abstract. In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we quantify the uncertainty of the predicted boundaries. Our approach is
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Multilevel Delayed Acceptance MCMC SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2023-01-25 M. B. Lykkegaard, T. J. Dodwell, C. Fox, G. Mingas, R. Scheichl
SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 1, Page 1-30, March 2023. Abstract. We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the multilevel MCMC approach of Dodwell et al. [SIAM/ASA J. Un-certain. Quantif
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A Multilevel Stochastic Collocation Method for Schrödinger Equations with a Random Potential SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-20 Tobias Jahnke, Benny Stein
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1753-1780, December 2022. Abstract. We propose and analyze a numerical method for time-dependent linear Schrödinger equations with uncertain parameters in both the potential and the initial data. The random parameters are discretized by stochastic collocation on a sparse grid, and the sample solutions in the nodes are approximated
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Calibration of Inexact Computer Models with Heteroscedastic Errors SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-20 Chih-Li Sung, Beau David Barber, Berkley J. Walker
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1733-1752, December 2022. Abstract. Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting experimental data becomes essential in many scientific fields, ranging from engineering to biology. However, most of the existing
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On Negative Transfer and Structure of Latent Functions in Multioutput Gaussian Processes SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-20 Moyan Li, Raed Kontar
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1714-1732, December 2022. Abstract. The multioutput Gaussian process ([math]) is based on the assumption that outputs share commonalities; however, if this assumption does not hold, negative transfer will lead to decreased performance relative to learning outputs independently or in subsets. In this article, we first define negative
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Scaling Up Bayesian Uncertainty Quantification for Inverse Problems Using Deep Neural Networks SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-20 Shiwei Lan, Shuyi Li, Babak Shahbaba
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1684-1713, December 2022. Abstract. Due to the importance of uncertainty quantification (UQ), the Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov chain Monte Carlo (MCMC) tend to be computationally
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Penalized Projected Kernel Calibration for Computer Models SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-13 Yan Wang
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1652-1683, December 2022. Abstract. Projected kernel calibration is a newly proposed frequentist calibration method, which is asymptotic normal and semiparametric. Its loss function is usually referred to as the projected kernel (PK) loss function. In this work, we prove the uniform convergence of PK loss function and show that
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A Locally Adapted Reduced-Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-05 Zilong Zou, Drew P. Kouri, Wilkins Aquino
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1629-1651, December 2022. Abstract. The numerical solution of risk-averse optimization problems constrained by PDEs requires substantial computational effort resulting from the discretization of the underlying PDE in both the physical and stochastic dimensions. To practically solve these challenging optimization problems, one
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Uncertainty Quantification by Multilevel Monte Carlo and Local Time-Stepping for Wave Propagation SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-05 Marcus J. Grote, Simon Michel, Fabio Nobile
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1601-1628, December 2022. Abstract. Because of their robustness, efficiency, and non intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification for computing expected values of quantities of interest. Multilevel Monte Carlo (MLMC) methods significantly reduce the computational cost
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Test Comparison for Sobol Indices over Nested Sets of Variables SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-05 Thierry Klein, Nicolas Peteilh, Paul Rochet
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1586-1600, December 2022. Abstract. Sensitivity indices are commonly used to quantify the relative influence of any specific group of input variables on the output of a computer code. One crucial question is then to decide whether a given set of variables has a significant impact on the output. Sobol indices are often used to
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Statistical Finite Elements via Langevin Dynamics SIAM/ASA J. Uncertain. Quantif. (IF 2.0) Pub Date : 2022-12-05 Ömer Deniz Akyildiz, Connor Duffin, Sotirios Sabanis, Mark Girolami
SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1560-1585, December 2022. Abstract. The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesize finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which