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1. Multi-fidelity Monte Carlo: a pseudo-marginal approach

   Cai, Diana; Adams, Ryan P. (December 2022, Advances in Neural Information Processing Systems (NeurIPS))

   Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in apply- ing MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a high-fidelity physical simulation, an intractable integral, or a slowly-converging iterative algorithm. Thus, using an MCMC algorithms with an expensive target density becomes impractical, as these expensive computations need to be evaluated at each iteration of the algorithm. In practice, these computations often approximated via a cheaper, low- fidelity computation, leading to bias in the resulting target density. Multi-fidelity MCMC algorithms combine models of varying fidelities in order to obtain an ap- proximate target density with lower computational cost. In this paper, we describe a class of asymptotically exact multi-fidelity MCMC algorithms for the setting where a sequence of models of increasing fidelity can be computed that approximates the expensive target density of interest. We take a pseudo-marginal MCMC approach for multi-fidelity inference that utilizes a cheaper, randomized-fidelity unbiased estimator of the target fidelity constructed via random truncation of a telescoping series of the low-fidelity sequence of models. Finally, we discuss and evaluate the proposed multi-fidelity MCMC approach on several applications, including log-Gaussian Cox process modeling, Bayesian ODE system identification, PDE-constrained optimization, and Gaussian process parameter inference. 

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2. Analyzing Multi-Fidelity Simulation Optimization with Level Set Approximation Using Probabilistic Branch and Bound

   Linz, D.; Huang, H.; Zabinsky, Z. B. (December 2017, Proceedings of the 2017 Winter Simulation Conference)

   Simulated systems are often described with a variety of models of different complexity. Making use of these models, algorithms can use low complexity, “low-fidelity” models or meta-models to guide sampling for purposes of optimization, improving the probability of generating good solutions with a small number of observations. We propose an optimization algorithm that guides the search for solutions on a high-fidelity model through the approximation of a level set from a low-fidelity model. Using the Probabilistic Branch and Bound algorithm to approximate a level set for the low-fidelity model, we are able to efficiently locate solutions inside of a target quantile and therefore reduce the number of high-fidelity evaluations needed in searches. The paper provides an algorithm and analysis showing the increased probability of sampling high-quality solutions within a low-fidelity level set. We include numerical examples that demonstrate the effectiveness of the multi-fidelity level set approximation method to locate solutions. 

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3. Effect of imperfect homodyne visibility on multi-spatial-mode two-mode squeezing measurements

   https://doi.org/10.1364/OE.379033  

   Gupta, Prasoon; Speirs, Rory_W; Jones, Kevin_M; Lett, Paul_D (January 2020, Optics Express)

   We study the effect of homodyne detector visibility on the measurement of quadrature squeezing for a spatially multi-mode source of two-mode squeezed light. Sources like optical parametric oscillators (OPO) typically produce squeezing in a single spatial mode because the nonlinear medium is within a mode-selective optical cavity. For such a source, imperfect interference visibility in the homodyne detector couples in additional vacuum noise, which can be accounted for by introducing an equivalent loss term. In a free-space multi-spatial-mode system imperfect homodyne detector visibility can couple in uncorrelated squeezed modes, and hence can cause faster degradation of the measured squeezing. We show experimentally the dependence of the measured squeezing level on the visibility of homodyne detectors used to probe two-mode squeezed states produced by a free space four-wave mixing process in⁸⁵Rb vapor, and also demonstrate that a simple theoretical model agrees closely with the experimental data. 

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4. Multi-fidelity Bayesian Optimization with Multiple Information Sources of Input-dependent Fidelity

   Fan, Mingzhou; Yoon, Byung-Jun; Dougherty, Edward; Urban, Nathan; Alexander, Francis; Arróyave, Raymundo; Qian, Xiaoning (April 2024, UAI 2024 Conference)

   By querying approximate surrogate models of different fidelity as available information sources, Multi-Fidelity Bayesian Optimization (MFBO) aims at optimizing unknown functions that are costly or infeasible to evaluate. Existing MFBO methods often assume that approximate surrogates have consistently high or low fidelity across the input domain. However, approximate evaluations from the same surrogate can have different fidelity at different input regions due to data availability and model constraints, especially when considering machine learning surrogates. In this work, we investigate MFBO when multi-fidelity approximations have input-dependent fidelity. By explicitly capturing input dependency for multi-fidelity queries in a Gaussian Process (GP), our new input-dependent MFBO (iMFBO) with learnable noise models better captures the fidelity of each information source in an intuitive way. We further design a new acquisition function for iMFBO and prove that the queries selected by iMFBO have higher quality than those by naive MFBO methods, with a derived sub-linear regret bound. Experiments on both synthetic and real-world data demonstrate its superior empirical performance. 

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5. Multi-Fidelity Reduced-Order Models for Multiscale Damage Analyses With Automatic Calibration

   https://doi.org/10.1115/DETC2022-90163  

   Deng, Shiguang; Mora, Carlos; Apelian, Diran; Bostanabad, Ramin (August 2022, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Predicting the fracture behavior of macroscale components containing microscopic porosity relies on multiscale damage models which typically ignore the manufacturing-induced spatial variabilities in porosity. This simplification is made due to the prohibitive computational costs associated with explicitly modeling spatially varying microstructures in a macroscopic component. To address this challenge, we propose a data-driven framework that integrates a mechanistic reduced-order model (ROM) with a calibration scheme based on latent map Gaussian processes (LMGPs). Our ROM drastically accelerates direct numerical simulations (DNS) by using a stabilized damage algorithm and systematically reducing the degrees of freedom via clustering. Since clustering affects local strain fields and hence the fracture response, we construct a multi-fidelity LMGP to inversely estimate the damage parameters of an ROM as a function of microstructure and clustering level such that the ROM faithfully surrogates DNS. We demonstrate the application of our framework in predicting the damage behavior of a multiscale metallic component with spatially varying porosity. 

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