Related papers: Derivative-informed neural operator acceleration o…

Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development…

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that…

The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may…

When conducting Bayesian inference, delayed acceptance (DA) Metropolis-Hastings (MH) algorithms and DA pseudo-marginal MH algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased estimate…

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

This paper presents an efficient mesh deformation method based on boundary integration and neural operators, formulating the problem as a linear elasticity boundary value problem (BVP). To overcome the high computational cost of traditional…

In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed…

Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly…

Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…

We introduce a GPU-accelerated Monte Carlo framework for nonconvex, free-final-time trajectory optimization problems. This framework makes use of the prox-linear method, which belongs to the larger family of sequential convex programming…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Particle accelerators are enabling tools for scientific exploration and discovery in various disciplines. Finding optimized operation points for these complex machines is a challenging task, however, due to the large number of parameters…

Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually,…

Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this…

Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in…

Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect…

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…

Computational inference of causal relationships underlying complex networks, such as gene-regulatory pathways, is NP-complete due to its combinatorial nature when permuting all possible interactions. Markov chain Monte Carlo (MCMC) has been…

Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…