Related papers: Bayesian Inference for PDE-based Inverse Problems …
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…
Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically…
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
Data-driven inverse optimization seeks to estimate unknown parameters in an optimization model from observations of optimization solutions. Many existing methods are ineffective in handling noisy and suboptimal solution observations and…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
We consider the problem of estimating the transition dynamics $T^*$ from near-optimal expert trajectories in the context of offline model-based reinforcement learning. We develop a novel constraint-based method, Inverse Transition Learning,…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
We propose a novel machine learning framework for solving optimization problems governed by large-scale partial differential equations (PDEs) with high-dimensional random parameters. Such optimization under uncertainty (OUU) problems may be…
The computational cost of solving an inverse problem governed by PDEs, using multiple experiments, increases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear…
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
In most relevant cases in the Bayesian analysis of ODE inverse problems, a numerical solver needs to be used. Therefore, we cannot work with the exact theoretical posterior distribution but only with an approximate posterior deriving from…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…
Physics-Informed Machine Learning (PIML) offers a powerful paradigm of integrating data with physical laws to address important scientific problems, such as parameter estimation, inferring hidden physics, equation discovery, and state…