Related papers: Solving Inverse Problems in Stochastic Self-Organi…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
An effective way to model the complex real world is to view the world as a composition of basic components of objects and transformations. Although humans through development understand the compositionality of the real world, it is…
Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal variables are captured in the high-dimensional observations. We instead consider a partially…
The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…
Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
Causality inference is prone to spurious causal interactions, due to the substantial confounders in a complex system. While many existing methods based on the statistical methods or dynamical methods attempt to address misidentification…
The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming…
In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the…