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Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…
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…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
As an example of topic where biology and physics meet, we present the issue of protein folding and stability, and the development of thermodynamics-based bioinformatics tools that predict the stability and thermal resistance of proteins and…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Quantifying the effects of amino acid mutations in proteins presents a significant challenge due to the vast combinations of residue sites and amino acid types, making experimental approaches costly and time-consuming. The Potts model has…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown…
Implicit Processes (IPs) represent a flexible framework that can be used to describe a wide variety of models, from Bayesian neural networks, neural samplers and data generators to many others. IPs also allow for approximate inference in…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…
We consider the Ising, and more generally, $q$-state Potts Glauber dynamics on random $d$-regular graphs on $n$ vertices at low temperatures $\beta \gtrsim \frac{\log d}{d}$. The mixing time is exponential in $n$ due to a bottleneck between…
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are…
We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…