Related papers: Applications of ML-Based Surrogates in Bayesian Ap…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

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…

Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…

Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…

The performance of error correction in the surface code can be enhanced by leveraging the knowledge of the noise model for physical qubits. To provide accurate noise information to the decoder in parallel with quantum computation, an…

Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using…

We propose a surrogate function for efficient yet principled use of score-based priors in Bayesian imaging. We consider ill-posed inverse imaging problems in which one aims for a clean image posterior given incomplete or noisy measurements.…

Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is…

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D…

Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…

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…

In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\theta )$ and $f_{NN}(x;\psi)$ to approximate the solution $u^{*}(x)$ and the…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…

The problem of locating an odor source in turbulent flows is central to key applications such as environmental monitoring and disaster response. We address this challenge by designing an algorithm based on Bayesian inference, which uses…

To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…

Solving inverse problems, where we find the input values that result in desired values of outputs, can be challenging. The solution process is often computationally expensive and it can be difficult to interpret the solution in…