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

Mean field games (MFGs) describe the collective behavior of large populations of interacting agents. In this work, we tackle ill-posed inverse problems in potential MFGs, aiming to recover the agents' population, momentum, and environmental…

The theory-guided convolutional neural network (TgCNN) framework, which can incorporate discretized governing equation residuals into the training of convolutional neural networks (CNNs), is extended to two-phase porous media flow problems…

We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining…

Neural networks for LHC physics have to be accurate, reliable, and controlled. Using neural surrogates for the prediction of loop amplitudes as a use case, we first show how activation functions are systematically tested with…

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…

Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining…

Travel time tomography for the velocity structure of a medium is a highly non-linear and non-unique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but…

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…

Success of machine learning (ML) in the modern world is largely determined by abundance of data. However at many industrial and scientific problems, amount of data is limited. Application of ML methods to data-scarce scientific problems can…

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…

Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…

This paper presents an approach for developing a neural network inverse model of a piezoelectric positioning stage, which exhibits rate-dependent, asymmetric hysteresis. It is shown that using both the velocity and the acceleration as…

Invertible neural networks are a recent technique in machine learning promising neural network architectures that can be run in forward and reverse mode. In this paper, we will be introducing invertible surrogate models that approximate…

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes…

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…

In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a…

Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear inverse problems with neural network coders. First we…

Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable…