Related papers: Stochastic solutions to mixed linear and nonlinear…
In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
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…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…