相关论文: Sparse identification of nonlocal interaction kern…
We present a unified, finite-element-native variational inference framework for very high-dimensional Bayesian spatial field reconstruction in physics-based problems governed by partial differential equations (PDEs) that are nonlinear in…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the…
The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…
We study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…
In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…
Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…
We address the numerical solution of minimal norm residuals of {\it nonlinear} equations in finite dimensions. We take inspiration from the problem of finding a sparse vector solution by using greedy algorithms based on iterative residual…
In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…
We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
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…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Basis pursuit is the problem of finding a vector with smallest $\ell_1$-norm among the solutions of a given linear system of equations. It is a well-known convex relaxation of the sparse affine feasibility problem, where sparse solutions to…