Related papers: Optimizing performance of the deconvolution model …
Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…
We study the numerical approximation of a class of degenerate parabolic stochastic partial differential equations on non-compact metric graphs, which naturally arise in the asymptotic analysis of Hamiltonian flows under small noise…
There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval $[0,1] \subset \mathbb R$, but little is known about the multidimensional situation. This article tries…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…
The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…
This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Let $(Y_i,\theta_i)$, $i=1,...,n$, be independent random vectors distributed like $(Y,\theta) \sim G^*$, where the marginal distribution of $\theta$ is completely unknown, and the conditional distribution of $Y$ conditional on $\theta$ is…
Short-and-sparse deconvolution (SaSD) aims to recover a short kernel and a long and sparse signal from their convolution. In the literature, formulations of blind deconvolution is either a convex programming via a matrix lifting of…
In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However,…
This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…