相关论文: The Back and Forth Nudging algorithm for data assi…

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…

We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…

This paper examines the properties of a regularization of Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as convectively filtered Burgers (CFB) equation. A physical motivation…

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…

A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…

Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler…

We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…

We study different approaches to implementing sparse-in-time observations into the the Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces a "data assimilation window" separate from the observational…

We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…

In a recent paper, Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary…

Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…

In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…

In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regularization penalizes transport couplings by the squared $L^2$…

Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that…

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…

We study distributed convex optimization with two ubiquitous forms of coupling: consensus constraints and global affine equalities. We first design a linearized method of multipliers for the consensus optimization problem. Without…