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

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…

We obtain a sharp limit H\"older continuity of the solution for the transport equations thanks to a vanishing viscosity analysis. We also derive the same control for parabolic equations and for inviscid Burgers' equation. Eventually, under…

Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that general nudging techniques can also tackle another crucial…

A new nudging method for data assimilation, delay-coordinate nudging, is presented. Delay-coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each…

In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…

We establish a convergence theorem for a certain type of stochastic gradient descent, which leads to a convergent variant of the back-propagation algorithm

The Backpropagation algorithm relies on the abstraction of using a neural model that gets rid of the notion of time, since the input is mapped instantaneously to the output. In this paper, we claim that this abstraction of ignoring time,…

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

In this paper, we propose algorithms that exploit negative curvature for solving noisy nonlinear nonconvex unconstrained optimization problems. We consider both deterministic and stochastic inexact settings, and develop two-step algorithms…

Theoretical and computational properties of a vector equation $Ax-\|x\|_1x=b$ are investigated, where $A$ is an invertible $M$-matrix and $b$ is a nonnegative vector. Existence and uniqueness of a nonnegative solution is proved. Fixed-point…

Optimal balance is a non-asymptotic numerical method to compute a point on the slow manifold for certain two-scale dynamical systems. It works by solving a modified version of the system as a boundary value problem in time, where the…

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure --…

In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-dimensional B\'enard convection problem. Specifically we consider the two-dimensional Boussinesq system of a layer of incompressible fluid between two…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…

This paper examines an averaging technique applied to the transport equations as an alternative to vanishing viscosity. Such techniques have been shown to be valid shock-regularizations of the Burgers equation and the Euler equations, but…

This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global…

We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…

A study is presented on the convergence of the computation of coupled advection-diffusion-reaction equations. In the computation, the equations with different coefficients and even types are assigned in two subdomains, and Schwarz iteration…