Related papers: An Efficient Meshfreee Implicit Filter for Nonline…

Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…

We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

In this paper, we give a causal solution to the problem of spline interpolation using H-infinity optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…

Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently,…

We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…

The implicit particle filter seeks to mitigate particle degeneracy by identifying particles in the target distribution's high-probability regions. This study is motivated by the need to enhance computational tractability in implementing…

Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…

In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…

Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…