Related papers: A Domain Decomposition Deep Neural Network Method …

Extreme learning machines (ELMs), which preset hidden layer parameters and solve for last layer coefficients via a least squares method, can typically solve partial differential equations faster and more accurately than Physics Informed…

We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…

Multi-Agent Path Finding (MAPF) involves determining paths for multiple agents to travel simultaneously and collision-free through a shared area toward given goal locations. This problem is computationally complex, especially when dealing…

In this paper we design an iterative domain decomposition method for free boundary problems with nonlinear flux jump condition. Our approach is related to damped Newton's methods. The proposed scheme requires, in each iteration, the…

This paper describes and establishes the iteration-complexity of a doubly accelerated inexact proximal point (D-AIPP) method for solving the nonconvex composite minimization problem whose objective function is of the form $f+h$ where $f$ is…

We present new Neumann-Neumann algorithms based on a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, the Lagrange multiplier approach provides a coupled…

We propose a segmentation framework that uses deep neural networks and introduce two innovations. First, we describe a biophysics-based domain adaptation method. Second, we propose an automatic method to segment white and gray matter, and…

We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…

The purported "black box" nature of neural networks is a barrier to adoption in applications where interpretability is essential. Here we present DeepLIFT (Deep Learning Important FeaTures), a method for decomposing the output prediction of…

The Multi-Agent Path Finding (MAPF) problem aims to determine the shortest and collision-free paths for multiple agents in a known, potentially obstacle-ridden environment. It is the core challenge for robotic deployments in large-scale…

A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulations or grids on manifolds. Our method is numerically tested…

We present an algorithm that learns representations which explicitly compensate for domain mismatch and which can be efficiently realized as linear classifiers. Specifically, we form a linear transformation that maps features from the…

Defect detection is a critical research area in artificial intelligence. Recently, synthetic data-based self-supervised learning has shown great potential on this task. Although many sophisticated synthesizing strategies exist, little…

Unsupervised domain adaptation (UDA) techniques are vital for semantic segmentation in geosciences, effectively utilizing remote sensing imagery across diverse domains. However, most existing UDA methods, which focus on domain alignment at…

Recently, deep multiagent reinforcement learning (MARL) has become a highly active research area as many real-world problems can be inherently viewed as multiagent systems. A particularly interesting and widely applicable class of problems…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

We study the problem of multimodal physical scene understanding, where an embodied agent needs to find fallen objects by inferring object properties, direction, and distance of an impact sound source. Previous works adopt feed-forward…

In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable. The problem becomes even more severe when the model must…