Related papers: A Domain Decomposition Deep Neural Network Method …

Multi-Agent Path Finding (MAPF) is essential to large-scale robotic systems. Recent methods have applied reinforcement learning (RL) to learn decentralized polices in partially observable environments. A fundamental challenge of obtaining…

We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…

Mechanistic interpretability aims to understand the internal mechanisms learned by neural networks. Despite recent progress toward this goal, it remains unclear how best to decompose neural network parameters into mechanistic components. We…

Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process. This difficulty can be partly explained by the spectral…

In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic…

Multi-Agent Path Finding (MAPF) finds conflict-free paths for multiple agents from their respective start to goal locations. MAPF is challenging as the joint configuration space grows exponentially with respect to the number of agents.…

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…

A DeepCAPA (Deep Learning for Continuous Aperture Array (CAPA)) framework is proposed to learn beamforming in CAPA systems. The beamforming optimization problem is firstly formulated, and it is mathematically proved that the optimal…

Domain-decomposed variants of physics-informed neural networks (PINNs) such as finite basis PINNs (FBPINNs) mitigate some of PINNs' issues like slow convergence and spectral bias through localisation, but still rely on iterative nonlinear…

This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network…

This paper proposes a deep-learning-based method for recovering a signed distance function (SDF) of a given hypersurface represented by an implicit level set function. Using the flexibility of constructing a neural network, we use an…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

Recently, some challenging tasks in multi-agent systems have been solved by some hierarchical reinforcement learning methods. Inspired by the intra-level and inter-level coordination in the human nervous system, we propose a novel value…

We propose a novel deep learning (DL) approach to solve one-dimensional non-linear elliptic, parabolic, and hyperbolic problems on graphs. A system of physics-informed neural network (PINN) models is used to solve the differential…

We explore two differentiable deep declarative layers, namely least squares on sphere (LESS) and implicit eigen decomposition (IED), for learning the principal matrix features (PMaF). It can be used to represent data features with a…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…

Deformable medical image registration is a crucial aspect of medical image analysis. In recent years, researchers have begun leveraging auxiliary tasks (such as supervised segmentation) to provide anatomical structure information for the…

Multi-agent pathfinding (MAPF) remains a critical problem in robotics and autonomous systems, where agents must navigate shared spaces efficiently while avoiding conflicts. Traditional centralized algorithms with global information provide…