Related papers: Neural Green's Function Accelerated Iterative Meth…

Representation learning algorithms offer the opportunity to learn invariant representations of the input data with regard to nuisance factors. Many authors have leveraged such strategies to learn fair representations, i.e., vectors where…

Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We…

In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…

In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…

We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the…

This paper proposes an iterative generative model for solving the automatic colorization problem. Although previous researches have shown the capability to generate plausible color, the edge color overflow and the requirement of the…

We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key…

The Green's function, serving as a kernel function that delineates the interaction relationships of physical quantities within a field, holds significant research implications across various disciplines. It forms the foundational basis for…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a…

In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method…

This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. Specifically, we develop neural networks as a composition of several vector-valued functions. Although neural networks are…

Cooperative multi-agent reinforcement learning is a decentralized paradigm in sequential decision making where agents distributed over a network iteratively collaborate with neighbors to maximize global (network-wide) notions of rewards.…

Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior…

We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…