Related papers: Neural solver for sixth-order ordinary differentia…
Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…
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…
Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations.…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement…
Recently, there has been a lot of interest in using neural networks for solving partial differential equations. A number of neural network-based partial differential equation solvers have been formulated which provide performances…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Deep learning has been extended to a number of new domains with critical success, though some traditional orienteering problems such as the Travelling Salesman Problem (TSP) and its variants are not commonly solved using such techniques.…
In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an…
We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…
This research presents a novel method using an adversarial neural network to solve the eigenvalue topology optimization problems. The study focuses on optimizing the first eigenvalues of second-order elliptic and fourth-order biharmonic…
In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods.…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…