A machine-learning solver for modified diffusion equations

Abstract

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions.The idea can be easily adopted for dealing with multi-variable, coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.

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• Solving Differential Equation with Constrained Multilayer Feedforward Network
• Numerical Solution and Bifurcation Analysis of Nonlinear Partial Differential Equations with Extreme Learning Machines
• Neural Network Solutions to Differential Equations in Non-Convex Domains: Solving the Electric Field in the Slit-Well Microfluidic Device
• Studying First Passage Problems using Neural Networks: A Case Study in the Slit-Well Microfluidic Device
• Deep learning-based computational method for soft matter dynamics: Deep Onsager-Machlup method
• Multigrid Solver With Super-Resolved Interpolation