A Note on StiffDNN -- a DNN for Stiff Dynamic Systems

TL;DR

This paper introduces StiffDNN, a specialized neural network architecture designed to efficiently solve stiff dynamic systems by approximating different frequency components separately using Laplace transform insights.

Contribution

It proposes a novel DNN structure that targets different solution components based on frequency, improving the handling of stiff systems in differential equations.

Findings

Effective approximation of frequency components in stiff systems

Fast and uniform learning across frequency ranges

Potential for improved numerical stability in DNN solutions

Abstract

In this note, we will present a specially designed deep neural network (DNN), which will target components of the solution of different time rate individually through perspective of the Laplace s-transform of the solution. Each segment of s-frequency range will be approximated by a small size DNN separately after a reference central rate is factored out, leaving the rest of the frequencies confined within a short range of rates, and allowing fast and uniform learning by normal DNN.