Differential Informed Auto-Encoder

TL;DR

This paper introduces a differential informed auto-encoder that learns the intrinsic structure of data through differential equations and generates new data consistent with this structure using physics-informed neural networks.

Contribution

It presents a novel auto-encoder framework that incorporates differential equations and physics-informed neural networks for data representation and generation.

Findings

Successfully captures the data's intrinsic differential structure.

Generates new data consistent with the learned differential equations.

Enhances data modeling with physics-informed neural networks.

Abstract

In this article, an encoder was trained to obtain the inner structure of the original data by obtain a differential equations. A decoder was trained to resample the original data domain, to generate new data that obey the differential structure of the original data using the physics-informed neural network.