CM-GAI: Continuum Mechanistic Generative Artificial Intelligence Theory for Data Dynamics

TL;DR

This paper introduces a continuum mechanics-based theoretical framework for generative AI that extends optimal transport theory to model data dynamics, enabling effective data generation with limited data in engineering and beyond.

Contribution

The paper develops a novel continuum mechanics-based theory that generalizes optimal transport for data dynamics, applicable to diverse generative tasks with small data.

Findings

Successfully generates stress-strain responses outside experimental range

Generates temperature-dependent stress fields under thermal loading

Produces plastic strain fields under transient dynamic loading

Abstract

Generative artificial intelligence (GAI) plays a fundamental role in high-impact AI-based systems such as SORA and AlphaFold. Currently, GAI shows limited capability in the specialized domains due to data scarcity. In this paper, we develop a continuum mechanics-based theoretical framework to generalize the optimal transport theory from pure mathematics, which can be used to describe the dynamics of data, realizing the generative tasks with a small amount of data. The developed theory is used to solve three typical problem involved in many mechanical designs and engineering applications: at material level, how to generate the stress-strain response outside the range of experimental conditions based on experimentally measured stress-strain data; at structure level, how to generate the temperature-dependent stress fields under the thermal loading; at system level, how to generate the plastic strain fields under transient dynamic loading. Our results show the proposed theory can complete the generation successfully, showing its potential to solve many difficult problems involved in engineering applications, not limited to mechanics problems, such as image generation. The present work shows that mechanics can provide new tools for computer science. The limitation of the proposed theory is also discussed.