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

TL;DR

CM-GAI introduces a continuum-mechanics–driven generalization of optimal transport to enable data-driven generation under severe data scarcity. By formulating time-dependent transport on a high-dimensional probability space and enforcing mass-conservation and physics-based dynamics via Physics-Informed Neural Networks, the approach generates material constitutive data, temperature-dependent stress fields, and transient plastic strains from limited observations. The results across 2D/6D problems demonstrate accurate generation and meaningful extrapolation, offering a data-efficient world-model framework with broad potential in engineering and beyond. The work also discusses limitations, including extension to richer constitutive models and higher-dimensional data manifolds, pointing to future integration with manifold learning and more complex physics.

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.

Figures (29)

• Figure 1: Conceptual framework of CM-GAI in unknown data generation. The general problem for generating the relationship between features under the specified state when the data under the other states are known.
• Figure 2: Time-independent optimal transport. The original probability distribution in the space $X$ and the target probability distribution in the space $Y$ are colored by red and blue, respectively.
• Figure 3: Time-dependent optimal transport. The mapping $T$ is a function of time $t$, which can move the mass from $t=0$ to $t=1$ along the trajectory to the target.
• Figure 4: A simple example for time-independent optimal transport.
• Figure 5: A simple example for time-dependent optimal transport.