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.

翻译：生成式人工智能（GAI）在诸如SORA和AlphaFold等高影响力人工智能系统中发挥着基础性作用。当前，由于数据稀缺，GAI在专业领域中的应用能力有限。本文发展了一个基于连续介质力学的理论框架，将最优传输理论从纯数学领域进行推广，该框架可用于描述数据的动力学特性，从而实现基于少量数据的生成任务。所发展的理论被用于解决许多机械设计与工程应用中涉及的三个典型问题：在材料层面，如何基于实验测量的应力-应变数据，生成实验条件范围之外的应力-应变响应；在结构层面，如何生成热载荷下与温度相关的应力场；在系统层面，如何生成瞬态动态载荷下的塑性应变场。我们的结果表明，所提出的理论能够成功完成生成任务，显示出其解决工程应用中诸多难题的潜力，且不仅限于力学问题，例如图像生成。本工作表明，力学可以为计算机科学提供新的工具。文中亦讨论了所提理论的局限性。