Towards AI Co-Scientist: Automatic Governing Law Discovery

Scientific law discovery has historically been limited by human reasoning and data scarcity, despite the vast search space of possible formulations. Advances in generative AI and abundant physical data now enable AI models to extract interpretable structures, such as symmetries, differential equations, and conserved quantities, and use them as inductive biases in predictive and generative tasks.

Jianke's research aims to develop an AI co-scientist, a unified system that can (1) autonomously discover governing structures from raw observations, (2) translate these discoveries into flexible inductive biases to improve downstream tasks, and (3) orchestrate modular tools under a top-level planner to generate hypotheses, implement models that satisfy physical constraints, and complete the pipeline from data→law→model→prediction.

This thesis proposal presents the following milestones toward this goal. First, we formulate the problem of symmetry discovery and introduce two models, LieGAN and LaLiGAN, that discover invariance and equivariance from data using a generative adversarial framework. Second, we incorporate symmetry into the task of governing equation discovery, showing that symmetry is a powerful inductive bias in the discovery of other physical laws. Together, these serve as the building blocks towards a fully functional AI co-scientist system