Two major research breakthroughs from Xi'an Jiaotong University's (XJTU) School of Mathematics and Statistics were recently published online in the international journal Nature Communications.

Professor Sun Jian's team introduced TS-DFM, a geometric deep learning method that integrates AI generative capabilities with the geometric constraints of chemical reactions. By utilizing a geometric flow model guided by optimal transport, this method maps the evolution of interatomic distances and chemical bond structures during a reaction. The approach ensures that the model's generative process aligns with the underlying physical laws of chemistry.

Meanwhile, Professor Yang Shusen's team developed Deflex, a method that bridges the representation power of deep learning with the formalized expressiveness of symbolic learning.

Deflex consists of two main subsystems. Powered by energy-based models and self-attention networks, Deflexformer unifies multi-modal laws and captures highly complex relationships.

Utilizing lambda calculus-enhanced symbolic regression, Deflexpressor allows the system to express and search for complex mathematical formulas containing high-order structures like mappings, summations, and reductions.

Focusing on chemical reaction transition state prediction and formula discovery in complex systems, respectively, both achievements are built on the innovative integration of mathematics and artificial intelligence. This highlights the crucial supporting role that mathematical methods play in AI for Science research.