Lingnan Fellow of the Lingnan University Institute for Advanced Study publishes paper in Nature Communications

The international top-tier journal Nature Communications has published online a groundbreaking research finding by the team led by Prof Zhang Dongxiao, Lingnan University Institute for Advanced Study (LUIAS)’s Lingnan Fellow, a member of the National Academy of Engineering (NAE), and Chair Professor of Eastern Institute of Technology, Ningbo (EIT). The paper, titled Generative discovery of partial differential equations by learning from math handbooks, was co-authored by Prof Zhang and scholars from Tsinghua University; the Ocean University of China; the University of Manchester; Peking University; the University of Oxford; Imperial College London; and the Eastern Institute of Technology, Ningbo.

The research team proposed a partial differential equations (PDE) discovery algorithm, EqGPT, a transformative leap for artificial intelligence (AI) from “data analyst” to “scientific creator,” which enables machines to discover new theories and governing equations autonomously like human scientists.

A paradigm-shifting breakthrough: AI moves from “finding patterns” to “creating equations”

The PDEs are a promising approach for uncovering the underlying laws governing complex systems - from the rise and fall of ocean waves to large-scale oil and gas migration, virtually all such phenomena depend on their precise formulation. Formerly these equations were derived manually by scientists, and conventional AI was only able to extract pre-existing patterns from data and not create entirely new equations.

The EqGPT algorithm developed by Prof Zhang and his team has overcome this longstanding limitation, and achieves dual-drive integration of knowledge and data. Current efforts can be categorised broadly into three approaches. The PDE dataset consists of 221 different PDEs collected from math handbooks with real-world observational data, giving the AI a robust theoretical foundation while keeping it tightly aligned with practical applications. Two techniques are introduced, including generative representation of equations (GRE) and scientifically augmented training (SAT). In the GRE, a structured equation encoding scheme is proposed, where equations are parsed into vocabularies composed of operators (arithmetic symbols) and fundamental physical terms. These units are combined to form sequence representations of free-form equations. In the SAT, a generative model, EqGPT, is trained to learn co-occurrence patterns among PDE terms from a dataset of PDEs collected from a mathematical handbook.

This enables the autonomous generation of free-form candidate equations directly from physically meaningful tokens, while filtering out mathematically implausible expressions implicitly, thereby improving both the efficiency and the relevance of the search process without relying on brute-force enumeration. Through a knowledge-guided loop of “generation–evaluation–optimisation”, PDEs that are both consistent with observed data and aligned with domain knowledge can be identified autonomously.

Discovery of new PDEs from real-world experimental data: from ocean waves to oil and gas reservoirs

Rigorous testing across multiple domains validates fully the practicality of the EqGPT algorithm with outstanding performance in complex scenarios. Validation results from diverse fields and scenarios not only comprehensively prove the reliability and adaptability of the algorithm, but also its tremendous potential in addressing real-world scientific problems, thereby facilitating its subsequent application in critical domains.

Prof Zhang, a world-famous scholar specialising in groundwater hydrology and energy engineering, joined LUIAS in March 2024, and this latest publication once again highlights consistent commitment to interdisciplinary innovation, research and knowledge transfer, and the dissemination of influential studies.

Since its formation, LUIAS has organised a series of thematic lectures and seminars, inviting distinguished scholars from various academic fields to share their valuable insights and expertise. LUIAS will also host the Lingnan University Distinguished Seminars (LUDS), where eminent scholars and experts will deliver keynote speeches and engage in academic exchanges with the community.