Multi-Source Data Unlocks Joint PDE Discovery with AI

A new framework called MCO-PDE (Multi-Competitive Optimization for PDEs) has been developed to automatically discover governing partial differential equations (PDEs) from diverse datasets. Traditional data-driven methods for equation discovery typically rely on single datasets, which can be limiting when observations are scarce. MCO-PDE addresses this by leveraging multiple datasets that describe the same physical system but originate from different initial or boundary conditions. The framework operates by first training individual neural surrogates for each distinct data source. Subsequently, a soft-competitive weighting mechanism is employed to dynamically assess the credibility of each dataset and synthesize a consensus global coefficient. This process, integrated with a genetic algorithm for structural search, allows MCO-PDE to simultaneously identify both the functional forms and parameters of the underlying physical laws. Demonstrations show that MCO-PDE can accurately recover canonical equations using as few as 50 observations per dataset across various cases. It effectively handles complex scenarios, including two- and three-dimensional domains with irregular boundaries and heterogeneous coefficients, and has successfully extracted meaningful physical laws from real-world wave-tank experiments.