Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization

2026-06-29

AI Summary

Discovering governing partial differential equations (PDEs) of complex physical systems from single-source observational data is often inaccurate under limited measurement conditions. To address this challenge, this work proposes the MCO-PDE framework, which integrates multi-source heterogeneous data through a soft competitive optimization mechanism. The approach trains independent neural surrogates and dynamically aggregates them via a novel soft-competition weighting strategy to jointly identify both the structure and parameters of shared PDEs. This strategy enables reliable assessment of data credibility and consensus-driven fusion across sources, facilitating automated scientific discovery even in scenarios with irregular boundaries and spatially varying coefficients. Using only 50 observation points per dataset, the method accurately recovers classical PDEs across seven benchmark problems and successfully extracts interpretable physical laws from real-world wave flume experiments.

Abstract

Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning. Current data-driven approaches typically operate on a single dataset, inherently limiting their performance when faced with restricted observations. In practice, multiple datasets are often available for the same physical system, distinguished only by distinct initial conditions or boundary configurations. Here, we present a competitive optimization framework designed to discover shared partial differential equations (PDEs) from multi-source datasets, termed MCO-PDE. The framework first trains independent neural surrogates for each data source, and then employs a soft-competitive weighting mechanism to dynamically assess dataset credibility and aggregate a consensus global coefficient. Integrated with a genetic algorithm for structural search, this approach simultaneously identifies the functional forms and parameters of the governing laws. We demonstrate that fusing as few as 50 observations per dataset across seven cases recovers canonical equations with high accuracy. The framework inherently handles two- and three-dimensional domains characterized by irregular boundaries and heterogeneous coefficients, and successfully extracts physically meaningful laws from real-world wave-tank experiments. Overall, this work establishes a promising route for automated scientific discovery via heterogeneous data fusion.

Problem

• governing equations
• multi-source datasets
• partial differential equations
• scientific discovery
• data fusion

Innovation

• competitive optimization
• multi-source data fusion
• governing PDE discovery
• neural surrogates
• genetic algorithm