MCO-PDE recovers governing equations from 50 observations per dataset
Researchers propose a competitive optimization framework that discovers governing partial differential equations by fusing observations from multiple datasets with distinct initial conditions.
A new preprint describes MCO-PDE, a framework that discovers shared partial differential equations across multiple datasets by training independent neural surrogates for each source and using soft-competitive weighting to assess dataset credibility. The method, posted to arXiv on July 1, 2026, combines this mechanism with a genetic algorithm for structural search to identify both functional forms and parameters of governing laws. It handles two- and three-dimensional domains with irregular boundaries and heterogeneous coefficients—conditions common in real-world experiments.
Current data-driven approaches for discovering governing equations typically operate on a single dataset, limiting performance when observations are sparse. In practice, multiple datasets are often available for the same physical system, distinguished only by distinct initial conditions or boundary configurations. MCO-PDE addresses this by aggregating information across sources rather than treating each dataset in isolation. The competitive weighting mechanism first trains independent neural surrogates, then dynamically weights their contributions based on credibility to produce a consensus global coefficient. The genetic algorithm searches the space of possible functional forms while the weighting mechanism handles parameter estimation. Testing across seven cases, the framework recovered canonical equations with high accuracy using as few as 50 observations per dataset. The authors validated the approach on real-world wave-tank experiments and successfully extracted physically meaningful laws from heterogeneous data.
