Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
Summary
This paper presents MCO-PDE, a competitive optimization framework that discovers shared partial differential equations from multiple observational datasets by combining neural surrogates, soft-competitive weighting, and genetic algorithms for structure search. It demonstrates high accuracy in recovering canonical equations from limited data and handles complex geometries and real-world experiments.
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# Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization Source: [https://arxiv.org/abs/2606.30699](https://arxiv.org/abs/2606.30699) [View PDF](https://arxiv.org/pdf/2606.30699) > 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\. ## Submission history From: Dongxiao Zhang \[[view email](https://arxiv.org/show-email/9f5b1336/2606.30699)\] **\[v1\]**Mon, 29 Jun 2026 07:35:59 UTC \(2,828 KB\)
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