Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
A new competitive optimization framework, MCO-PDE, discovers shared partial differential equations from multiple datasets, overcoming limitations of single-dataset methods by dynamically assessing data credibility via soft-competitive weighting, recovering canonical equations with high accuracy from as few as 50 observations per dataset.
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[Submitted on 29 Jun 2026]
Title:Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization
View a PDF of the paper titled Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization, by Hao Xu and 3 other authors
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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.
Subjects:
Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
Cite as: arXiv:2606.30699 [cs.LG]
(or arXiv:2606.30699v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.30699
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Dongxiao Zhang [view email] [v1] Mon, 29 Jun 2026 07:35:59 UTC (2,828 KB)
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