Discovering PDEs from Multiple Experiments
This addresses the challenge of automated PDE discovery for researchers dealing with multiple experimental datasets, though it appears incremental as it builds on existing deep learning methods with a sparsity enhancement.
The paper tackles the problem of discovering partial differential equations (PDEs) from multiple experiments with inherent variability, introducing a randomised adaptive group Lasso sparsity estimator in a deep learning framework to promote grouped sparsity, resulting in more generalizable PDEs from noisy datasets.
Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.