  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.
