Abstract: When modeling dynamical systems from real-world data samples, the
distribution of data often changes according to the environment in which they
are captured, and the dynamics of the system itself vary from one environment
to another. Generalizing across environments thus challenges the conventional
frameworks. The classical settings suggest either considering data as i.i.d.
and learning a single model to cover all situations or learning
environment-specific models. Both are sub-optimal: the former disregards the
discrepancies between environments leading to biased solutions, while the
latter does not exploit their potential commonalities and is prone to scarcity
problems. We propose LEADS, a novel framework that leverages the commonalities
and discrepancies among known environments to improve model generalization.
This is achieved with a tailored training formulation aiming at capturing
common dynamics within a shared model while additional terms capture
environment-specific dynamics. We ground our approach in theory, exhibiting a
decrease in sample complexity with our approach and corroborate these results
empirically, instantiating it for linear dynamics. Moreover, we concretize this
framework for neural networks and evaluate it experimentally on representative
families of nonlinear dynamics. We show that this new setting can exploit
knowledge extracted from environment-dependent data and improves generalization
for both known and novel environments.