  Machine learning methods can be a valuable aid in the scientific process, but
they need to face challenging settings where data come from inhomogeneous
experimental conditions. Recent meta-learning methods have made significant
progress in multi-task learning, but they rely on black-box neural networks,
resulting in high computational costs and limited interpretability. Leveraging
the structure of the learning problem, we argue that multi-environment
generalization can be achieved using a simpler learning model, with an affine
structure with respect to the learning task. Crucially, we prove that this
architecture can identify the physical parameters of the system, enabling
interpreable learning. We demonstrate the competitive generalization
performance and the low computational cost of our method by comparing it to
state-of-the-art algorithms on physical systems, ranging from toy models to
complex, non-analytical systems. The interpretability of our method is
illustrated with original applications to physical-parameter-induced adaptation
and to adaptive control.
