  Modeling nonlinear spatiotemporal dynamical systems has primarily relied on
partial differential equations (PDEs). However, the explicit formulation of
PDEs for many underexplored processes, such as climate systems, biochemical
reaction and epidemiology, remains uncertain or partially unknown, where very
limited measurement data is yet available. To tackle this challenge, we propose
a novel deep learning architecture that forcibly encodes known physics
knowledge to facilitate learning in a data-driven manner. The coercive encoding
mechanism of physics, which is fundamentally different from the penalty-based
physics-informed learning, ensures the network to rigorously obey given
physics. Instead of using nonlinear activation functions, we propose a novel
elementwise product operation to achieve the nonlinearity of the model.
Numerical experiment demonstrates that the resulting physics-encoded learning
paradigm possesses remarkable robustness against data noise/scarcity and
generalizability compared with some state-of-the-art models for data-driven
modeling.
