Hard Encoding of Physics for Learning Spatiotemporal Dynamics
This addresses the problem of modeling complex systems like climate or epidemiology with scarce data and uncertain physics, offering a novel approach that is not incremental but introduces a new encoding mechanism.
The authors tackled the challenge of modeling spatiotemporal dynamics with limited data and uncertain physics by proposing a deep learning architecture that forcibly encodes known physics, ensuring rigorous adherence. The method demonstrated robustness against data noise/scarcity and improved generalizability compared to state-of-the-art models.
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.