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Partial differential equations (PDEs) are central to describing and modellingcomplex physical systems that arise in many disciplines across science andengineering. However, in many realistic applications PDE modelling provides anincomplete description of the physics of interest. PDE-based machine learningtechniques are designed to address this limitation. In this approach, the PDEis used as an inductive bias enabling the coupled model to rely on fundamentalphysical laws while requiring less training data. The deployment ofhigh-performance simulations coupling PDEs and machine learning to complexproblems necessitates the composition of capabilities provided by machinelearning and PDE-based frameworks. We present a simple yet effective couplingbetween the machine learning framework PyTorch and the PDE system Firedrakethat provides researchers, engineers and domain specialists with a highproductive way of specifying coupled models while only requiring trivialchanges to existing code.

Physics-driven machine learning models coupling PyTorch and Firedrake