Scaling up Deep Learning for PDE-based Models

Philipp Haehnel
Trinity College Dublin
School of Mathematics

Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using PDE solvers. Thereby, the uses were limited to domains, where the PDE solver was applicable, but no further. We present methods for training a deep-learning model on small domains, while applying the trained models on larger domains, with consistency constraints ensuring that the solutions are physically meaningful across the boundaries of the small domains. We demonstrate the results on an air-pollution forecasting model for Dublin, Ireland.

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