2023/03/13 by Nacime Bouziani, David A. Ham, Bouziani, Nacime +1 · 1 citation
Computer Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Mathematical Software (cs.MS) #Model Reduction and Neural Networks #Modeling and Simulation Systems #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2303.06871
openalex publication_date 2023/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Partial differential equations (PDEs) are central to describing and modelling complex physical systems that arise in many disciplines across science and engineering. However, in many realistic applications PDE modelling provides an incomplete description of the physics of interest. PDE-based machine learning techniques are designed to address this limitation. In this approach, the PDE is used as an inductive bias enabling the coupled model to rely on fundamental physical laws while requiring less training data. The deployment of high-performance simulations coupling PDEs and machine learning to complex problems necessitates the composition of capabilities provided by machine learning and PDE-based frameworks. We present a simple yet effective coupling between the machine learning framework PyTorch and the PDE system Firedrake that provides researchers, engineers and domain specialists with a high productive way of specifying coupled models while only requiring trivial changes to existing code.