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.

翻译：偏微分方程（PDE）是描述和建模科学与工程多学科中复杂物理系统的核心工具。然而，在许多实际应用中，PDE建模仅能提供对目标物理过程的不完整描述。基于PDE的机器学习技术旨在解决这一局限性，其通过将PDE作为归纳偏置，使耦合模型在依赖基本物理定律的同时，减少对训练数据的需求。将高性能PDE与机器学习耦合的仿真应用于复杂问题，需要整合机器学习框架与PDE求解系统的能力。我们提出了一种简单而有效的耦合方法，将机器学习框架PyTorch与PDE系统Firedrake相结合，为研究人员、工程师和领域专家提供了一种高效指定耦合模型的途径，且仅需对现有代码进行微小的改动。