In the trend of hybrid Artificial Intelligence techniques, Physical-Informed Machine Learning has seen a growing interest. It operates mainly by imposing data, learning, or architecture bias with simulation data, Partial Differential Equations, or equivariance and invariance properties. While it has shown great success on tasks involving one physical domain, such as fluid dynamics, existing methods are not adapted to tasks with complex multi-physical and multi-domain phenomena. In addition, it is mainly formulated as an end-to-end learning scheme. To address these challenges, we propose to leverage Bond Graphs, a multi-physics modeling approach, together with Message Passing Graph Neural Networks. We propose a Neural Bond graph Encoder (NBgE) producing multi-physics-informed representations that can be fed into any task-specific model. It provides a unified way to integrate both data and architecture biases in deep learning. Our experiments on two challenging multi-domain physical systems - a Direct Current Motor and the Respiratory System - demonstrate the effectiveness of our approach on a multivariate time-series forecasting task.

翻译：在混合人工智能技术的发展趋势中，物理信息机器学习日益受到关注。其主要通过仿真数据、偏微分方程或等变性与不变性属性，施加数据、学习或架构偏置来实现。尽管该方法在涉及单一物理领域（如流体动力学）的任务上取得了巨大成功，但现有方法并不适用于具有复杂多物理场、多领域现象的任务。此外，该方法主要被表述为端到端的学习方案。为应对这些挑战，我们提出利用键合图（一种多物理场建模方法）与消息传递图神经网络相结合。我们提出了一种神经键合图编码器，该编码器可生成多物理场信息表征，并能馈入任何任务特定模型。它为在深度学习中统一整合数据和架构偏置提供了一种方法。我们在两个具有挑战性的多领域物理系统——直流电机与呼吸系统——上进行的实验，证明了我们的方法在多变量时间序列预测任务上的有效性。