Bond Graphs for multi-physics informed Neural Networks for multi-variate time series

TL;DR

This paper introduces a novel approach combining Bond Graphs with Graph Neural Networks to improve multi-physics modeling in multi-variate time series forecasting, addressing limitations of existing physics-informed neural networks.

Contribution

It proposes a Neural Bond Graph Encoder that integrates multi-physics knowledge into deep learning models for complex multi-domain systems.

Findings

Effective forecasting on DC Motor and Respiratory System datasets.

Unified framework for data and architecture biases in multi-physics modeling.

Improved performance over traditional physics-informed neural networks.

Abstract

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.