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

arXiv: https://arxiv.org/abs/2405.13586 · HTML: https://mlsanity.com/paper/2405.13586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Protein Representation Learning by Geometric Structure Pretraining](https://mlsanity.com/paper/2203.06125/) (2022)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting](https://mlsanity.com/paper/2211.02989/) (2022)
- [Equivariant Message Passing Neural Network for Crystal Material Discovery](https://mlsanity.com/paper/2302.00485/) (2023)

## Abstract (arXiv)

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.