Pierre-Yves Richard

Alexis-Raja Brachet, Pierre-Yves Richard, Céline Hudelot

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.

Alexis-Raja Brachet, Pierre-Yves Richard, Céline Hudelot

While boundaries between data modalities are vanishing, the usual successful deep models are still challenged by simple ones in the time-series forecasting task. Our hypothesis is that this task needs models that are able to learn the data underlying dynamics. We propose to validate it through both systemic and empirical studies. We develop an original $\texttt{PRO-DYN}$ nomenclature to analyze existing models through the lens of dynamics. Two observations thus emerged: $\textbf{1}$. under-performing architectures learn dynamics at most partially, $\textbf{2}$. the location of the dynamics block at the model end is of prime importance. We conduct extensive experiments to confirm our observations on a set of performance-varying models with diverse backbones. Results support the need to incorporate a learnable dynamics block and its use as the final predictor.