Changfu Zou - Physics-based ML

Physics-Based Machine Learning: Methodology and Application

[1] Huang, Y., Zou, C. Li, Y., & Wik, T. (2023). MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling. arXiv:2304.14422 [PDF]. Received the Best Presentation Award of the 2022 International Conference on Energy and AI.

A Python tutorial about PINN and MINN is given at [Link].

The concept of integrating physics-based and data-driven approaches has become popular for modeling sustainable energy systems. However, the existing literature mainly focuses on the data-driven surrogates generated to replace physics-based models. These models often trade accuracy for speed but lack the generalisability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in the modeling of real-world dynamic systems for optimization and control purposes. In this work, we propose a novel architecture for generating model-integrated neural networks (MINN) to allow integration on the level of learning physics-based dynamics of a general system consisting of differential-algebraic equations. The obtained architecture systematically solves an unsettled research problem in control-oriented modeling, i.e., how to obtain an optimally simplified model that is physically insightful, numerically accurate, and computationally tractable simultaneously.

Existing physics-based integration strategies for the blending of neural networks and physics-based models in order to retain their individual merits. (a) A data-driven surrogate model using supervised learning requires relevant and representative training data generated by snapshots of the physics-based model solutions. (b) A surrogate model regularised physical constraints within the PINN framework, of which the PINN loss is composed of the loss due to model-data inconsistency and the loss owing to physical constraints. (c) The PINN workflow for inverse problems used to identify physical parameters as part of parametric PDEs.

The proposed MINN architecture for dynamic systems. (a) An iterative update of the hidden states, output, and conserved quantities is controlled by input u(t) at time t through physics-based hidden units. The time stepping is adaptive to the dynamics thanks to a skipping mechanism via the numerical solver. (b) The design of a physics-based hidden unit contains physics-based equations, a deep learning-enabled function G_NN and an output function Y.

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