MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling

• URL: http://arxiv.org/abs/2304.14422v2
• Date: Thu, 30 Jan 2025 10:34:10 GMT
• Title: MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling
• Authors: Yicun Huang, Changfu Zou, Yang Li, Torsten Wik,
• Abstract summary: We propose a novel machine learning architecture, termed model-integrated neural networks (MINN) MINN learns the physics-based dynamics of general autonomous or non-autonomous systems consisting of partial differential-algebraic equations (PDAEs) We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries.
• Score: 2.1303885995425635
• License:
• Abstract: 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 generalizability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in modeling real-world dynamic systems for optimization and control purposes. We propose a novel machine learning architecture, termed model-integrated neural networks (MINN), that can learn the physics-based dynamics of general autonomous or non-autonomous systems consisting of partial differential-algebraic equations (PDAEs). The obtained architecture systematically solves an unsettled research problem in control-oriented modeling, i.e., how to obtain optimally simplified models that are physically insightful, numerically accurate, and computationally tractable simultaneously. We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries and show that MINN is extremely data-efficient to train while being sufficiently generalizable to previously unseen input data, owing to its underlying physical invariants. The MINN battery model has an accuracy comparable to the first principle-based model in predicting both the system outputs and any locally distributed electrochemical behaviors but achieves two orders of magnitude reduction in the solution time.

Related papers

• Adapting Physics-Informed Neural Networks to Improve ODE Optimization in Mosquito Population Dynamics [0.019972837513980313]
  We propose a PINN framework with several improvements for forward and inverse problems for ODE systems. The framework tackles the gradient imbalance and stiff problems posed by mosquito ordinary differential equations. Preliminary results indicate that physics-informed machine learning holds significant potential for advancing the study of ecological systems.
  arXiv  Detail & Related papers  (2024-06-07T17:40:38Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems [0.0]
  We propose a physics-guided hybrid approach for modeling non-autonomous systems under control. This is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy. Experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model.
  arXiv  Detail & Related papers  (2022-04-27T14:33:02Z)
• EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
  We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting. We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
  arXiv  Detail & Related papers  (2022-02-21T18:59:03Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Neural ODE and DAE Modules for Power System Dynamic Modeling [2.342020413587919]
  In practical power systems, dynamic component modeling has long faced the challenges of model determination and model calibration. In this paper, based on the general framework of neural ordinary differential equations (ODEs), a modified neural ODE module and a neural differential-algebraic equations (DAEs) module for power system dynamic component modeling are proposed. The modules adopt an autoencoder to raise the dimension of state variables, model the dynamics of components with artificial neural networks (ANNs) and keep the numerical integration structure.
  arXiv  Detail & Related papers  (2021-10-25T14:15:45Z)
• Integrating Electrochemical Modeling with Machine Learning for Lithium-Ion Batteries [0.0]
  This paper presents a new approach to integrate a physics-based model with machine learning to achieve high-precision modeling for lithium-ion batteries (LiBs) We propose two hybrid physics-machine learning models based on the approach, which blend a single particle model with thermal dynamics (SPMT) with a feedforward neural network (FNN) to perform physics-informed learning of a LiB's dynamic behavior.
  arXiv  Detail & Related papers  (2021-03-22T04:53:38Z)
• Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling [86.9726984929758]
  We focus on the integration of incomplete physics models into deep generative models. We propose a VAE architecture in which a part of the latent space is grounded by physics. We demonstrate generative performance improvements over a set of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-02-25T20:28:52Z)
• Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics [3.214927790437842]
  Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. Our findings are of interest for model-based control and system identification of mechanical systems.
  arXiv  Detail & Related papers  (2020-05-29T15:10:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.