Domain-Decoupled Physics-informed Neural Networks with Closed-Form Gradients for Fast Model Learning of Dynamical Systems

Henrik Krauss, Henrik Krauss, Tim-Lukas Habich, Max Bartholdt, Thomas Seel, Moritz Schappler

2024

Abstract

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate un-modeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction speed compared to classical numerical integration methods for nonlinear state-space models, making them suitable for real-time control applications. We introduce the domain-decoupled physics-informed neural network (DD-PINN) to address current limitations of PINC in handling large and complex nonlinear dynamical systems. The time domain is decoupled from the feed-forward neural network to construct an Ansatz function, allowing for calculation of gradients in closed form. This approach significantly reduces training times, especially for large dynamical systems, compared to PINC, which relies on graph-based automatic differentiation. Additionally, the DD-PINN inherently fulfills the initial condition and supports higher-order excitation inputs, simplifying the training process and enabling improved prediction accuracy. Validation on three systems – a nonlinear mass-spring-damper, a five-mass-chain, and a two-link robot – demonstrates that the DD-PINN achieves significantly shorter training times. In cases where the PINC’s prediction diverges, the DD-PINN’s prediction remains stable and accurate due to higher physics loss reduction or use of a higher-order excitation input. The DD-PINN allows for fast and accurate learning of large dynamical systems previously out of reach for the PINC.

Paper Citation

in Harvard Style

Krauss H., Habich T., Bartholdt M., Seel T. and Schappler M. (2024). Domain-Decoupled Physics-informed Neural Networks with Closed-Form Gradients for Fast Model Learning of Dynamical Systems. In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-717-7, SciTePress, pages 55-66. DOI: 10.5220/0012935200003822

in Bibtex Style

@conference{icinco24,
author={Henrik Krauss and Tim-Lukas Habich and Max Bartholdt and Thomas Seel and Moritz Schappler},
title={Domain-Decoupled Physics-informed Neural Networks with Closed-Form Gradients for Fast Model Learning of Dynamical Systems},
booktitle={Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2024},
pages={55-66},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012935200003822},
isbn={978-989-758-717-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Domain-Decoupled Physics-informed Neural Networks with Closed-Form Gradients for Fast Model Learning of Dynamical Systems
SN - 978-989-758-717-7
AU - Krauss H.
AU - Habich T.
AU - Bartholdt M.
AU - Seel T.
AU - Schappler M.
PY - 2024
SP - 55
EP - 66
DO - 10.5220/0012935200003822
PB - SciTePress