The hard-constraint PINNs for interface optimal control problems

Lai MC, Song Y, Yuan X, Yue H, Zeng T (2024)

Publication Language: English

Publication Status: In review

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

URI: https://arxiv.org/abs/2308.06709

Abstract

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations (PDEs) with interfaces and some control constraints.

The resulting algorithm is mesh-free and scalable to different PDEs, and it ensures the control constraints rigorously.

Since the boundary and interface conditions, as well as the PDEs, are all treated as soft constraints by lumping them into a weighted loss function, it is necessary to learn them simultaneously and there is no guarantee that the boundary and interface conditions can be satisfied exactly.

This immediately causes difficulties in tuning the weights in the corresponding loss function and training the neural networks.

To tackle these difficulties and guarantee the numerical accuracy, we propose to impose the boundary and interface conditions as hard constraints in PINNs by developing a novel neural network architecture.

The resulting hard-constraint PINNs approach guarantees that both the boundary and interface conditions can be satisfied exactly and they are decoupled from the learning of the PDEs.

Its efficiency is promisingly validated by some elliptic and parabolic interface optimal control problems.

Authors with CRIS profile

Yongcun Song Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Nankai University (NKU) / 南开大学 CN China (CN) University of Hong Kong (HKU) / 香港大學 HK Hong Kong (HK) National Yang Ming Chiao Tung University TW Taiwan (TW)

How to cite

APA:

Lai, M.-C., Song, Y., Yuan, X., Yue, H., & Zeng, T. (2024). The hard-constraint PINNs for interface optimal control problems. (Unpublished, In review).

MLA:

Lai, Ming-Chih, et al. The hard-constraint PINNs for interface optimal control problems. Unpublished, In review. 2024.

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