Deep learning of free boundary and Stefan problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:428

Article

Wang, Sifan¹  Perdikaris, Paris² 

[1] Univ Penn, Grad Grp Appl Math & Computat Sci, Philadelphia, PA 19104 USA

[2] Univ Penn, Dept Mech Engn & Appl Mech, Philadelphia, PA 19104 USA

关键词: Physics-informed neural networks;    Phase transitions;    Partial differential equations;    Scientific machine learning;   

DOI  :  10.1016/j.jcp.2020.109914

来源: Elsevier

【 摘 要 】

Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free