Deep learning of free boundary and Stefan problems

Wang, Sifan; Perdikaris, Paris

doi:10.1016/j.jcp.2020.109914

Deep learning of free boundary and Stefan problems

Journal Article · Thu Oct 15 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109914· OSTI ID:1852840

Wang, Sifan ^[1]; ^[2]

Univ. of Pennsylvania, Philadelphia, PA (United States). Graduate Group in Applied Mathematics and Computational Science; Univ. of Pennsylvania, Philadelphia, PA (United States)
Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Mechanichal Engineering and Applied Mechanics

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: SC0019116

OSTI ID:: 1852840

Alternate ID(s):: OSTI ID: 1775916
OSTI ID: 23203467

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 428; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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