Shamsulhaq Basir 

Scientific Machine Learning for Transport Phenomena in Thermal and Fluid Sciences

ABSTRACT: 

Physics-informed neural networks (PINNs) have become popular as part of the rapidly expanding deep learning field in recent years. However, their origins date back to the early 1990s, when neural networks were adopted as meshless numerical methods to solve partial differential equations (PDEs). PINNs incorporate known physics into the objective function as a regularization term, necessitating hyperparameter tuning to ensure convergence. However, lack of a validation dataset or a priori knowledge of the solution can make PINNs impractical. Moreover, learning inverse problems with multi-fidelity data is difficult since it can lead to overfitting noise or underfitting high-fidelity data. To overcome these obstacles, this dissertation introduces physics and equality constrained artificial neural networks (PECANNs) as a deep learning framework for forward and inverse PDE problems with multi-fidelity data fusion. The backbone of this framework is a constrained optimization formulation that embeds governing equations along with low- and high-fidelity data in a principled fashion using an adaptive augmented Lagrangian method. Additionally, the framework is extended to learn the solution of large-scale PDE problems through a novel Schwarz-type domain decomposition method with a generalized Robin-type interface condition. The efficacy and versatility of the PECANN approach are demonstrated by solving several challenging forward and inverse PDE problems that arise in thermal and fluid sciences.

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Meeting ID: 282 607 4340