物理法則に基づく深層学習モデルPINNsによる流体運動の順・逆解析

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  • Physics-Informed Neural Networks for Forward and Inverse Problems of Fluid Dynamics

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<p>Due to severe tsunami damage caused by 2011 off the Pacific coast of Tohoku Earthquake and recent torrential rain disasters occurring in various places, the demand for predictive simulation technology have been rapidly growing. For disaster predictions, one needs to perform large-scale and high-resolution simulations which require highly expensive computational costs. Several approximation techniques have been developed to avoid them; however, many parameters are often determined based on empirical laws and approximated simulation could still be consuming considerable costs. In this context, this work presents the application of a class of neural networks, PINNs (Physics-Informed Neural Networks) to both forward and inverse problems. The characteristic of PINNs is its predictions of physical quantities of interest are guaranteed by physical laws, initial, or boundary conditions. This is because it forms the loss function as a combination of predictive and physical loss. Predictive loss is the difference between the ground truth and PINNs prediction, while physical loss is defined as how much PINNs prediction satisfies the governing equations and physical conditions. This paper investigates PINNs applicability by introducing a hyper parameter (weighting factor) to control the effect of predictive and physical loss and demonstrates its performance through numerical examples. Results suggest physical loss-weighted training is much more effective than predictive loss-weighted learning for both forward and inverse problems, especially when training data is corrupted with arbitrary noise.</p>

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