Can I read Revising the Structure of Recurrent Neural Networks to Eliminate Numerical Derivatives in Forming Physics Informed Loss Terms with Respect to Time on EtoBox?

Revising the Structure of Recurrent Neural Networks to Eliminate Numerical Derivatives in Forming Physics Informed Loss Terms with Respect to Time by Jahani-nasab, Mahyar; Bijarchi, Mohamad Ali is a scholarly article available to read on EtoBox.

What is Revising the Structure of Recurrent Neural Networks to Eliminate Numerical Derivatives in Forming Physics Informed Loss Terms with Respect to Time about?

Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the complexities of numerical derivatives into the training process of these models. In this study, we propose modifying the structure of the traditional RNN to enable the prediction of each block over a time interval, making it possible to calculate the derivative of the output with respect to time using the backpropagation algorithm. To achieve this, the time intervals of these blocks are overlapped, defining a mutual loss function between them. Additionally, the employment of conditional hidden states enables us to achieve a unique solution for each block. The forget factor is utilized to control the influence of the conditional hidden state on the prediction of the subsequent block. This new model, termed the Mutual Interval RNN (MI-RNN), is applied to solve three different benchmarks: the Burgers equation, unsteady heat conduction in an irregular domain, and the Green vortex problem. Our results demonstrate that MI-RNN can find the exact solution

Author

Jahani-nasab, Mahyar; Bijarchi, Mohamad Ali

Published

2024

Language

EN