FD-Net with Auxiliary Time Steps: Fast Prediction of PDEs using Hessian-Free Trust-Region Methods
This work addresses the challenge of modeling complex physical systems in engineering, but it appears incremental as it builds on existing neural network and optimization methods without claiming major breakthroughs.
The study tackled the problem of learning hidden partial differential equations from data to predict future dynamics, proposing a finite-difference inspired convolutional neural network that predicts evolution with few parameters and comparing second-order TRCG with first-order ADAM optimizers for efficiency.
Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate future dynamical behavior. The methodology designs the filter sizes such that they mimic the finite difference between the neighboring points. By learning the governing equation, the network predicts the future evolution of the solution by using only a few trainable parameters. In this paper, we provide numerical results to compare the efficiency of the second-order Trust-Region Conjugate Gradient (TRCG) method with the first-order ADAM optimizer.