Activation function trade-offs for training efficiency of Physics-Informed Neural Networks used in solving 1D Burgers’ Equation
Analyzing the impact of the choice of adaptive activation function on the speed and accuracy of generating PDE solutions using PINNs
R. Mihail (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jing Sun – Mentor (TU Delft - Pattern Recognition and Bioinformatics)
A. Heinlein – Mentor (TU Delft - Numerical Analysis)
Tie-xing Wang – Mentor
H.S. Hung – Graduation committee member (TU Delft - Pattern Recognition and Bioinformatics)
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Abstract
Physics-Informed Neural Networks(PINNs) have emerged as a potent, versatile solution to solving both forward and inverse problems regarding partial differential equations(PDEs), accomplished through integrating laws of physics into the learning process. The applications of this new approach are endless, as these types of equations appear across numerous fields: fluids mechanics, quantum mechanics, electrochemistry and many others. Ever since their conception, researchers have continuously improved the flexibility and performance of PINNs through advancements in the architecture of neural networks, optimization algorithms, creative sampling methods and many more. As computational power and the interest of researchers grow, the revolutionary potential of PINNs is closer to fulfillment than ever. This paper aims to examine a small part of this evolutionary process, specifically the performance and flexibility of different activation functions used in the training of the PINN, as well as potential problems this approach could solve.