Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm
The paper explores whether Physics-Informed Neural Networks (PINNs) require deep architectures by introducing shallow models using the Levenberg–Marquardt algorithm. The research addresses both forward and inverse problems across various benchmark equations like Burgers and Schrödinger. Results showed that this approach is highly efficient, with the LM algorithm significantly outperforming BFGS in speed and final loss values.