Model Predictive Control for Adaptive Weighting in Physics Informed Neural Network Training

Sammanfattning

Physics informed neural networks (PINNs) combine data driven learning with known physical equations and have shown promising results in modeling physical systems with limited data. However, the training of PINNs can be sensitive to the weighting of the loss terms. For the physics based loss term it can be particularly crucial when the underlying physical model is uncertain. This thesis investigates the potential to use Model Predictive Control (MPC) to control the weighting of the cost function’s physics based loss term. To do this, an MPC controller and a PINN was constructed in the Python programming language using SciPy and TensorFlow along with Numpy. Then the MPC controller was incorporated into the training process by periodically updating the physics loss weight. This was tested on simulated data. The results indicated that the MPC controlled PINN showed increased robustness when compared to the ’vanilla’ PINN. However, it also exhibited higher variance across the training runs compared to the vanilla and simpler control strategies. These findings highlight both the potential and some of the limitations of MPC controlled PINN training and motivate further research into reducing variability and alternative control strategies for PINN training.