Short Description

Physics-informed neural networks (PINNs) use ordinary or partial differential equations (DEs) to regularize classical supervised network training. The resulting network, which takes spatiotemporal coordinates at its input and responds with state variables of the considered system under investigation, thus approximates the solution function of the DE. As such, PINNs can be used for both solving DEs (when initial and boundary conditions are given as data points) and for inverse problems (where the parameters of the DE shall be inferred from simulation or measurement data).

The field of physics-informed machine learning, to which PINNs belong, is claimed to achieve higher accuracy with less data and less computational costs than classical, supervised learning approaches. The aim of this project is to assess this claim for PINNs. On the one hand, the physics-informed regularization term requires additional computations. Furthermore, this regularization term increases the complexity of the learning problem, often resulting in a larger number of epochs required for convergence. On the other hand, the provision of physics information can result in improved accuracy in both interpolation as well as extrapolation settings. In summary, the exact interplay between accuracy, data requirements, and computational training effort for PINNs is not entirely clear.

Your Tasks

• Review the current literature on the energy-performance trade-off of PINNs
• Identify a set of ordinary and partial DEs for representative experiments
• Investigate the trade-offs between accuracy (in interpolation/extrapolation settings), data requirements, and computational training costs (number of epochs until convergence, number of FLOPS per epoch, etc.) for a variety of training hyperparameters (number of collocation points, regularization parameters, network architectures, etc.)

Your Profile

• Good mathematical skills; prior knowledge in differential equations is beneficial
• Interest and profound knowledge in deep learning
• Practical experience in deep learning frameworks (TensorFlow, PyTorch)

Contact

Bernhard Geiger (geiger@tugraz.at)