An extended physics informed neural network for preliminary analysis of parametric optimal control problems
This work addresses efficiency issues in simulating parametrized phenomena for applications like optimal control, but it appears incremental as it builds on existing physics informed learning strategies.
The authors tackled the computational expense of parametric partial differential equations in real-time and many-query settings by proposing an extended physics informed neural network, resulting in faster training and more accurate parametric predictions.
In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally expensive most of all in a real-time and many-query setting. Thus, our main goal is to provide a physics informed learning paradigm to simulate parametrized phenomena in a small amount of time. The physics information will be exploited in many ways, in the loss function (standard physics informed neural networks), as an augmented input (extra feature employment) and as a guideline to build an effective structure for the neural network (physics informed architecture). These three aspects, combined together, will lead to a faster training phase and to a more accurate parametric prediction. The methodology has been tested for several equations and also in an optimal control framework.