Advanced Algorithms for Physics-Informed Neural Networks Reconstruction of Complex Flows

Reconstructing fluid mechanics problems from partial data is essential in science and engineering, especially regarding optimal design, biomedical and geophysical flows, parameter estimation, and more. These inverse problems are often ill-posed; thus, it’s challenging (sometimes even impossible) to solve them using traditional methods. Moreover, generating simulated data for ill-posed inverse problems can become very costly since simulations must be performed several times to either discover missing physics or calibrate the free parameters in the model. We’ll show a physics-informed neural network framework for reconstructing two examples of complex fluid mechanics problems: gravity currents and bubble dynamics. It reconstructs the other missing fields (velocity, pressure, etc.), given a set of sparse partial data, such as heavy fluid concentration in gravity currents or snapshots of the bubble position. We also discuss optimal sensor placement and dimensionality reduction for gravity current.