Abstract

Artificial Intelligence (AI) in the form of Machine Learning through Neural Networks is rapidly transforming the practice of scientific simulation in general, and Computational Fluid Dynamics (CFD) in particular. Of special importance to CFD is the subset known as Physics Informed Machine Learning (PIML). Since the first known use of neural networks to solve partial differential equations by Lagaris in 1998, there has been an exponential increase in applying neural networks to solve otherwise intractable partial differential equations.

The simplest approach is to use a meshless collocation method and determine the unknown coefficients of the neural network by minimizing the residual of the governing equations at the collocation points. However, this has many limitations. the preferred option now is that of Physics Informed Neural Network (PINN), also called Physics Informed Machine Learning (PIML). The first use of this technique was by Raissi et.al.(2017) and involved the joint use of data driven techniques and the governing equations. Now it appears more than likely that, for scientific computing, the PINN may take its place alongside the well-known methods such as the Finite Difference Method (FDM), the Finite Volume Method (FVM) and the Finite Element Method (FEM).

One major advantage of Neural Network is that, once trained, the neural network is quick to evaluate and is more compact in terms of storage than a typical numerical method. Another major advantage is that PINN predictions can be easily integrated with data generated from experimental studies and real time data obtained from actual operations of a prototype or a target system. Further, the neural network can be trained to modify its predictions based on real time data received, say, through IoT. This makes PINN very useful in solving inverse problems, uncertainty predictions and development of fast Surrogates or Digital Twins for a real system.

The PINN, applied to CFD, does have some shortcomings. The training process is usually very slow and computationally intensive. Further it is often sensitive to the network architecture. Also, currently PINN only takes the spatial coordinates of the collocation points and time as inputs. This implies that the PINN is trained for a specific boundary and initial condition, which restricts its use in practical systems. On the other hand, the field of research is extremely active and it is expected that these shortcomings can be overcome or minimized so as to provide a real alternative to established numerical methods.

The talk concludes with a case study to illustrate the use of PINN to solve a CFD application for a real life system.