CFD, AI and Machine
Learning
Akshai K. Runchal
Madhukar M. Rao & Rajagopal Pachalla
CFD Virtual Reality Institute
Analytic & Computational Research, Inc
runchal@ACRiCFD.com
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.