Title : Using Graduated Optimization to Improve Solution of Physics Informed Neural Network in Non-Linear Two Phase Flow Through Porous Media
Machine Learning models are often used to make inferences on data that originate from some physical phenomena. For such applications, we might want the inferences to follow the laws of physics. Physics-informed neural networks (PINN) provide us with a mechanism to incorporate physical constraints on the data in the form of differential equations. In this work, we study the use of pins in the field of Reservoir Simulation particularly in solving the arguably canonical Buckley Leverette equation for nonlinear two-phase flow through porous media. Related work attempting to solve this equation using PINNs could not solve this equation as it belongs to the class of hyperbolic partial differential equations, which contains discontinuities in the solution. The discontinuity in the solution gives rise to a highly non-convex loss landscape for PINN, and so any second-order quasi-newton optimization method would get stuck in a local minimum and fail to find a good solution unless there is a very good initialization. We solve this problem using graduated optimization and show that adding a diffusion term in the Buckley Leverette equation helps us generate a tuneable smooth loss landscape. Our method was able to provide better initialization for PINN, which in term was able to find a better solution to the Buckley Leverette equation as compared to the original PINN optimization.
Audience Take Away:
- Making predictions on the behavior of a Reservoir is of great value. The audience will learn a mechanism by which physically correct predictions about a Reservoir can be made from noisy data.
- Learn how such predictions can be made even for complex problems involving hyperbolic partial differential equations.
- This will provide an example where we make a time-series prediction of a reservoir based on historical data to maximize oil production.