Porous media seminar series

About the event

Porous Media Seminar Series: Physics-informed deep neural network (DNN) method for solving inverse problems and learning unknown physics

Presented by: Dr. Alexandre Tartakovsky, Lab Fellow, Mathematician at Pacific Northwest National Lab

When: March 6, 2020 4:10

Where: SPARK 212, Zoom: 221-746-3531

Abstract:

I will describe a physics-informed deep neural network (DNN) method for solving inverse partial differential equation (PDE) problems and learning unknown physics. I will consider several applications, including the estimation of hydraulic conductivity from a tracer test and learning constitutive relationships from unsaturated flow experiments.

In the parameter estimation problem, we use the flow and advection-dispersion equations in addition to the measurements of hydraulic conductivity, head, and concentration to train DNNs representing the hydraulic conductivity, head, and concentration fields. For learning unknown pressure-conductivity relationship, we use measurements of capillary pressure and the Richards equation to train DNNs representing the unsaturated conductivity function and capillary pressure. Since it is difficult to measure unsaturated conductivity in the field, we assume that no measurements of unsaturated conductivity are available.

The proposed approach enforces PDE constraints by minimizing the PDE residuals at select points in the simulation domain. We demonstrate that physics constraints increase the accuracy of DNN approximations of sparsely observed functions and allow for training DNNs when no direct measurements of the functions of interest are available. For the saturated conductivity estimation problem, we show that the physics-informed DNN method is more accurate than the state-of-the-art maximum a posteriori probability method. For the unsaturated flow in homogeneous porous media, we find that the proposed method can accurately estimate the pressure-conductivity relationship based on the capillary pressure measurements only, even in the presence of measurement noise.