Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems

Understand

We develop a physics-informed machine learning approach for large-scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two-dimensional steady-state subsurface flow model of the Hanford Site given synthetic measurements of said variables.

• In our approach, we extend the physics-informed conditional Karhunen-Lo\'{e}ve expansion (PICKLE) method for modeling subsurface flow with unknown flux (Neumann) and varying head (Dirichlet) boundary conditions.
• We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large-scale problems.
• Both methods use a mesh to discretize the computational domain.