46 citations · 46 across the 4 of their papers we have counts for
4 papers
DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems
Craig R. Gin, Daniel E. Shea, Steven L. Brunton +1
Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge i…
Deep Learning Models for Global Coordinate Transformations that Linearize PDEs
Craig Gin, Bethany Lusch, Steven L. Brunton +1
We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE. Our architecture is motivated by the…
Stability Results on Radial Porous Media and Hele-Shaw Flows with Variable Viscosity Between Two Moving Interfaces
Craig Gin, Prabir Daripa
We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results i…
Time-dependent injection strategies and interfacial stability in multi-layer Hele-Shaw and porous media flows
Craig Gin, Prabir Daripa
We study the stability of multi-layer radial flows in porous media within the Hele-Shaw model. We perform a linear stability analysis for radial flows consisting of an arbitrary nu…