2 papers
math.NA2024
Sequential data assimilation for PDEs using shape-morphing solutions
Zachary T. Hilliard, Mohammad Farazmand
Shape-morphing solutions (also known as evolutional deep neural networks, reduced-order nonlinear solutions, and neural Galerkin schemes) are a new class of methods for approximati…
math.NA2023
Enforcing conserved quantities in Galerkin truncation and finite volume discretization
Zachary T. Hilliard, Mohammad Farazmand
Finite-dimensional truncations are routinely used to approximate partial differential equations (PDEs), either to obtain numerical solutions or to derive reduced-order models. The…