Core Concepts
Discovering slow invariant manifolds using a physics-informed neural network approach.
Abstract
A physics-informed neural network (PINN) method is proposed to approximate slow invariant manifolds (SIMs) for stiff systems of ODEs. Unlike traditional methods, this approach decomposes the vector field into fast and slow components simultaneously, providing explicit SIM functionals. The PINN framework is evaluated on benchmark problems like Michaelis-Menten and TMDD mechanisms, outperforming other GSPT methods. By solving the invariance equation within GSPT using symbolic differentiation, the PINN scheme offers accurate SIM approximations close to boundaries. The paper discusses the methodology's advantages over traditional model reduction techniques and data-driven ML approaches.
Stats
The PINN framework is assessed via three benchmark problems.
500 points per trajectory were recorded for analysis.
ϵrel = 0.05 and ϵabs = 10^-10 were used as criteria for identifying periods with constant M.