Adaptive simplification of complex multiscale systems

TL;DR

This paper introduces an adaptive method for simplifying large multiscale dissipative systems by constructing hierarchies of slow invariant manifolds, enabling accurate reduced descriptions of complex dynamics.

Contribution

It presents a novel, fully adaptive approach for systematically reducing complex multiscale systems using hierarchies of slow invariant manifolds, with simple implementation across dimensions.

Findings

Validated on hydrogen-air auto-ignition system

Achieved reduction to cascade of slow invariant manifolds

Demonstrated accurate reduced system dynamics

Abstract

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics. Accurate reduced description is achieved, by construction of a hierarchy of slow invariant manifolds, with an embarrassingly simple implementation in any dimension. The method is validated with the auto-ignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observed.