Compressive Transition Path Sampling

TL;DR

This paper introduces a novel approach using Compressed Sensing to efficiently reconstruct transition paths in rare event simulations, potentially enabling longer time-scale simulations in complex systems.

Contribution

It presents a formalism for applying Compressed Sensing to trajectory reconstruction, addressing under-sampling issues and enhancing simulation capabilities for rare events.

Findings

Formalism for CS-based trajectory reconstruction

Potential to significantly extend simulation time-scales

Discussion of implementation and challenges

Abstract

Algorithms for rare event complex systems simulations are proposed. Compressed Sensing (CS) has {\it revolutionized} our understanding of limits in signal recovery and has forced us to re-define Shannon-Nyquist sampling theorem for sparse recovery. A formalism to reconstruct trajectories and transition paths via CS is illustrated as proposed algorithms. The implication of under-sampling is quite important. This formalism could increase the tractable time-scales {\it immensely} for simulation of statistical mechanical systems and rare event simulations. While, long time-scales are known to be a major hurdle and a challenge for realistic complex simulations for rare events. The outline of how to implement, test and possible challenges on the proposed approach are discussed in detail.