Data-driven reconstruction of spatiotemporal phase dynamics for traveling and oscillating patterns via Bayesian inference

TL;DR

This paper introduces a Bayesian inference-based data-driven method to reconstruct spatiotemporal phase dynamics of traveling and oscillating patterns in reaction-diffusion systems, validated on Gray-Scott models.

Contribution

It develops a novel approach that directly reconstructs phase equations from time-series data, extending phase reduction theory with data-driven techniques.

Findings

Accurately reconstructs deterministic phase equations from simulation data.

Works effectively in weak-noise regimes with stable fixed points.

Demonstrates applicability to Gray-Scott reaction-diffusion models.

Abstract

Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns. Spatiotemporal phase dynamics are described by spatial and temporal phases that represent the position and oscillation of the pattern, respectively. Using Bayesian inference, our method directly reconstructs phase equations from time-series data. When tested on simulation data from coupled Gray-Scott models exhibiting traveling breathers, the method accurately reconstructs the deterministic part of the phase equations in the weak-noise regime, in which the phase dynamics converge to a linearly stable fixed point.