Data-driven reconstruction of spatiotemporal phase dynamics for traveling and oscillating patterns via Bayesian inference
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917437402775552 |
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| author | Arai, Takahiro Aoyagi, Toshio Kawamura, Yoji |
| author_facet | Arai, Takahiro Aoyagi, Toshio Kawamura, Yoji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23727 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-driven reconstruction of spatiotemporal phase dynamics for traveling and oscillating patterns via Bayesian inference Arai, Takahiro Aoyagi, Toshio Kawamura, Yoji Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability 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. |
| title | Data-driven reconstruction of spatiotemporal phase dynamics for traveling and oscillating patterns via Bayesian inference |
| topic | Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2604.23727 |