[論文レビュー] A Dynamical Microscope for Multivariate Oscillatory Signals: Validating Regime Recovery on Shared Manifolds

Łukasz Furman, Ludovico Minati+1 more|arXiv (Cornell University)|Feb 11, 2026

Neural Networks and Reservoir Computing被引用数 0

ひとこと要約

trajectory-centric framework (dynamical microscope) を提案し、 multichannel signals を circular phase–amplitude features に符号化し、autoencoder で latent trajectories を学習し、shared manifold 上の flow および幾何学で regime を定量化する； topology-switching Stuart–Landau oscillator によって検証。

ABSTRACT

Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts multichannel signals into circular phase--amplitude features, learns a data-driven latent trajectory representation with an autoencoder, and quantifies dynamical regimes through trajectory geometry and flow field metrics. Using a coupled Stuart--Landau oscillator network with topology-switching as ground-truth validation, we demonstrate that the framework recovers differences in dynamical laws even when regimes occupy overlapping regions of state space. Group differences can be expressed as changes in latent trajectory speed, path geometry, and flow organization on a shared manifold, rather than requiring discrete state separation. Speed and explored variance show strong regime discriminability ($η^2 > 0.5$), while some metrics (e.g., tortuosity) capture trajectory geometry orthogonal to topology contrasts. The framework provides a principled approach for analyzing regime structure in multivariate time series from neural, physiological, or physical systems.

研究の動機と目的

• Motivate a trajectory-centric view of multivariate oscillatory signals and metastability beyond discrete state labels.
• Develop a circular phase–amplitude representation and a latent-trajectory autoencoder for continuous dynamics.
• Define and compute flow-field and geometric trajectory metrics (speed, variance, tortuosity, occupancy, divergence, curl).
• Validate regime recovery under topology-switching in a ground-truth coupled Stuart–Landau oscillator network.
• Assess metric discriminability of regime differences and discuss implications for neural, physiological, or physical data.

提案手法

• Encode multichannel signals as circular phase–amplitude features per channel.
• Learn a continuous latent trajectory h(t) via an autoencoder without regime labels.
• Estimate a 2D flow field from latent trajectories and compute velocity-based metrics.
• Compute intrinsic metrics in full latent space (speed, speed CV, tortuosity, explored variance, occupancy entropy, divergence, curl).
• Validate with topology-switching Stuart–Landau oscillators (global, cluster, sparse, ring) across 160 s, with ground-truth regime labels for visualization only.
• Perform one-way ANOVA across regimes to assess discriminability using eta-squared (η2).

Figure 1 : Workflow schematic of the dynamical microscope framework. Multichannel oscillatory signals are transformed into circular phase–amplitude features, encoded into a latent trajectory via autoencoder, and analyzed using flow field estimation and trajectory metrics. The depicted “trajectory” i

実験結果

リサーチクエスチョン

• RQ1 Can regime differences be recovered when regimes occupy overlapping regions of state space (shared manifold)?
• RQ2 Which trajectory-based metrics (speed, variance, geometry, flow) best discriminate coupling topologies?
• RQ3 Do flow-field patterns provide regime-specific information beyond occupancy or discrete states?
• RQ4 How does kinetic-energy-like intermittency relate to regime differences across topologies?

主な発見

Metric	F-statistic	p-value	η²
Mean Speed	67.8	4.2×10^-30	0.509
Explored Variance	70.3	6.7×10^-31	0.518
Tortuosity	0.61	0.61	0.009

• Speed and explored variance show strong regime discriminability with η2 > 0.5.
• Latent kinetic energy captures complementary intermittency with η2 = 0.21.
• Tortuosity shows negligible discriminability for this topology-contrast scenario (η2 ≈ 0.009).
• Regimes occupy overlapping regions in the latent space, but flow-field patterns reveal coherent directional differences.
• Regime-specific flow metrics (curl/divergence) differentiate topologies even on a shared manifold.
• Global coupling yields fastest, most exploratory dynamics; ring coupling yields slowest, most confined dynamics.

Figure 2 : Raw observations from coupled oscillator simulation. Top: multichannel time series (selected channels) showing regime switches as vertical dashed lines. Middle: power spectral density (mean across channels) with characteristic oscillator peak. Bottom: Hilbert amplitude envelope (channel 0