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Area of Science:

  • Physical Systems Analysis
  • Computational Physics
  • Time Series Modeling

Background:

  • Continuous natural systems evolve through space and time.
  • Hidden Markov models (HMMs), developed for discrete data, are widely used for time series analysis in physical systems.
  • The application of discrete frameworks to continuous data raises interpretability questions.

Purpose of the Study:

  • To investigate the implications of using discrete-time, discrete-state Hidden Markov Models (HMMs) for analyzing data from continuously evolving physical systems.
  • To determine the conditions under which HMMs provide interpretable results for physical systems.
  • To explore the influence of measurement protocols and modeling choices on HMM inference.

Main Methods:

  • Generation of synthetic data using Langevin dynamics in an effective potential.
  • Analysis of synthetic data using Hidden Markov Models (HMMs).
  • Exploration of how data acquisition schemes affect HMM-recovered states.

Main Results:

  • The discrete-state approximation in HMMs acts as an abstraction, with inferred states often reflecting modeling choices rather than underlying physical potential features.
  • HMM-inferred states can be manipulated by adjusting the data acquisition scheme.
  • Misleadingly reproducible intermediate states can be recovered even for systems in a single potential well.

Conclusions:

  • HMMs offer an elegant mathematical framework for time series inference but require cautious application in physical modeling due to inherent limitations.
  • Awareness of HMM limitations is crucial for accurate physical interpretation.
  • Generalizations of HMMs to continuous space and time, alongside robust measurement noise modeling, are important for physical systems.