Maximally predictive states: from partial observations to long timescales
arXiv:2105.12811 · doi:10.1063/5.0129398
Abstract
Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally-predictive states by concatenating measurements in time, partitioning the resulting sequences using maximum entropy, and choosing the sequence length to maximize short-time predictive information. Transitions between these states yield a simple approximation of the transfer operator, which we use to reveal timescale separation and long-lived collective modes through the operator spectrum. Applicable to both deterministic and stochastic processes, we illustrate our approach through partial observations of the Lorenz system and the stochastic dynamics of a particle in a double-well potential. We use our transfer operator approach to provide a new estimator of the Kolmogorov-Sinai entropy, which we demonstrate in discrete and continuous-time systems, as well as the movement behavior of the nematode worm .
arXiv comment22 pages, 14 figures
References in corpus (23)
- Scikit-learn: Machine Learning in Python
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Identification of slow molecular order parameters for Markov model construction
- Chaos as an Intermittently Forced Linear System
- Ergodic theory, Dynamic Mode Decomposition and Computation of Spectral Properties of the Koopman operator
- Entropy estimation of symbol sequences
- Data-driven model reduction and transfer operator approximation
- Transport in time-dependent dynamical systems: Finite-time coherent sets
- On the numerical approximation of the Perron-Frobenius and Koopman operator
- Coherent sets for nonautonomous dynamical systems
- Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
- Estimating good discrete partitions from observed data: symbolic false nearest neighbors
- Parameter Estimation for Multiscale Diffusions
- Inferring the dynamics of underdamped stochastic systems
- Delay-coordinate maps and the spectra of Koopman operators
- Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics
- Violation of detailed balance accelerates relaxation
- Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics
- Building general Langevin models from discrete data sets
- Kernel-based Prediction of Non-Markovian Time Series
- Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems
- Nonequilibrium Statistical Mechanics and Optimal Prediction of Partially-Observed Complex Systems
- Recurrent Neural Networks for Partially Observed Dynamical Systems