Maximally predictive ensemble dynamics from data

  title={Maximally predictive ensemble dynamics from data},
  author={Antonio Carlos Costa and Tosif Ahamed and David J. Jordan and Greg J. Stephens},
We leverage the interplay between microscopic variability and macroscopic order to connect physical descriptions across scales directly from data, without underlying equations. We reconstruct a state space by concatenating measurements in time, building a maximum entropy partition of the resulting sequences, and choosing the sequence length to maximize predictive information. Trading non-linear trajectories for linear, ensemble evolution, we analyze reconstructed dynamics through transfer… 
Chaos as an interpretable benchmark for forecasting and data-driven modelling
  • W. Gilpin
  • Computer Science
    NeurIPS Datasets and Benchmarks
  • 2021
A growing database currently comprising 131 known chaotic dynamical systems spanning continents such as astro-physics, climatology, and biochemistry is presented, paired with precomputed multivariate and univariate time series.
Processive and Distributive Non-Equilibrium Networks Discriminate in Alternate Limits
This work shows that for a general class of proofreading networks, energetic discrimination requires processivity and kinetic discrimination requiring distributivity, and shows that mixed networks, in which one product is favored energetically and the other kinetically, are introduced.


Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems.
  • Cohen, Procaccia
  • Computer Science
    Physical review. A, General physics
  • 1985
There is not the slightest doubt that the prehistoric child had his head slapped for rattling mammoth's bones when his father was trying to sleep, but complaints against noise during the recognized sleeping hours have only come from the sick.
The Fundamental Role of Pirouettes in Caenorhabditis elegans Chemotaxis
It is suggested that chemotaxis is produced by a series of pirouettes that reorient the animal to the gradient, and the pirouette model of C. elegans chemot axis is sufficient and general.
Capturing the continuous complexity of behaviour in Caenorhabditis elegans
A data-driven framework based on theory of dynamical systems is applied to characterize nematode behaviour and explain its complexity through deterministic chaotic dynamics.
On the Approximation of Complicated Dynamical Behavior
We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai--Ruelle--Bowen
Statistically optimal almost-invariant sets
Chaos as an intermittently forced linear system
A universal, data-driven decomposition of chaos as an intermittently forced linear system is presented, combining delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates.
Relatively Coherent Sets as a Hierarchical Partition Method
An extension to generalize the concept to hierarchically define relatively coherent sets based on adjusting the finite time coherent sets to use relative measures restricted to sets which are developed iteratively and hierarchically in a tree of partitions is presented.
and G
  • J. 16 Stephens, Resolving coiled shapes reveals new reorientation behaviors in C. elegans, eLife 5(e17227)
  • 2016