Topological Entropy Correlates with the Predictive Power of Multiplexed Ensemble Reservoir Computing.

Area of Science:

• Computational Biology
• Dynamical Systems Theory
• Machine Learning

Background:

• Modeling nonlinear, multiscale, and chaotic biological processes is challenging.
• Traditional deep learning models require large datasets and lack interpretability for time-resolved biological systems.
• Standard reservoir computing (RC) architectures struggle with high-dimensional biological data and complex temporal regimes.

Purpose of the Study:

• Introduce Dynamical System Machine Learning (DynML), a novel multiplexed reservoir framework.
• Address limitations of existing models in capturing complex biological dynamics.
• Unify biological time-series modeling and conventional machine learning tasks.

Main Methods:

• DynML utilizes heterogeneous Lorenz reservoirs to encode biological signals.
• A single global readout captures stage-dependent dynamics.
• Reservoir topological entropy is used to predict model performance.

Main Results:

• DynML accurately models gene-expression dynamics in liver regeneration and *Drosophila* embryogenesis.
• Reservoir topological entropy quantitatively predicts biological forecasting accuracy.
• DynML demonstrates generality on MNIST handwritten digit classification using a Rossler-based chaotic reservoir.

Conclusions:

• DynML provides a scalable, interpretable, and computationally efficient framework.
• The framework unifies biological time-series modeling and machine learning.
• DynML leverages dynamical systems for advanced computational biology applications.