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Stochastic cloning of dynamical systems with hidden variables
Andrey V Andreev1, Alexander N Pisarchik2, Nikita Kulagin1
1Immanuel Kant Baltic Federal University, Baltic Center for Neurotechnology and Artificial Intelligence, Kaliningrad 236041, Russia.
Physical Review. E
|August 19, 2025
Summary
This study introduces a novel method combining reservoir computing and nonlinear dynamics to predict stochastic systems. It differentiates between strong (exact) and weak (statistical) prediction, showing strong prediction requires a deterministic link between external noise and system response.
Area of Science:
- Physics
- Computer Science
- Mathematics
Background:
- Stochastic systems present challenges in prediction due to inherent randomness and potential unobserved dynamics.
- Reservoir computing (RC) offers a framework for time-series prediction, but its application to partially observed stochastic systems is complex.
- Understanding the conditions for accurate system replication is crucial for advancing predictive modeling.
Purpose of the Study:
- To develop and validate an approach combining reservoir computing and nonlinear dynamics for replicating stochastic system behavior.
- To systematically investigate the conditions enabling "strong" (exact trajectory) versus "weak" (statistical) system cloning.
- To leverage external noise excitation as a tool for inferring hidden dynamics in complex systems.
Main Methods:
- Combining reservoir computing principles with nonlinear dynamics analysis.
- Utilizing external noise excitation to probe system responses and infer hidden states.
- Systematically evaluating the relationship between external noise and system output to determine cloning strength.
- Testing the approach on the FitzHugh-Nagumo neuron model and a diode-pumped erbium-doped fiber laser.
Main Results:
- Demonstrated the feasibility of the combined approach both theoretically and experimentally.
- Established that "strong" cloning is achievable only when a deterministic functional relationship exists between external noise and system response.
- Successfully constructed a "strong" clone for the FitzHugh-Nagumo neuron model, enabling accurate dynamics prediction.
- Achieved only a "weak" clone for the fiber laser system, providing statistical prediction capabilities.
Conclusions:
- The proposed method effectively replicates stochastic system behavior, with cloning strength dependent on underlying system dynamics.
- External noise excitation is a viable technique for uncovering hidden dynamics and assessing predictability.
- Highlights the potential of integrating machine learning (reservoir computing) with nonlinear dynamics for advanced system identification and prediction in diverse scientific fields.
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