Simulating extrapolated dynamics with parameterization networks

TL;DR

This paper introduces parameterization networks, a neural network architecture designed to accurately simulate and extrapolate the long-term behavior of dynamical systems beyond observed data, demonstrated on the logistic map.

Contribution

The paper presents a novel neural network architecture that maintains the integrity of extrapolated dynamics and controls overfitting, enabling better long-term simulation of nonlinear systems.

Findings

Successfully extrapolated chaotic and nonlinear phenomena from non-chaotic training data

Demonstrated the approach on the logistic map with high fidelity

Extrapolation is more effective when learning occurs at a higher level of abstraction

Abstract

An artificial neural network architecture, parameterization networks, is proposed for simulating extrapolated dynamics beyond observed data in dynamical systems. Parameterization networks are used to ensure the long term integrity of extrapolated dynamics, while careful tuning of model hyperparameters against validation errors controls overfitting. A parameterization network is demonstrated on the logistic map, where chaos and other nonlinear phenomena consistent with the underlying model can be extrapolated from non-chaotic training time series with good fidelity. The stated results are a lot less fantastical than they appear to be because the neural network is only extrapolating between quadratic return maps. Nonetheless, the results do suggest that successful extrapolation of qualitatively different behaviors requires learning to occur on a level of abstraction where the corresponding behaviors are more similar in nature.