Piecewise integrable neural network: An interpretable chaos identification framework

Artificial Neural Networks (ANNs) are an effective data-driven approach to model chaotic dynamics. Although ANNs are universal approximators which easily incorporate mathematical structure, physical information and constrains, they are scarcely interpretable. Here we develop a neural network framework in which the chaotic dynamics is reframed into piecewise models. The discontinuous formulation defines switching laws representative of the bifurcations mecha- nisms, providing to recover the system of differential equations and its primitive (or integral) which describe the chaotic regime.