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Discovering mathematical models that characterize the observed behavior ofdynamical systems remains a major challenge, especially for systems in achaotic regime. The challenge is even greater when the physics underlying suchsystems is not yet understood, and scientific inquiry must solely rely onempirical data. Driven by the need to fill this gap, we develop a frameworkthat learns mathematical expressions modeling complex dynamical behaviors byidentifying differential equations from noisy and sparse observable data. Wetrain a small neural network to learn the dynamics of a system, its rate ofchange in time, and missing model terms, which are used as input for a symbolicregression algorithm to autonomously distill the explicit mathematical terms.This, in turn, enables us to predict the future evolution of the dynamicalbehavior. The performance of this framework is validated by recovering theright-hand sides and unknown terms of certain complex, chaotic systems such asthe well-known Lorenz system, a six-dimensional hyperchaotic system, and thenon-autonomous Sprott chaotic system, and comparing them with their knownanalytical expressions.

AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression