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The temporal dynamics of integrated silicon resonators has been modeled usinga set of equations coupling the internal energy, the temperature and the freecarrier population. Owing to its simplicity, Newton's law of cooling is thetraditional choice for describing the thermal evolution of such systems. Inthis work, we theoretically and experimentally prove that this can beinadequate in monolithic planar devices, leading to inaccurate predictions. Anew equation, that we train to reproduce the correct temperature behaviour, isintroduced to fix the discrepancies with the experimental results. We discussthe limitations and the range of validity of our refined model, identifyingthose cases where Netwon's law provides, nevertheless, accurate solutions. Ourmodeling describes the phenomena underlying thermal and free carrierinstabilities, and is a valuable tool for the engineering of photonic systemswhich relay on resonator dynamical states, such as all optical spiking neuralnetworks or reservoirs for neuromorphic computing.

On the modeling of thermal and free carrier nonlinearities in Silicon On Insulator microring resonators