A Direct Method Approach for Data-Driven Inference of High Accuracy Adaptive Phase-Isostable Reduced Order Models

Phase-amplitude reduction techniques have shown great promise for identifying analytically tractable reduced order models in applications involving strongly perturbed and strongly coupled oscillatory dynamical systems. However, efficient methods for inference of these reduced order models from data are still needed. In this work, a data-driven strategy for inference of the necessary terms comprising an adaptive phase-isostable reduced order model is proposed. This strategy requires no more data than the well-established direct method used for obtaining standard phase reduced models, i.e., the application of a series of pulse inputs and the subsequent examination of the relaxation to the underlying limit cycle. Illustrative examples are provided for a collection of numerical models where the resulting adaptive phase-isostable reduced order equations are substantially more accurate than models obtained using standard phase reduction.(c) 2023 Elsevier B.V. All rights reserved.