Data-Driven Inference of Susceptibility, Correlation, and Dynamic Responses via Machine Learning

Understanding how complex systems respond to external perturbations is essential to characterize the intrinsic properties of the systems and then to control their responses. Despite some preliminary trials via either analytical modeling or numerical calculations, it is usually difficult to directly calculate the responses of complex systems (with high degrees of freedom) to strong perturbations. Here, we propose a flexible and data-driven protocol based on neural networks, allowing us to infer the responses of complex systems from collected data, while seamlessly incorporating prior physical knowledge to ensure consistency with underlying laws. We validate this protocol using four representative examples, by calculating susceptibility in ϕ4 theory, N-point correlation function of homopolymers, dynamic response function of homopolymer blends, and Jacobian matrix for determining the stability of the Duffing system, from the data generated by numerical calculations or simulations. In all cases, the inferred responses are consistent with theoretical results, without imposing analytical approximations used to derive the reference solutions. These examples demonstrate the applicability of the proposed protocol for extracting response functions in diverse physical systems and provide a basis for its extension to related problems in other research fields.