PISI: Physical Information Based Solver-Interactive Network Structure Reconstruction

Inference of the interactive network structure of the physical world that is captured by nonlinear dynamic systems is a long-standing goal for machine learning. Existing inference methods have shown limited incorporation of physical system information and solver interaction capabilities. We present a comprehensive Physical Information based Solver-Interactive (PISI) network structure identification framework that incorporates network topology, physical constraints, and bidirectional solver interaction in nonlinear dynamical systems. To this end, we first develop a physical information-based graphical neural network (PIGNN). The PIGNN cells are embedded as the basic integration units to iterative interact with dynamical solver. The dynamical systems’s physical information can be flexibly added to the iterative interaction for PIGNN training. The above stages are trained end-to-end using a Runge–Kutta solver. The network structure inferring capability of the proposed framework is demonstrated through two kuramoto systems. Our PISI methodology, integrating graph topology, physical constraints, and solver interactivity shows advantages in trajectory prediction and structure reconstruction compared to state-of-the-art methods.