To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity, making the solution of the parameter inverse problem from observed spatiotemporal data a challenging task. Starting from the observed data obtained from such systems, we propose a novel framework that facilitates the investigation of parameter identification for multi-state systems governed by spatiotemporal varying parametric partial differential equations. Our framework consists of two integral components: a constrained self-adaptive physics-informed neural networks, encompassing a sub-network, and a finite mixture model with Gaussian components, as our methodology for parameter identification and change-point detection. Through our scheme, we can accurately estimate the unknown varying parameters of the complex multi-state system. Furthermore, we have showcased the efficacy of our framework on two numerical cases: the 1D Burgers’ equation with time-varying parameters and the 2D wave equation with a space-varying parameter.