This paper proposes a mechanistically constrained, data-driven framework for subdiffusive anomalous diffusion modeling in heterogeneous media by integrating fractional differential equations with neural networks. A time-fractional diffusion model is first established for heterogeneous media, where a spatially varying diffusion coefficient characterizes medium heterogeneity. A joint learning architecture is then constructed, consisting of a state network that approximates the diffusion field and a parameter network that identifies unknown medium parameters. Observational data, governingequation residuals, and initial-boundary conditions are incorporated into a unified physics-informed loss function, enabling simultaneous field reconstruction and parameter identification. To handle the nonlocality of the fractional derivative, a history-dependent numerical discretization is employed and embedded into the neural-network training process. Numerical experiments show that the proposed method can accurately reconstruct anomalous diffusion fields under various heterogeneous settings, while effectively identifying spatially varying diffusion coefficients and fractional-order parameters. In addition, the framework maintains good robustness under sparse and noisy observations. These results indicate that the integration of fractional differential equations and neural networks provides an effective approach for the modeling and inversion of anomalous diffusion processes in heterogeneous media.

anomalous diffusion, heterogeneous media, fractional diffusion equation, neural networks