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Alzheimer's disease (AD) is a heterogeneous, multifactorial neurodegenerative disorder characterized by beta-amyloid, pathologic tau, and neurodegeneration. There are no effective treatments for Alzheimer's disease at a late stage, urging for early intervention. However, existing statistical inference approaches of AD subtype identification ignore the pathological domain knowledge, which could lead to ill-posed results that are sometimes inconsistent with the essential neurological principles. Integrating systems biology modeling with machine learning, we propose a novel pathology steered stratification network (PSSN) that incorporates established domain knowledge in AD pathology through a reaction-diffusion model, where we consider non-linear interactions between major biomarkers and diffusion along brain structural network. Trained on longitudinal multimodal neuroimaging data, the biological model predicts long-term trajectories that capture individual progression pattern, filling in the gaps between sparse imaging data available. A deep predictive neural network is then built to exploit spatiotemporal dynamics, link neurological examinations with clinical profiles, and generate subtype assignment probability on an individual basis. We further identify an evolutionary disease graph to quantify subtype transition probabilities through extensive simulations. Our stratification achieves superior performance in both inter-cluster heterogeneity and intra-cluster homogeneity of various clinical scores. Applying our approach to enriched samples of aging populations, we identify six subtypes spanning AD spectrum, where each subtype exhibits a distinctive biomarker pattern that is consistent with its clinical outcome. PSSN provides insights into pre-symptomatic diagnosis and practical guidance on clinical treatments, which may be further generalized to other neurodegenerative diseases.