Learning dynamics and convergence of machine learning driven neural ordinary differential equations model for housing price prediction

Traditional housing price prediction models often struggle to capture the complex dynamics of nonlinear and multi-scale time series. To address this challenge, this study proposes a machine learning–driven framework of neural ordinary differential equations (NODEs) designed to enhance both predictive accuracy and interpretability. The methodology integrates historical housing prices, macroeconomic indicators, and geospatial variables, with empirical mode decomposition (EMD) applied for multi-scale feature extraction. A dual-branch neural ODE architecture is developed: the main branch employs an adaptive gated GRU–ODE unit to model endogenous housing price dynamics, while the auxiliary branch fuses exogenous economic factors through time-varying convolution and attention mechanisms. At the theoretical level, a Lyapunov-based proof of convergence is derived, and an adaptive Hessian optimizer (AdaHessian) with Nesterov momentum is introduced to guarantee superlinear convergence. Experiments on the Zillow dataset (2004–2023) show that the proposed model achieves an RMSE of 0.03 for 12-month forecasts, converges within 200 epochs, and improves training stability with KL divergence reduced to 0.9. Beyond performance gains, the framework offers policy-relevant outputs, including long-horizon forecasts with uncertainty bounds, scenario analyses of macroeconomic shocks, and interpretable attribution of key drivers. These results confirm the framework's ability to capture the nonlinear continuous evolution of housing prices, while providing a scalable tool for spatiotemporal economic modeling with direct implications for policymakers, urban planners, and investors.