A Unified Framework of the Seonggil Field Equations and HJB Tensor PDEs for High-Dimensional Gene Regulatory Networks via scRNA-seq Integration

This paper presents a unified geometric control framework for high-dimensional gene regulatory networks, bridging rigorous theoretical physics with practical Cellular Control Therapeutics. We integrate the Seonggil Field Equations with a stochastic Hamilton-Jacobi Bellman (HJB) tensor PDE on a Riemannian manifold. To directly apply this theoretical PDE to empirical single- cell RNA sequencing (scRNA-seq) datasets, we overcome the destructive measurement limitations of scRNA-seq by replacing point-to-point trajectory tracking with a distribution-matching paradigm. Utilizing a Deep Forward-Backward StochasticDifferential Equation (FBSDE) architecture combined with a Multi-scale Maximum Mean Discrepancy (MMD) Hybrid Loss, we enable the optimal transport and control of cellular populations towards healthy states. The complete theoretical derivation and its PyTorch pipeline are provided.