A Unified Framework of the Seonggil Field Equations and HJB Tensor PDEs for High-Dimensional Gene Regulatory Networks via scRNA-seq Integration
Year: 2026
Type: preprint
Abstract: 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.
Author: Lee, Seonggil
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7212454251
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