Real-Time Causal Dynamics on Geometric Latent Spaces for Precision Therapeutic Monitoring

Despite impact in early-stage drug discovery, the exploration of artificial intelligence in therapeutic drug monitoring, a key bottleneck in patient care, has remained limited. We present Real-Time Causal Geometric Flows (RT-CGF), a geometry-aware, causal, and adaptive framework for therapeutic drug monitoring of narrow-therapeutic-index drugs, addressing a longstanding gap in translating from discovery to deployment. Unlike traditional models that rely on fixed, population-level dynamics, RT-CGF redefines TDM as a dynamical system on learned Finsler manifolds, where pharmacokinetic trajectories evolve as geodesics under patient-specific geometric constraints. This previously unexplored formulation enables real-time adaptation to physiological shifts (e.g, acute kidney injury) while preserving causal invariance. Extending stochastic intervention calculus for continuous-time counterfactuals and persistent homology regularization for topological consistency, RT-CGF achieves fewer dosing errors and improved AUC in adverse event detection on representative clinical datasets. Beyond its methodological novelty, RT-CGF introduces an interesting possibility for precision medicine by harmonizing Finsler-geometric dynamical systems, counterfactual reasoning, and persistent homology constraints, a convergence that transcends the limitations of static, population-level models to enable adaptive, patient-specific policy frameworks with implications for safety, assurance and regulation efforts for digital drug development.