Physiologically Aware Flow Matching: Jacobian Constraints for Dose-Consistent Forecasting

Accurate forecasts under observed treatment plans do not guarantee physiologically consistent responses to altered ones: state-dependent dosing couples treatment to patient state, so models trained on such records learn associations that contradict physiology. We introduce Physiologically Aware Flow Matching (PAFM), a conditional flow-matching framework for probabilistic forecasting under planned treatments. PAFM regularizes the Jacobian of the velocity field with respect to pharmacokinetically smoothed treatment drivers, with physiological priors specifying the sign of each sensitivity and a band for its magnitude. The penalty is evaluated at sampled flow states and operates without a mechanistic outcome model or rollouts under alternative plans. We develop autoregressive (AR-PAFM) and joint-horizon (JH-PAFM) formulations, which constrain sensitivities at individual forecast steps and across forecast positions respectively, and evaluate both on two simulated closed-loop benchmarks. On glucose, every unregularized model integrates a glucose-raising response to added insulin; the penalty restores near-perfect directional and dose-ordering consistency in both formulations, and JH-PAFM achieves lower mean RMSE than all regularized baselines. On mean arterial pressure, both formulations reach full directional and dose-ordering consistency under propofol and norepinephrine infusions, with JH-PAFM lower than AR-PAFM in mean RMSE and calibration error.