  Dosing models often use differential equations to model biological dynamics.
Neural differential equations in particular can learn to predict the derivative
of a process, which permits predictions at irregular points of time. However,
this temporal flexibility often comes with a high sensitivity to noise, whereas
medical problems often present high noise and limited data. Moreover, medical
dosing models must generalize reliably over individual patients and changing
treatment policies. To address these challenges, we introduce the Neural Eigen
Stochastic Differential Equation algorithm (NESDE). NESDE provides
individualized modeling (using a hypernetwork over patient-level parameters);
generalization to new treatment policies (using decoupled control); tunable
expressiveness according to the noise level (using piecewise linearity); and
fast, continuous, closed-form prediction (using spectral representation). We
demonstrate the robustness of NESDE in both synthetic and real medical
problems, and use the learned dynamics to publish simulated medical gym
environments.
