Neural ODE
Simulates how a tumor responds to treatment over time
Fit to patient-derived xenograft growth curves
Fast emulator matches numerical solver
No NaN/Inf in 10,000 simulations
Single trajectory inference time
Predictions that violate biological constraints
Overview
A physics-based simulation — like the equations that describe population dynamics in ecology — but parameterized individually for each patient. It models tumor growth, drug effect, and immune response as competing forces over time. Given a patient's parameters and a treatment schedule, it simulates what happens over the next 12-18 months: when does the tumor respond, when does resistance emerge, and through which mechanism. Supports sequential treatments, combinations, and pulsed chemotherapy schedules.
Inputs
5 inputsN0[K]Initial clone populations
rho[K]Clone growth rates
beta[K, D]Drug sensitivity coefficients
omega[1]Immune killing coefficient
treatment_schedule[T, D]Drug dosing over time
Outputs
3 outputstrajectory[T, K]Clone populations over time
tumor_burden[T]Total tumor burden over time
clone_fractions[T, K]Relative clone proportions
Mathematical Formulation
Lotka-Volterra with drug and immune effects
Immune effector cell dynamics
Backward sensitivity for gradients
Key Features
- Lotka-Volterra competition dynamics
- Drug effect as multiplicative kill term
- Immune effect as predator-prey interaction
- Dopri5 adaptive solver
- Adjoint method for O(1) memory backprop
Key Innovations
- 1Interpretable ODE dynamics with biological meaning
- 2Treatment schedule integration in continuous time
- 3Stable numerical integration with adaptive stepping
- 4Gradient computation without storing full trajectory
Hyperparameters
Dopri5 (adaptive RK4/5)1e-51e-610,000True1e-6Training Details
ODE parameters come from Hypernet. Neural ODE is differentiable end-to-end via adjoint sensitivity. Trained jointly with Hypernet using survival and trajectory losses.