Coverage-Controlled Adaptive Time Sampling

Use this as an inference-time controller for neural-ODE integration, latent-dynamics rollout, sensor acquisition, or teacher-forcing time selection. First train a base predictor normally and calibrate q, L_hat, and L_hat_pred as in the conformal tube method. Choose a safety threshold epsilon larger than q. Start with the available irregular observation times or with the endpoints of a rollout interval. For each interval [t_k,t_(k+1)], use the conservative radius q+Gamma(t_(k+1)-t_k)/2. If it exceeds epsilon, insert a midpoint, evaluate or integrate the model there, and repeat. A priority-queue implementation can always split the interval with the largest current bound. Pseudocode is: while max_interval_length > 2*(epsilon-q)/Gamma, split the longest interval; after each split, recompute local bounds if state-dependent slopes are used. The paper supplies the linear gap-inflation law and regularity-based guarantee; neural predictor slopes are estimated from adjacent solver evaluations. The first cheap experiment is a neural ODE pendulum or Lorenz predictor with fixed end-time accuracy, comparing uniform RK evaluation with adaptive splitting under randomly sampled observations. The predicted sharp signature is a refinement threshold h_c=2(epsilon-q)/Gamma: the maximum tube radius crosses epsilon when the largest gap crosses h_c, while adaptive sampling uses fewer evaluations than a uniform grid and preserves dense-grid coverage near the target level.