The Williams GTDR Formula: A Gauss-TaylorDerivative Reconstruction Integrator for Low-NFEContinuous-Time Machine Learning
Year: 2026
Type: preprint
Abstract: We introduce the Williams GTDR Formula (Gauss-Taylor Derivative Reconstruction Integrator), an explicit numerical integrator for ordinary differential equations (ODEs) achieving third-order local accuracy with only 3 function evaluations per step. A Romberg extrapolation patch raises the scheme to effective fourth-order accuracy, matching classical Runge-Kutta 4 (RK4) while reducing per-step function evaluations by 25%. In Neural ODEs and score-based diffusion models, each function evaluation is a full neural network forward pass — making evaluation count the dominant computational cost. Benchmarks confirm 25–33% NFE reduction versus RK4 at equivalent accuracy, with a clear implementation path in existing Neural ODE and diffusion model frameworks.
Author: OCHIENG, WILLIAMS
Institution: Kenyatta University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166339757
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