  Near the limits of adhesion, the forces generated by a tire are nonlinear and
intricately coupled. Efficient and accurate modelling in this region could
improve safety, especially in emergency situations where high forces are
required. To this end, we propose a novel family of tire force models based on
neural ordinary differential equations and a neural-ExpTanh parameterization.
These models are designed to satisfy physically insightful assumptions while
also having sufficient fidelity to capture higher-order effects directly from
vehicle state measurements. They are used as drop-in replacements for an
analytical brush tire model in an existing nonlinear model predictive control
framework. Experiments with a customized Toyota Supra show that scarce amounts
of driving data -- less than three minutes -- is sufficient to achieve
high-performance autonomous drifting on various trajectories with speeds up to
45mph. Comparisons with the benchmark model show a $4 \times$ improvement in
tracking performance, smoother control inputs, and faster and more consistent
computation time.
