  Kernel-based machine learning approaches are gaining increasing interest for
exploring and modeling large dataset in recent years. Gaussian process (GP) is
one example of such kernel-based approaches, which can provide very good
performance for nonlinear modeling problems. In this work, we first propose a
grey-box modeling approach to analyze the forces in cross country skiing races.
To be more precise, a disciplined set of kinetic motion model formulae is
combined with data-driven Gaussian process regression model, which accounts for
everything unknown in the system. Then, a modeling approach is proposed to
analyze the kinetic flow of both individual and clusters of skiers. The
proposed approaches can be generally applied to use cases where positioned
trajectories and kinetic measurements are available. The proposed approaches
are evaluated using data collected from the Falun Nordic World Ski
Championships 2015, in particular the Men's cross country $4\times10$ km relay.
Forces during the cross country skiing races are analyzed and compared.
Velocity models for skiers at different competition stages are also evaluated.
Finally, the comparisons between the grey-box and black-box approach are
carried out, where the grey-box approach can reduce the predictive uncertainty
by $30\%$ to $40\%$.
