Abstract Hydraulic axial turbines are more frequently utilized for grid regulation purposes. Sometimes, they must be operated at Speed-No-Load (SNL) conditions, which for some machines is characterized by a varying number of large vortical flow structures extending from the vaneless space to the draft tube. In the current study, the configuration varies between two and three vortices, introducing detrimental pressure pulsations throughout the turbine. A recent study shows that the vortices can be mitigated by individually controlling the guide vanes. Since optimization of the distributor layout is linked with a large degree of freedom, machine learning is deployed to find the optimal setup cost-effectively. A reduced numerical Computational-Fluid-Dynamics (CFD) model is built and used to generate input for Gaussian process regression surrogate models by performing 2000 steady-state simulations with varying distributor layouts. The surrogate models predict that the optimal layout is to open seven out of 20 guide vanes in succession while keeping the remaining ones closed. However, detailed time-dependent CFD simulations show that placing opened guide vanes on opposite sides of the runner axis is better; it reduces the pressure amplitude peaks corresponding to a two- and three-vortex configuration, and the maximal pressure pulsations by as much as 88% in the vaneless space compared to regular SNL operation. Meanwhile, the radial force on the runner and pressure pulsations on the runner blades are reduced by more than 83% and 55%, respectively, compared to deploying the surrogate models' optimal layout prediction.