We study stochastic interacting particle methods with and without field coupling for high dimensional concentration and singularity formation phenomena. In case of entropy production of reverse-time diffusion processes, the method computes concentrated invariant measures mesh-free up to dimension 16 at a linear complexity rate based on solving a principal eigenvalue problem of non-self-adjoint advection-diffusion operators. In case of fully parabolic chemotaxis nonlinear dynamics in 3D, the method captures critical mass for finite time singularity formation and blowup time at low costs through a smoother field without relying on self-similarity.