  We combine hydrodynamic and modulated energy techniques to study the large
deviations of systems of particles with pairwise singular repulsive
interactions and additive noise. In particular, we consider periodic Riesz
interactions indexed by parameter $\mathbf{s}\in[0,d-2)$ for $d\geq 3$ on the
torus. When $\mathbf{s}=0$, that is, when the interaction potential is
logarithmic, we establish a full LDP for the empirical trajectories of the
particles given sufficiently strong convergence of the initial conditions. When
$\mathbf{s}\in(0,d-2)$, we give an LDP upper bound and partial lower bounds.
Additionally, we show a local LDP holds in a stronger distance.
