  In this work, we introduce multi-Novikov algebras, a generalisation of
Novikov algebras with several binary operations indexed by a given set, and
show that the multi-indices recently introduced in the context of singular
stochastic partial differential equations can be interpreted as free
multi-Novikov algebras. This is parallel to the fact that decorated rooted
trees arising in the context of regularity structures are related to free
multi-pre-Lie algebras.
