  Dynamics of coarse-grained particle systems derived via the Mori-Zwanzig
projection formalism commonly take the form of a (generalized) Langevin
equation with configuration-dependent friction and diffusion tensors. In this
article, we introduce a class of equivariant representations of tensor-valued
functions based on the Atomic Cluster Expansion (ACE) framework that allows for
efficient learning of such configuration-dependent friction and diffusion
tensors from data. Besides satisfying the correct equivariance properties with
respect to the Euclidean group E(3), the resulting heat bath models satisfy a
fluctuation-dissipation relation. Moreover, our models can be extended to
include additional symmetries, such as momentum conservation, to preserve the
hydrodynamic properties of the particle system. We demonstrate the capabilities
of the model by constructing a model of configuration-dependent tensorial
electronic friction calculated from first principles that arises during
reactive molecular dynamics at metal surfaces.
