  Including covariant information, such as position, force, velocity or spin is
important in many tasks in computational physics and chemistry. We introduce
Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise
equivariant graph networks, such that node and edge attributes are not
restricted to invariant scalars, but can contain covariant information, such as
vectors or tensors. This model, composed of steerable MLPs, is able to
incorporate geometric and physical information in both the message and update
functions. Through the definition of steerable node attributes, the MLPs
provide a new class of activation functions for general use with steerable
feature fields. We discuss ours and related work through the lens of
equivariant non-linear convolutions, which further allows us to pin-point the
successful components of SEGNNs: non-linear message aggregation improves upon
classic linear (steerable) point convolutions; steerable messages improve upon
recent equivariant graph networks that send invariant messages. We demonstrate
the effectiveness of our method on several tasks in computational physics and
chemistry and provide extensive ablation studies.
