Atoms rearrange themselves during materials synthesis; understanding this self-organization choreography would help the design of novel synthesis recipes. Yet, the mechanisms of such phase transformations are often governed by statistically improbable atomic transitions - known as rare events - that are challenging to investigate by direct, brute-force sampling with conventional atomistic simulations. The transition-state theory framework has been successfully applied for numerous rare-event sampling techniques, which require prior knowledge of reaction coordinates to be encoded in a committor function. Here we show how E(3)-equivariant graph neural networks can be used to simultaneously learn physically appropriate reaction coordinates and committors, solely from molecular dynamics simulations near the start and end states of a reaction. This approach is applied to two dramatically different systems and associated mechanisms, namely the conformational transition in a alanine dipeptide molecule and the solid-liquid transition in the solidification of the CrFeNi metallic alloy. We demonstrated that this approach reduces the need for human intervention in designing reaction coordinates and committor functions, which may enable the high-throughput study of transition states.