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A simultaneously accurate and computationally efficient parametrization ofthe energy and atomic forces of molecules and materials is a long-standing goalin the natural sciences. In pursuit of this goal, neural message passing haslead to a paradigm shift by describing many-body correlations of atoms throughiteratively passing messages along an atomistic graph. This propagation ofinformation, however, makes parallel computation difficult and limits thelength scales that can be studied. Strictly local descriptor-based methods, onthe other hand, can scale to large systems but do not currently match the highaccuracy observed with message passing approaches. This work introducesAllegro, a strictly local equivariant deep learning interatomic potential thatsimultaneously exhibits excellent accuracy and scalability of parallelcomputation. Allegro learns many-body functions of atomic coordinates using aseries of tensor products of learned equivariant representations, but withoutrelying on message passing. Allegro obtains improvements over state-of-the-artmethods on the QM9 and revised MD-17 data sets. A single tensor product layeris shown to outperform existing deep message passing neural networks andtransformers on the QM9 benchmark. Furthermore, Allegro displays remarkablegeneralization to out-of-distribution data. Molecular dynamics simulationsbased on Allegro recover structural and kinetic properties of an amorphousphosphate electrolyte in excellent agreement with first principlescalculations. Finally, we demonstrate the parallel scaling of Allegro with adynamics simulation of 100 million atoms.

Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics