Local Equivariant Representations for Large-Scale Atomistic Dynamics | S. Batzner and A. Musaelian

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Paper “Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics”: arxiv.org/abs/2204.05249
Abstract: A simultaneously accurate and computationally efficient parametrization of the energy and atomic forces of molecules and materials is a long-standing goal in the natural sciences. In pursuit of this goal, neural message passing has lead to a paradigm shift by describing many-body correlations of atoms through iteratively passing messages along an atomistic graph. This propagation of information, however, makes parallel computation difficult and limits the length scales that can be studied. Strictly local descriptor-based methods, on the other hand, can scale to large systems but do not currently match the high accuracy observed with message passing approaches. This work introduces Allegro, a strictly local equivariant deep learning interatomic potential that simultaneously exhibits excellent accuracy and scalability of parallel computation. Allegro learns many-body functions of atomic coordinates using a series of tensor products of learned equivariant representations, but without relying on message passing. Allegro obtains improvements over state-of-the-art methods on the QM9 and revised MD-17 data sets. A single tensor product layer is shown to outperform existing deep message passing neural networks and transformers on the QM9 benchmark. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Molecular dynamics simulations based on Allegro recover structural and kinetic properties of an amorphous phosphate electrolyte in excellent agreement with first principles calculations. Finally, we demonstrate the parallel scaling of Allegro with a dynamics simulation of 100 million atoms.
Authors: Albert Musaelian, Simon Batzner, Anders Johansson, Lixin Sun, Cameron J. Owen, Mordechai Kornbluth, Boris Kozinsky
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The confusion about the message passing (ref slide at 56:30 time stamp) happened because the presenters failed to communicate that Y_{i, k} is constant, irrespective of the number of layers. Only different tunable weights (W_{i, k}) are introduced in each layer. So in each passing the GPU doesn't need to communicate with other GPUs to get the updated value of Y's, and h_{i, j} is already available in the local GPU.