FlashCart: Fast Cartesian Tensor Products for Equivariant Interatomic Potentials

2026-10-05

AI Summary

This study addresses the limitation imposed by the high computational cost of equivariant architectures on the accuracy of interatomic potentials by proposing an efficient simulation method that recursively constructs and compresses equivariant features. By introducing Cartesian tensor product notation simplification, fixed-width feature compression, and automated GPU kernel generation, the approach enables low-cost modeling of high-order correlations. The research demonstrates that increasing the correlation order improves both accuracy and efficiency more effectively than merely scaling up model size. Evaluated on the SPICE-MACE-OFF benchmark, a model with only 5.6 million parameters achieves lower errors while delivering inference speeds ten times faster than a 189-million-parameter Transformer.

Abstract

Machine-learned interatomic potentials extend atomistic simulations beyond the length- and timescales accessible to electronic-structure methods. However, the computational cost of equivariant architectures limits the local correlations they can represent in practice and therefore their achievable accuracy. Here we introduce FlashCart, which makes higher-order correlations affordable by combining generated GPU kernels with an architecture that recursively builds equivariant features and compresses them to a fixed width at each step. We express tensor products in independent Cartesian components and symbolically simplify them and their derivatives, producing fused kernels that often outperform optimized spherical counterparts. We then show that increasing correlation order improves accuracy more efficiently than increasing width, depth, or tensor rank. On SPICE-MACE-OFF, FlashCart models advance the measured accuracy-efficiency frontier: a model with $5.6$ million parameters achieves lower energy and force errors and $10\times$ faster inference than a transformer with $189$ million parameters.

Problem

• equivariant interatomic potentials
• computational cost
• higher-order correlations
• machine learning
• tensor products

Innovation

• Equivariant interatomic potentials
• Cartesian tensor products
• GPU kernel fusion
• Higher-order correlations
• Symbolic simplification