[Paper Review] Equivariant Interatomic Potentials without Tensor Products

Thiago Reschützegger, Sarp Aykent+6 more|arXiv (Cornell University)|Jan 21, 2026

Machine Learning in Materials Science0 citations

TL;DR

Geodite is a tensor product–free equivariant interatomic potential that matches leading MLIPs in accuracy while being 3–5× faster, enabling scalable, physically faithful large-scale simulations. It is trained on MPtrj and validated across benchmarks including Matbench Discovery and MDR.

ABSTRACT

Foundational machine-learned interatomic potentials have emerged as powerful tools for atomistic simulations, promising near first-principles accuracy across diverse chemical spaces at a fraction of the cost of quantum-mechanical calculations. However, the most accurate equivariant architectures rely on Clebsch-Gordan tensor products whose computational cost scales steeply with angular resolution, creating a trade-off between model expressiveness and inference speed that ultimately limits practical applications. Here we introduce Geodite, an equivariant message-passing architecture that replaces tensor products while incorporating physical priors to ensure smooth, well-behaved potential energy surfaces. Trained on the Materials Project trajectories dataset of inorganic crystals, Geodite-MP achieves accuracy competitive with leading methods on benchmarks for materials stability prediction, thermal conductivity, phonon-derived properties, and nanosecond-scale molecular dynamics, while running $3 ext{--}5 imes$ faster than models performing similarly. By combining predictive accuracy, computational efficiency, and physicality, Geodite enables faster large-scale atomistic simulations and high-throughput screening that would otherwise be computationally prohibitive.

Motivation & Objective

• Motivate the need for efficient equivariant MLIPs that avoid costly Clebsch–Gordan tensor products.
• Introduce Geodite, a tensor-product-free architecture with physical priors for smooth PES and short-range repulsion.
• Demonstrate Geodite-MP trained on MPtrj competes on stability, phonon, and MD benchmarks.
• Show substantial speedups (3–5×) over comparable models while maintaining accuracy for large-scale simulations.

Proposed method

• Geodite is an equivariant message-passing network that avoids Clebsch–Gordan tensor products by using inner products of steerable features to preserve O(3) equivariance.
• Features initializations include voxel-like atom embeddings, scalar edge features from atom pairs, and distance-aware radial embeddings with smooth cutoffs.
• Interaction block combines modified self-attention and spatial filtering to update invariant and steerable node features with equivariant messages.
• Equivariant coupling block allows invariant and steerable features to exchange information; edge updates refine representations via inner products with node features.
• Physical priors are integrated via vacuum embedding for isolated-atom limit, attenuation-based smooth cutoff to enforce short-range behavior, ZBL-inspired short-range repulsion with learnable screening, and density-based normalization to stabilize training.
• Predicted energies are obtained by summing atomic contributions; forces arise from automatic differentiation to ensure conservation.

Experimental results

Research questions

• RQ1 Can a tensor-product-free equivariant architecture match or exceed the accuracy of CG-based MLIPs on inorganic materials benchmarks?
• RQ2 How do physical priors (smoothness, short-range repulsion, correct asymptotics) affect PES quality and MD stability in Geodite-MP?
• RQ3 What are the trade-offs between accuracy and computational efficiency in large-scale simulations using Geodite-MP compared to tensor-product-based counterparts?
• RQ4 Is Geodite-MP capable of capturing higher-order PES derivatives and maintaining stability in long MD trajectories for solid-state electrolytes?

Key findings

• Geodite-MP achieves competitive accuracy on Matbench Discovery, with F1 around 0.771 and κ_SRME ≈ 0.499, while using fewer parameters and a 6 Å cutoff with Lmax = 2.
• Geodite-MP delivers substantial speedups, running ~3× faster than NequIP-MP-L and ~2.5× faster than Allegro-MP-L, and ~5× faster than some baselines in per-atom, per-step inference.
• On diatomic and PES smoothness metrics, Geodite-MP attains superior or near-top scores, showing smooth binding curves and effective short-range repulsion dominated by a ZBL-like term.
• 1 ns MD simulations across 49 solid-state electrolytes show high fidelity to AIMD structures, with RDF overlap mean ~0.958, comparable to top models yet achieved much faster (under 5 hours vs days for some peers).
• Geodite-MP maintains stability and accurately reproduces local structure across varied temperatures, demonstrating reliable long-timescale performance.