Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials

Machine learning interatomic potentials (MLIPs) have become a hallmark of AI for scientific simulation. While efforts on new architectures and datasets have led to increasingly accurate and general models, the choice of optimizer for training has largely remained unexplored, defaulting to Adam and its variants in the community. Here, we implement and systematically compare a class of recently proposed matrix-structured optimizers, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models. We find that these optimizers can substantially outperform Adam in both convergence speed and final accuracy. SOAP and SOAP-Muon emerge as robust and consistently strong methods, while Muon only provides partial gains relative to Adam. The improvements are particularly pronounced under partial force supervision. Our results indicate that optimizer choice is an overlooked yet impactful design axis for MLIPs.

$\mathrm{Cl}(3,0)$ interatomic potentials, despite their algebraic elegance, predict force magnitudes accurately but force directions poorly. Across ten rMD17 molecules, every $L \leq 1$ baseline in our twelve-model study attains aggregate force-cosine similarity below $0.25$. The cause is structural. The geometric product of two vectors in $\mathbb{R}^3$ realises only the $L=0$ and $L=1$ components of its irreducible representation content, leaving the symmetric-traceless rank-2 component absent from the per-edge bilinear that drives each message-passing layer. We address this with CliffordSTF, which couples the Clifford multivector to closed-form symmetric-traceless tensor tracks at ranks two and three through bilinear cross-track contractions, using a single learned bilinear and no Clebsch--Gordan tables, Wigner-$D$ matrices, or e3nn calls. On rMD17, CliffordSTF raises aggregate force-cosine similarity from $0.055$ (base Clifford) to $0.551$, an order-of-magnitude relative directional gain, alongside improved magnitude accuracy (force MAE $15.8\%$ lower; energy MAE $10.9\%$ lower). It outperforms all CG-free or body-ordered baselines in our study (all $\leq 0.17$). On catalysis benchmarks, CliffordSTF achieves the best out-of-distribution S2EF energy MAE on OC22 in our experiments, and the best in-distribution energy MAE among $L \geq 2$ methods on OC22 IS2RE. An eleven-variant ablation shows the two tracks are complementary: neither alone matches the combined model.

Universal Machine Learning Interatomic Potentials (uMLIPs), pre-trained on massively diverse datasets encompassing inorganic materials and organic molecules across the entire periodic table, serve as foundational models for quantum-accurate physical simulations. However, uMLIP training requires second-order derivatives, which lack corresponding parallel training frameworks; moreover, scaling to the billion-parameter regime causes explosive growth in computation and communication overhead, making its training a tremendous challenge. We introduce MatRIS-MoE, a billion-parameter Mixture-of-Experts model built upon invariant architecture, and {Janus}, a pioneering high-dimensional distributed training framework for uMLIPs with hardware-aware optimizations. Deployed across two Exascale supercomputers, our code attains a peak performance of 1.2/1.0 EFLOPS (24%/{35.5%} of theoretical peak) in single precision at over 90% parallel efficiency, compressing the training of billion-parameter uMLIPs from weeks to hours. This work establishes a new high-water mark for AI-for-Science (AI4S) foundation models at Exascale and provides essential infrastructure for rapid scientific discovery.