# Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size

arXiv: https://arxiv.org/abs/2304.10061 · HTML: https://mlsanity.com/paper/2304.10061/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials](https://mlsanity.com/paper/2209.10702/) (2022)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations](https://mlsanity.com/paper/2205.08306/) (2022)
- [Towards Electronic Structure-Based Ab-Initio Molecular Dynamics Simulations with Hundreds of Millions of Atoms](https://mlsanity.com/paper/2104.08245/) (2021)

## Built on by (most cited first, 30 of 33)

- [TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentials](https://mlsanity.com/paper/2306.06482/) (2023)
- [LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite](https://mlsanity.com/paper/2309.16342/) (2023)
- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Science](https://mlsanity.com/paper/2305.14247/) (2023)
- [Navigating protein landscapes with a machine-learned transferable coarse-grained model](https://mlsanity.com/paper/2310.18278/) (2023)
- [Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fields](https://mlsanity.com/paper/2403.09549/) (2024)
- [Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks](https://mlsanity.com/paper/2503.23794/) (2025)
- [EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers](https://mlsanity.com/paper/2604.09130/) (2026)
- [Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctions](https://mlsanity.com/paper/2307.09337/) (2023)
- [Stability-Aware Training of Machine Learning Force Fields with Differentiable Boltzmann Estimators](https://mlsanity.com/paper/2402.13984/) (2024)
- [MOFSimBench: Evaluating Universal Machine Learning Interatomic Potentials In Metal--Organic Framework Molecular Modeling](https://mlsanity.com/paper/2507.11806/) (2025)
- [Overcoming systematic softening in universal machine learning interatomic potentials by fine-tuning](https://mlsanity.com/paper/2405.07105/) (2024)
- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [Learning Interatomic Potentials at Multiple Scales](https://mlsanity.com/paper/2310.13756/) (2023)
- [A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics](https://mlsanity.com/paper/2401.15122/) (2024)
- [Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion](https://mlsanity.com/paper/2502.09890/) (2025)
- [DistMLIP: A Distributed Inference Platform for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2506.02023/) (2025)
- [LTAU-FF: Loss Trajectory Analysis for Uncertainty in Atomistic Force Fields](https://mlsanity.com/paper/2402.00853/) (2024)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [Grappa -- A Machine Learned Molecular Mechanics Force Field](https://mlsanity.com/paper/2404.00050/) (2024)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2607.02499/) (2026)
- [Smooth Dynamic Cutoffs for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2601.21147/) (2026)
- [Towards scientific machine learning for granular material simulations -- challenges and opportunities](https://mlsanity.com/paper/2504.08766/) (2025)
- [Efficient Parallelization of Message Passing Neural Network Potentials for Large-scale Molecular Dynamics](https://mlsanity.com/paper/2505.06711/) (2025)
- [Considerations in the use of ML interaction potentials for free energy calculations](https://mlsanity.com/paper/2403.13952/) (2024)
- [Implicit Delta Learning of High Fidelity Neural Network Potentials](https://mlsanity.com/paper/2412.06064/) (2024)
- [Distributed Equivariant Graph Neural Networks for Large-Scale Electronic Structure Prediction](https://mlsanity.com/paper/2507.03840/) (2025)
- [Learning 3D Anisotropic Noise Distributions Improves Molecular Force Field Modeling](https://mlsanity.com/paper/2510.22123/) (2025)
- [Equivariant Evidential Deep Learning for Interatomic Potentials](https://mlsanity.com/paper/2602.10419/) (2026)

## Abstract (arXiv)

This work brings the leading accuracy, sample efficiency, and robustness of deep equivariant neural networks to the extreme computational scale. This is achieved through a combination of innovative model architecture, massive parallelization, and models and implementations optimized for efficient GPU utilization. The resulting Allegro architecture bridges the accuracy-speed tradeoff of atomistic simulations and enables description of dynamics in structures of unprecedented complexity at quantum fidelity. To illustrate the scalability of Allegro, we perform nanoseconds-long stable simulations of protein dynamics and scale up to a 44-million atom structure of a complete, all-atom, explicitly solvated HIV capsid on the Perlmutter supercomputer. We demonstrate excellent strong scaling up to 100 million atoms and 70% weak scaling to 5120 A100 GPUs.