Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Prediction (2411.04219v1)

Abstract: Recent advancements in equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. Using spherical harmonics (SH) and tensor products (TP), these equivariant networks gain enhanced physical understanding, like symmetries and many-body interactions. Beyond encoding physical insights, SH and TP are also crucial to represent equivariant polynomial functions. In this work, we analyze the equivariant polynomial functions for the equivariant architecture, and introduce a novel equivariant network, named PACE. The proposed PACE utilizes edge booster and the Atomic Cluster Expansion (ACE) technique to approximate a greater number of $SE(3) \times S_n$ equivariant polynomial functions with enhanced degrees. As experimented in commonly used benchmarks, PACE demonstrates state-of-the-art performance in predicting atomic energy and force fields, with robust generalization capability across various geometric distributions under molecular dynamics (MD) across different temperature conditions. Our code is publicly available as part of the AIRS library https://github.com/divelab/AIRS/.

• The paper introduces PACE, an equivariant graph network that approximates high-degree polynomials for enhanced force field prediction.
• It employs spherical harmonics, tensor products, and the ACE technique to extend prediction capabilities beyond traditional second-degree functions.
• Benchmarks on rMD17, 3BPA, and AcAc datasets demonstrate state-of-the-art energy and force accuracy with robust generalization.

Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Prediction

The paper presents an in-depth exploration of equivariant graph network approaches for approximating high-degree polynomial functions and their application to force field prediction in molecular dynamics. With a focus on the use of spherical harmonics (SH) and tensor products (TP), the proposed method leverages these tools to represent and predict molecular energy and forces efficiently.

Equivariant Networks and Polynomial Function Approximation

Equivariant networks are designed to respect symmetries present in molecular systems, such as permutation, translation, and rotation invariance. Recently, these networks have significantly improved the accuracy of predicting molecular energies and force fields. The work introduces a novel network architecture, PACE, which expands the representation capacity of existing models by approximating a wider range of $SE(3) \times S_n$ equivariant polynomial functions through an innovative edge booster and the Atomic Cluster Expansion (ACE) technique.

PACE distinguishes itself by its ability to handle $SE(3)$-equivariant polynomials of higher degrees, thereby enhancing the network's expressiveness and predictive capabilities. Current methods are limited in the degree of polynomial functions they can approximate, typically spanning up to second-degree polynomials. PACE extends beyond these limitations, approximating higher-degree polynomials by leveraging the tensor contractions enabled in the ACE framework.

Theoretical and Practical Implications

The theoretical insights provided by PACE are profound. The network constructs a comprehensive $D$-spanning family, allowing it to approximate polynomial functions equivalent to those defined with higher degrees of symmetry. The paper explores the underlying mathematics, illustrating how spherical harmonics and tensor products can be harnessed to cover more extensive function spaces than existing methods.

On the practical front, PACE is rigorously tested against established benchmarks like rMD17, 3BPA, and AcAc datasets. The results indicate that PACE not only achieves state-of-the-art performance in energy and force predictions but also demonstrates strong generalization across different temperature-induced geometric distributions.

Future Directions in AI Developments

The advancements exhibited by PACE hold promise for future developments in AI, particularly in the domain of quantum chemistry and material science. The novel edge booster technique and enhanced expressivity of the network herald opportunities for even more precise and efficient force field predictions. Combining these with continued innovations in tensor computations could yield high-fidelity simulations of complex molecular systems.

Furthermore, the concept of expanding function approximation capabilities beyond second-degree polynomials opens new research avenues in machine learning. This could extend beyond quantum chemistry to other fields requiring symmetry-adapted predictions and modeling, thus broadening the impact of AI in scientific computations and simulations.