RotNet: A Rotationally Invariant Graph Neural Network for Quantum Mechanical Calculations

Abstract Deep learning has proven promising in biological and chemical applications, aiding in accurate predictions of properties such as atomic forces, energies, and material band gaps. Traditional methods with rotational invariance, one of the most crucial physical laws for predictions made by machine learning, have relied on Fourier transforms or specialized convolution filters, leading to complex model design and reduced accuracy and efficiency. However, models without rotational invariance exhibit poor generalization ability across datasets. Addressing this contradiction, this work proposes a rotationally invariant graph neural network, named RotNet, for accurate and accelerated quantum mechanical calculations that can overcome the generalization deficiency caused by rotations of molecules. RotNet ensures rotational invariance through an effective transformation and learns distance and angular information from atomic coordinates. Benchmark experiments on three datasets (protein fragments, electronic materials, and QM9) demonstrate that the proposed RotNet framework outperforms popular baselines and generalizes well to spatial data with varying rotations. The high accuracy, efficiency, and fast convergence of RotNet suggest that it has tremendous potential to significantly facilitate studies of protein dynamics simulation and materials engineering while maintaining physical plausibility.