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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. [ABSTRACT FROM AUTHOR]

Effective full quantum mechanics (FQM) calculation of protein remains a grand challenge and of great interest in computational biology with substantial applications in drug discovery, protein dynamic simulation and protein folding. However, the huge computational complexity of the existing QM methods impends their applications in large systems. Here, we design a transfer-learning-based deep learning (TDL) protocol for effective FQM calculations (TDL-FQM) on proteins. By incorporating a transfer-learning algorithm into deep neural network (DNN), the TDL-FQM protocol is capable of performing calculations at any given accuracy using models trained from small datasets with high-precision and knowledge learned from large amount of low-level calculations. The high-level double-hybrid DFT functional and high-level quality of basis set is used in this work as a case study to evaluate the performance of TDL-FQM, where the selected 15 proteins are predicted to have a mean absolute error of 0.01 kcal/mol/atom for potential energy and an average root mean square error of 1.47 kcal/mol/ |$ {\rm A^{^{ \!\!\!o}}} $| for atomic forces. The proposed TDL-FQM approach accelerates the FQM calculation more than thirty thousand times faster in average and presents more significant benefits in efficiency as the size of protein increases. The ability to learn knowledge from one task to solve related problems demonstrates that the proposed TDL-FQM overcomes the limitation of standard DNN and has a strong power to predict proteins with high precision, which solves the challenge of high precision prediction in large chemical and biological systems. [ABSTRACT FROM AUTHOR]

Accurate simulation of protein folding is a unique challenge in understanding the physical process of protein folding, with important implications for protein design and drug discovery. Molecular dynamics simulation strongly requires advanced force fields with high accuracy to achieve correct folding. However, the current force fields are inaccurate, inapplicable and inefficient. We propose a machine learning protocol, the inductive transfer learning force field (ITLFF), to construct protein force fields in seconds with any level of accuracy from a small dataset. This process is achieved by incorporating an inductive transfer learning algorithm into deep neural networks, which learn knowledge of any high-level calculations from a large dataset of low-level method. Here, we use a double-hybrid density functional theory (DFT) as a case functional, but ITLFF is suitable for any high-precision functional. The performance of the selected 18 proteins indicates that compared with the fragment-based double-hybrid DFT algorithm, the force field constructed by ITLFF achieves considerable accuracy with a mean absolute error of 0.0039 kcal/mol/atom for energy and a root mean square error of 2.57  |$\mathrm{kcal}/\mathrm{mol}/{\AA}$| for force, and it is more than 30 000 times faster and obtains more significant efficiency benefits as the system increases. The outstanding performance of ITLFF provides promising prospects for accurate and efficient protein dynamic simulations and makes an important step toward protein folding simulation. Due to the ability of ITLFF to utilize the knowledge acquired in one task to solve related problems, it is also applicable for various problems in biology, chemistry and material science. [ABSTRACT FROM AUTHOR]