Andrés Guzmán-Cordero

Austin Cheng, Cher Tian Ser, Marta Skreta et al.

Machine learning has been pervasively touching many fields of science. Chemistry and materials science are no exception. While machine learning has been making a great impact, it is still not reaching its full potential or maturity. In this perspective, we first outline current applications across a diversity of problems in chemistry. Then, we discuss how machine learning researchers view and approach problems in the field. Finally, we provide our considerations for maximizing impact when researching machine learning for chemistry.

Andrés Guzmán-Cordero, Felix Dangel, Gil Goldshlager et al.

Natural gradient methods significantly accelerate the training of Physics-Informed Neural Networks (PINNs), but are often prohibitively costly. We introduce a suite of techniques to improve the accuracy and efficiency of energy natural gradient descent (ENGD) for PINNs. First, we leverage the Woodbury formula to dramatically reduce the computational complexity of ENGD. Second, we adapt the Subsampled Projected-Increment Natural Gradient Descent algorithm from the variational Monte Carlo literature to accelerate the convergence. Third, we explore the use of randomized algorithms to further reduce the computational cost in the case of large batch sizes. We find that randomization accelerates progress in the early stages of training for low-dimensional problems, and we identify key barriers to attaining acceleration in other scenarios. Our numerical experiments demonstrate that our methods outperform previous approaches, achieving the same $L^2$ error as the original ENGD up to $75\times$ faster.