Automatic differentiation represents a paradigm shift in scientific programming, where evaluating both functions and their derivatives is required for most applications. By removing the need to explicitly derive expressions for gradients, development times can be be shortened, and calculations simplified. For these reasons, automatic differentiation has fueled the rapid growth of a variety of sophisticated machine learning techniques over the past decade, but is now also increasingly showing its value to support {\it ab initio} simulations of quantum systems, and enhance computational quantum chemistry. Here we present an open-source differentiable quantum chemistry simulation code, DQC, and explore applications facilitated by automatic differentiation: (1) calculating molecular perturbation properties; (2) reoptimizing a basis set for hydrocarbons; (3) checking the stability of self-consistent field wave functions; and (4) predicting molecular properties via alchemical perturbations.
Physics-informed learning has shown to have a better generalization than learning without physical priors. However, training physics-informed deep neural networks requires some aspect of physical simulations to be written in a differentiable manner. Unfortunately, some operations and functionals commonly used in physical simulations are scattered, hard to integrate, and lack higher order derivatives which are needed in physical simulations. In this work, we present $ξ$-torch, a library of differentiable functionals for scientific simulations. Example functionals are a root finder and an initial value problem solver, among others. The gradient of functionals in $ξ$-torch are written based on their analytical expression to improve numerical stability and reduce memory requirements. $ξ$-torch also provides second and higher order derivatives of the functionals which are rarely available in existing packages. We show two applications of this library in optimizing parameters in physics simulations. The library and all test cases in this work can be found at https://github.com/xitorch/xitorch/ and the documentation at https://xitorch.readthedocs.io.
Improving the predictive capability of molecular properties in ab initio simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum chemistry modelling remains severely limited by the scarcity and heterogeneity of appropriate experimental data. Here we show how training a neural network to replace the exchange-correlation functional within a fully-differentiable three-dimensional Kohn-Sham density functional theory (DFT) framework can greatly improve simulation accuracy. Using only eight experimental data points on diatomic molecules, our trained exchange-correlation networks enable improved prediction accuracy of atomization energies across a collection of 104 molecules containing new bonds and atoms that are not present in the training dataset.
Computer simulations are invaluable tools for scientific discovery. However, accurate simulations are often slow to execute, which limits their applicability to extensive parameter exploration, large-scale data analysis, and uncertainty quantification. A promising route to accelerate simulations by building fast emulators with machine learning requires large training datasets, which can be prohibitively expensive to obtain with slow simulations. Here we present a method based on neural architecture search to build accurate emulators even with a limited number of training data. The method successfully accelerates simulations by up to 2 billion times in 10 scientific cases including astrophysics, climate science, biogeochemistry, high energy density physics, fusion energy, and seismology, using the same super-architecture, algorithm, and hyperparameters. Our approach also inherently provides emulator uncertainty estimation, adding further confidence in their use. We anticipate this work will accelerate research involving expensive simulations, allow more extensive parameters exploration, and enable new, previously unfeasible computational discovery.