Discrete Fourier Transform Improves the Prediction of the Electronic Properties of Molecules in Quantum Machine Learning

High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and chemical degrees of freedom introduces enormous complexity, which the current state-of-the-art tools are not yet designed to handle. The availability of large molecular databases generated by quantum mechanics (QM) computations using first principles open new venues for data science to accelerate the discovery of new compounds. In recent years, models that combine QM with machine learning (ML) known as QM/ML models have been successful at delivering the accuracy of QM at the speed of ML. The goals are to develop a framework that will accelerate the extraction of knowledge and to get insights from quantitative process-structure-property-performance relationships hidden in materials data via a better search of the chemical compound space, and to infer new materials with targeted properties. In this study, we show that by integrating well-known signal processing techniques such as discrete Fourier transform in the QM/ML pipeline, the outcomes can be significantly improved in some cases. We also show that the spectrogram of a molecule may represent an interesting molecular visualization tool.Comment: 4 pages, 3 figures, 2 tables. Accepted to present at 32nd IEEE Canadian Conference in Electrical Engineering and Computer Scienc

Prediction of the Atomization Energy of Molecules Using Coulomb Matrix and Atomic Composition in a Bayesian Regularized Neural Networks

Exact calculation of electronic properties of molecules is a fundamental step for intelligent and rational compounds and materials design. The intrinsically graph-like and non-vectorial nature of molecular data generates a unique and challenging machine learning problem. In this paper we embrace a learning from scratch approach where the quantum mechanical electronic properties of molecules are predicted directly from the raw molecular geometry, similar to some recent works. But, unlike these previous endeavors, our study suggests a benefit from combining molecular geometry embedded in the Coulomb matrix with the atomic composition of molecules. Using the new combined features in a Bayesian regularized neural networks, our results improve well-known results from the literature on the QM7 dataset from a mean absolute error of 3.51 kcal/mol down to 3.0 kcal/mol.Comment: Under review ICANN 201

Unified Representation of Molecules and Crystals for Machine Learning

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can potentially reduce these costs significantly by accurately interpolating between reference calculations. For this, kernel learning approaches crucially require a single Hilbert space accommodating arbitrary atomistic systems. We introduce a many-body tensor representation that is invariant to translations, rotations and nuclear permutations of same elements, unique, differentiable, can represent molecules and crystals, and is fast to compute. Empirical evidence is presented for energy prediction errors below 1 kcal/mol for 7k organic molecules and 5 meV/atom for 11k elpasolite crystals. Applicability is demonstrated for phase diagrams of Pt-group/transition-metal binary systems.Comment: Revised version, minor changes throughou

Crystal Structure Representations for Machine Learning Models of Formation Energies

We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an Ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix by using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a data set of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37 eV/atom for the respective representations

SchNet: A continuous-filter convolutional neural network for modeling quantum interactions

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. This includes rotationally invariant energy predictions and a smooth, differentiable potential energy surface. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work

Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization