Integer linear programming for unsupervised training set selection in molecular machine learning

Abstract

Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we demonstrate the relevance of an ILP formulation to select molecular training sets for predictions of size-extensive properties. We show that our algorithm outperforms existing unsupervised training set selection approaches, especially when predicting properties of molecules larger than those present in the training set. We argue that the reason for the improved performance is due to the selection that is based on the notion of local similarity (i.e., per-atom) and a unique ILP approach that finds optimal solutions efficiently. Altogether, this work provides a practical algorithm to improve the performance of physics-inspired machine learning models and offers insights into the conceptual differences with existing training set selection approaches.

29 pages + SI (15 pages)

References in corpus (33)

• On representing chemical environments
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Machine learning for molecular simulation
• Less is more: sampling chemical space with active learning
• Comparing molecules and solids across structural and alchemical space
• Machine Learning Unifies the Modelling of Materials and Molecules
• Active learning of linearly parametrized interatomic potentials
• Machine Learning of Molecular Electronic Properties in Chemical Compound Space
• Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding
• Physics-inspired structural representations for molecules and materials
• ANI-1: A data set of 20M off-equilibrium DFT calculations for organic molecules
• FCHL revisited: faster and more accurate quantum machine learning
• Alchemical and structural distribution based representation for improved QML
• Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials
• Unified Representation of Molecules and Crystals for Machine Learning
• SELFIES and the future of molecular string representations
• Electronic Spectra from TDDFT and Machine Learning in Chemical Space
• A Transferable Machine-Learning Model of the Electron Density
• Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
• Accurate molecular polarizabilities with coupled-cluster theory and machine learning
• Machine Learning Inter-Atomic Potentials Generation Driven by Active Learning: A Case Study for Amorphous and Liquid Hafnium dioxide
• Structure-based Sampling and Self-correcting Machine Learning for Accurate Calculations of Potential Energy Surfaces and Vibrational Levels
• Machine learning of molecular properties: locality and active learning
• Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning
• QM7-X: A comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules
• Uncertainty estimation for molecular dynamics and sampling
• Using Gaussian Process Regression to Simulate the Vibrational Raman Spectra of Molecular Crystals
• Recursive evaluation and iterative contraction of $N$-body equivariant features
• Simulating solvation and acidity in complex mixtures with first-principles accuracy: the case of CH${}_3$SO${}_3$H and H${}_2$O${}_2$ in phenol
• 3DReact: Geometric deep learning for chemical reactions
• Molecular Quantum Chemical Data Sets and Databases for Machine Learning Potentials
• Assessing the persistence of chalcogen bonds in solution with neural network potentials
• Improved decision making with similarity based machine learning: Applications in chemistry