Efficient force field and energy emulation through partition of permutationally equivalent atoms

Abstract

Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. Integrating both atomic force and energy in predictions was found to be more accurate than using energy alone, yet it requires $O((NM{)}^3)$ computational operations for computing the likelihood function and making predictions, where $N$ is the number of atoms and $M$ is the number of simulated configurations in the training sample, due to the inversion of a large covariance matrix. The large computational need limits its applications to emulating simulation of small molecules. The computational challenge of using both gradient information and function values in GPs was recently noticed in statistics and machine learning communities, where conventional approximation methods, such as the low rank decomposition or sparse approximation, may not work well. Here we introduce a new approach, the atomized force field (AFF) model, that integrates both force and energy in the emulator with many fewer computational operations. The drastic reduction on computation is achieved by utilizing the naturally sparse structure of the covariance satisfying the constraints of the energy conservation and permutation symmetry of atoms. The efficient machine learning algorithm extends the limits of its applications on larger molecules under the same computational budget, with nearly no loss of predictive accuracy. Furthermore, our approach contains uncertainty assessment of predictions of atomic forces and potentials, useful for developing a sequential design over the chemical input space, with almost no increase in computational cost.

References in corpus (21)

• Practical Bayesian Optimization of Machine Learning Algorithms
• Neural Message Passing for Quantum Chemistry
• On representing chemical environments
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• SchNet - a deep learning architecture for molecules and materials
• Machine Learning of Accurate Energy-Conserving Molecular Force Fields
• PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
• Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields
• Machine learning a general purpose interatomic potential for silicon
• SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects
• FCHL revisited: faster and more accurate quantum machine learning
• Embedded Atom Neural Network Potentials: Efficient and Accurate Machine Learning with a Physically Inspired Representation
• sGDML: Constructing Accurate and Data Efficient Molecular Force Fields Using Machine Learning
• 86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy
• Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
• Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences
• Permutationally Invariant, Reproducing Kernel-Based Potential Energy Surfaces for Polyatomic Molecules: From Formaldehyde to Acetone
• Scaling Gaussian Process Regression with Derivatives
• High-Dimensional Gaussian Process Inference with Derivatives
• Emulating the First Principles of Matter: A Probabilistic Roadmap

Cited by in corpus (3)

• Reliable emulation of complex functionals by active learning with error control
• Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification
• Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence