Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods

Abstract

Permutationally invariant polynomial (PIP) regression has been used to obtain machine-learned (ML) potential energy surfaces, including analytical gradients, for many molecules and chemical reactions. Recently, the approach has been extended to moderate size molecules and applied to systems up to 15 atoms. The algorithm, including "purification of the basis", is computationally efficient for energies; however, we found that the recent extension to obtain analytical gradients, despite being a remarkable advance over previous methods, could be further improved. Here we report developments to compact further a purified basis and, more significantly, to use the reverse gradient approach to greatly speed up gradient evaluation. We demonstrate this for our recent 4-body water interaction potential. Comparisons of training and testing precision on the MD17 database of energies and gradients (forces) for ethanol against GP-SOAP, ANI, sGDML, PhysNet, pKREG, KRR, and other methods, which were recently assessed by Dral and co-workers, are given. The PIP fits are as precise as those using these methods, but the PIP computation time for energy and force evaluation is shown to be 10 to 1000 times faster. Finally, a new PIP PES is reported for ethanol based on a more extensive dataset of energies and gradients than in the MD17 database. Diffusion Monte Carlo calculations which fail on MD17-based PESs are successful using the new PES.

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Cited by in corpus (15)

• Neural Network Potentials for Chemistry: Concepts, Applications and Prospects
• q-AQUA: a many-body CCSD(T) water potential, including 4-body interactions, demonstrates the quantum nature of water from clusters to the liquid phase
• The MD17 Datasets from the Perspective of Datasets for Gas-Phase "Small" Molecule Potentials
• Neural network with optimal neuron activation functions based on additive Gaussian process regression
• $\Delta$-Machine Learning to Elevate DFT-based Potentials and a Force Field to the CCSD(T) Level Illustrated for Ethanol
• A $\Delta$-Machine Learning Approach for Force Fields, Illustrated by a CCSD(T) 4-body Correction to the MB-pol Water Potential
• Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension
• Quantum calculations on a new CCSD(T) machine-learned PES reveal the leaky nature of gas-phase $trans$ and $gauche$ ethanol conformers
• GPU-Accelerated Approximate Kernel Method for Quantum Machine Learning
• No Headache for PIPs: A PIP Potential for Aspirin Outperforms Other Machine-Learned Potentials
• Orders-of-coupling representation with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization
• Tell machine learning potentials what they are needed for: Simulation-oriented training exemplified for glycine
• Accurate neural-network-based fitting of full-dimensional two-body potential energy surfaces
• MOLPIPx: an end-to-end differentiable package for permutationally invariant polynomials in Python and Rust
• Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence