Polarisable multipolar electrostatics from the machine learning method Kriging: an application to alanine

Mills, Matthew J. L.; Popelier, Paul L. A.

doi:10.1007/s00214-012-1137-7

Cited by 64 publications

(46 citation statements)

References 74 publications

(69 reference statements)

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“…In this Article, we describe a new method which circumvents the necessity of a reference PES completely, enabling direct PIMD simulations on generic PESs at a fraction of the computational expense relative to the full PIMD simulation. Our scheme, referred to as ring-polymer interpolation (RPI), employs Gaussian process regression (GPR [52][53][54][55][56][57][58][59] ) to evaluate the forces and potential energy on the n-bead ring-polymers using only a small number of direct PES evaluations at each time-step; in this paper, we show that our RPI scheme is trivial to implement and systematically converges towards the exact PIMD simulation results for test cases including liquid water under ambient conditions 16 and liquid para-hydrogen at low temperatures. 35 Overall, RPI provides a straightforward approach to performing accurate and efficient PIMD simulations on arbitrary PESs without a reference PES.…”

Section: 41mentioning

confidence: 99%

Accelerated path-integral simulations using ring-polymer interpolation

Buxton

Habershon

2017

The Journal of Chemical Physics

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Path-integral (PI) molecular simulations can be used to calculate exact quantum statistical mechanical properties for complex systems containing many interacting atoms and molecules. The limiting computational factor in a PI simulation is typically the evaluation of the potential energy surface (PES) and forces at each ring-polymer "bead"; for an n-bead ring-polymer, a PI simulation is typically n times greater than the corresponding classical simulation. To address the increased computational effort of PI simulations, several approaches have been developed recently, most notably based on the idea of ring-polymer contraction (RPC) which exploits either the separation of the PES into short-range and long-range contributions or the availability of a computationally-inexpensive PES which can be incorporated to effectively smooth the ringpolymer PES; neither approach is satisfactory in applications to systems described by ab initio PESs. In this Article, we describe a new method, ring-polymer interpolation (RPI), which can be used to accelerate PI simulations without any prior assumptions about the PES. In simulations of liquid water under ambient conditions, where quantum effects are known to play a subtel role in influencing experimental observables such as diffusion coefficients and radial distribution functions, we find that RPI can accurately reproduce the results of fully-converged PI simulations, albeit with far fewer PES evaluations; this approach therefore opens up the possibility of large-scale PI simulations on ab initio PESs at lower computational effort than current methods.

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Section: 41mentioning

confidence: 99%

Accelerated path-integral simulations using ring-polymer interpolation

Buxton

Habershon

2017

The Journal of Chemical Physics

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Section: A New Approach: Gaussian Process Regressionmentioning

confidence: 99%

“…GPR, often referred to as kriging, 64,[66][67][68] is broadly representative of a class of machine-learning algorithms for regression of complex hypersurfaces based on limited input data. For example, recent work has employed Gaussian process methods 65 to achieve machine-learning of accurate PESs describing both atom and molecular chemical systems; the resulting Gaussian approximation potential (GAP [69][70][71] ) or kriging method 64,[66][67][68] offers a route to performing molecular simulations on PESs which approximate ab initio electronic structure, albeit at a much lower computational cost. Moving away from PES interpolation, machine learning methods such as kernel ridge regression, Bayesian inference, and artificial neural networks, have found application in relating ab initio atomization energies to simple molecular descriptors such as atomic partial charges, 78 in learning optimized exchangecorrelation functionals for density functional theory (DFT) calculations, 79,80 and in learning accurate interatomic PESs for large-scale molecular simulations.…”

Section: A New Approach: Gaussian Process Regressionmentioning

confidence: 99%

“…In particular, we propose using Gaussian process regression (GPR [64][65][66][67][68][69][70][71] ) to calculate PES matrix elements, using only single-point calculations performed along the trajectories q i (t) of time-dependent basis functions. In Section II, we first describe current approaches to calculating PES matrix elements, with a specific emphasis on simulations using GWP basis functions; we then describe our proposed GPR-based approach to approximating PES matrix elements for GWP basis sets.…”

Section: Introductionmentioning

confidence: 99%

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Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

Alborzpour

Tew

Habershon

2016

The Journal of Chemical Physics

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A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression The Journal of Chemical Physics 141, 144310 (2014); 10.1063/1.4897486Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation The Journal of Chemical Physics 148, 241704 (2018); 10.1063/1.5009347 THE JOURNAL OF CHEMICAL PHYSICS 145, 174112 (2016) Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each timestep; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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“…The electrostatic energy often defies simple computational solutions such as the still-ubiquitous static atom-centred point charges because atomic electron densities are anisotropic and polarise significantly due to changes in molecular geometry. In the past, we have reported on a different and new approach that predicts highrank multipolar and fully polarised electrostatic interaction energies in water clusters [1], ethanol [2], alanine [3], serine [4], N-methylacetamide and histidine [5], aromatic amino acids [6], hydrogen-bonded dimers [7], and atomic kinetic energies of methanol, N-methylacetamide, glycine, and triglycine [8]. These studies feature a developing force field, QCTFF, which predicts electrostatic multipole moments using machine learning, fully taking into account polarisation.…”

Section: Introductionmentioning

confidence: 99%