An adaptive interpolation scheme for molecular potential energy surfaces

Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa

doi:10.1063/1.4961148

Cited by 5 publications

(3 citation statements)

References 39 publications

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“…In the presented test cases of this work this is not the case. Note that with this modification our GPR method can be considered as one of multiple ways 40 in which one can adaptively refine a surrogate model of the PES. In our surrogate model for the PES we choose σ e = σ g = 1 × 10 −7 and l = 20.…”

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confidence: 99%

Gaussian Process Regression for Minimum Energy Path Optimization and Transition State Search

2019

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We implemented a gradient-based algorithm for finding minimum energy paths (MEPs) using Gaussian process regression (GPR). A subsequent search for transition states can be performed very fast. We describe the algorithm in detail and compare its performance to the nudged elastic band (NEB) method in 27 test systems. Additionally, three different possibilities for an initial guess of the path are evaluated. We found the new optimizer to considerably decrease the number of required energy and gradient evaluations.

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Section: ∑ ∑ ∑mentioning

confidence: 99%

Gaussian Process Regression for Minimum Energy Path Optimization and Transition State Search

2019

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“…to obtain simulation-based classification [60], or to derive multifidelity Monte Carlo approximations [40]. Kernel surrogates have been employed in optimal control problems [51,59], in the coupling of multi-scale simulations in biomechanics [25,69], in real time prediction for parameter identification and state estimation in biomechanical systems [29], in gas transport problems [22], in the reconstruction of potential energy surfaces [30], in the forecasting of time stepping methods [6], in the reduction of nonlinear dynamical systems [67], in uncertainty quantification [28], and for nonlinear balanced truncation of dynamical systems [5].…”

Section: Introductionmentioning

confidence: 99%

Kernel Methods for Surrogate Modeling

Santin¹,

Haasdonk²

2019

Preprint

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This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent experimental performance and elegant functional analytic background. These data-based techniques provide so called kernel expansions, i.e., linear combinations of kernel functions which are generated from given input-output point samples that may be arbitrarily scattered. In particular, these techniques are meshless, do not require or depend on a grid, hence are less prone to the curse of dimensionality, even for high-dimensional problems.In contrast to projection-based model reduction, we do not necessarily assume a high-dimensional model, but a general function that models input-output behavior within some simulation context. This could be some micro-model in a multiscale-simulation, some submodel in a coupled system, some initialization function for solvers, coefficient function in Partial Differential Equations (PDEs), etc.First, kernel surrogates can be useful if the input-output function is expensive to evaluate, e.g. is a result of a finite element simulation. Here, acceleration can be obtained by sparse kernel expansions. Second, if a function is available only via measurements or a few function evaluation samples, kernel approximation techniques can provide function surrogates that allow global evaluation.We present some important kernel approximation techniques, which are kernel interpolation, greedy kernel approximation and support vector regression. Pseudo-code is provided for ease of reproducibility. In order to illustrate the main features, commonalities and differences, we compare these techniques on a real-world application. The experiments clearly indicate the enormous acceleration potential.

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“…In the current literature, except for particular applications (see e.g. [27]), most papers about adaptive RBF collocation and multiscale methods only consider global approximation methods or RBF-finite difference (FD) local approaches (see [9,15,19,34]). In [19], the approximate solution is constructed with a multilevel approach in which compactly supported RBFs (CSRBFs) of smaller support are used on an increasingly finer mesh, similarly as done also in [25].…”

Section: Introductionmentioning

confidence: 99%

RBF-Based Partition of Unity Methods for Elliptic PDEs: Adaptivity and Stability Issues Via Variably Scaled Kernels

et al. 2018

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We investigate adaptivity issues for the approximation of Poisson equations via radial basis function-based partition of unity collocation. The adaptive residual subsampling approach is performed with quasi-uniform node sequences leading to a flexible tool which however might suffer from numerical instability due to ill-conditioning of the collocation matrices. We thus develop a hybrid method which makes use of the so-called variably scaled kernels. The proposed algorithm numerically ensures the convergence of the adaptive procedure.

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An adaptive interpolation scheme for molecular potential energy surfaces

Cited by 5 publications

References 39 publications

Gaussian Process Regression for Minimum Energy Path Optimization and Transition State Search

Gaussian Process Regression for Minimum Energy Path Optimization and Transition State Search

Kernel Methods for Surrogate Modeling

RBF-Based Partition of Unity Methods for Elliptic PDEs: Adaptivity and Stability Issues Via Variably Scaled Kernels

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