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Interpolating moving least-squares methods for fitting potential energy surfaces: A strategy for efficient automatic data point placement in high dimensions
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10.1063/1.2831790
/content/aip/journal/jcp/128/8/10.1063/1.2831790
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/8/10.1063/1.2831790
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Figures

Image of FIG. 1.
FIG. 1.

Example of automatic surface generation scheme: second- (green-dashes) and third- (red-dotted) degree fits to Morse function (blue solid) using five-point seed grid (diamonds). Peaks in squared difference surface (black solid) indicate locations for new data. Frames (a)–(d) follow the addition of three automatically generated points, and the resulting convergence of the functions. The energy and distance units are, respectively, kcal/mol and bohr.

Image of FIG. 2.
FIG. 2.

Convergence of IMLS automatic 3D surface generation (HCN) towards spectroscopic accuracy: rms error for fits to (1) energies-only (triangles), (2) energies and gradients (diamonds), and (3) energies, gradients, and Hessian data (squares), using the HDMR (12,9,7) basis.

Image of FIG. 3.
FIG. 3.

Convergence of IMLS automatic 6D surface generation (HOOH): rms error for fits to (1) energies-only (triangles), (2) energies and gradients (diamonds), and (3) energies, gradients, and Hessian data (squares). The fits including Hessian and/or gradient data use the HDMR (10,7,5,4) basis. The energies-only fit used the dynamic basis scheme (described in the results) ending up at the same basis (arrows indicate where the basis set is increased).

Image of FIG. 4.
FIG. 4.

Convergence of IMLS automatic 9D surface generation : mean error for fits to (1) energies-only (triangles) and (2) energies and gradient data (diamonds). The fit including gradient data used the HDMR (9,6,4,4) basis. The energies-only fit used the dynamic basis scheme (described in the results) ending up at the same basis (arrows indicate where the basis set is increased).

Image of FIG. 5.
FIG. 5.

Modular fitting method tested in 9D : mean error for fit to energies and gradient data. Using the HDMR (9,6,4,4) basis, sequential fits to five energy ranges [0–4000 (red), 4000–8000 (green), 8000–12 000 (dark blue), 12 000–16 000 (purple), and ] are compared with simultaneous fit of all five ranges (black).

Image of FIG. 6.
FIG. 6.

Biased accuracy fitting method tested in 9D : mean error for fit to energies and gradient data. Using the HDMR (9,6,4,4) basis, automated sequential fits to the five energy ranges (1) 0–4000, (2) 4000–8000, (3) 8000–12 000, (4) 12 000–16 000, and (5) were performed to differing accuracy targets (0.05, 0.10, 0.20, 0.30, and , respectively).

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/content/aip/journal/jcp/128/8/10.1063/1.2831790
2008-02-28
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interpolating moving least-squares methods for fitting potential energy surfaces: A strategy for efficient automatic data point placement in high dimensions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/8/10.1063/1.2831790
10.1063/1.2831790
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