A Statistical Method for Emulation of Computer Models With Invariance-Preserving Properties, With Application to Structural Energy Prediction

References

• Bartók, A. P. , and Csányi, G. (2015), “Gaussian Approximation Potentials: A Brief Tutorial Introduction,” International Journal of Quantum Chemistry , 115, 1051–1057. DOI: 10.1002/qua.24927.
   Web of Science ®Google Scholar
• Bartók, A. P. , Kondor, R. , and Csányi, G. (2013), “On Representing Chemical Environments,” Physical Review B , 87, 184115. DOI: 10.1103/PhysRevB.87.184115.
   Web of Science ®Google Scholar
• Behler, J. (2015), “Constructing High-Dimensional Neural Network Potentials: A Tutorial Review,” International Journal of Quantum Chemistry , 115, 1032–1050. DOI: 10.1002/qua.24890.
   Web of Science ®Google Scholar
• Behler, J. , and Parrinello, M. (2007), “Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces,” Physical Review Letters , 98, 146401. DOI: 10.1103/PhysRevLett.98.146401.
   PubMed Web of Science ®Google Scholar
• Breiman, L. , and Friedman, J. H. (1985), “Estimating Optimal Transformations for Multiple Regression and Correlation,” Journal of the American Statistical Association , 80, 580–598. DOI: 10.1080/01621459.1985.10478157.
   Web of Science ®Google Scholar
• Buja, A. , Hastie, T. , and Tibshirani, R. (1989), “Linear Smoothers and Additive Models,” The Annals of Statistics , 17, 453–510. DOI: 10.1214/aos/1176347115.
   Web of Science ®Google Scholar
• Currin, C. , Mitchell, T. , Morris, M. , and Ylvisaker, D. (1991), “Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments,” Journal of the American Statistical Association , 86, 953–963. DOI: 10.1080/01621459.1991.10475138.
   Web of Science ®Google Scholar
• Daw, M. S. , and Baskes, M. I. (1984), “Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals,” Physical Review B , 29, 6443. DOI: 10.1103/PhysRevB.29.6443.
   Web of Science ®Google Scholar
• Efron, B. , and Stein, C. (1981), “The Jackknife Estimate of Variance,” The Annals of Statistics , 9, 586–596. DOI: 10.1214/aos/1176345462.
   Web of Science ®Google Scholar
• Hastie, T. , and Tibshirani, R. (1986), “Generalized Additive Models,” Statistical Science , 1, 297–318. DOI: 10.1214/ss/1177013604.
   Google Scholar
• Johnson, M. E. , Moore, L. M. , and Ylvisaker, D. (1990), “Minimax and Maximin Distance Designs,” Journal of Statistical Planning and Inference , 26, 131–148. DOI: 10.1016/0378-3758(90)90122-B.
   Web of Science ®Google Scholar
• Joseph, V. R. , Gul, E. , and Ba, S. (2015), “Maximum Projection Designs for Computer Experiments,” Biometrika , 102, 371–380. DOI: 10.1093/biomet/asv002.
   Web of Science ®Google Scholar
• Kimeldorf, G. , and Wahba, G. (1971), “Some Results on Tchebycheffian Spline Functions,” Journal of Mathematical Analysis and Applications , 33, 82–95. DOI: 10.1016/0022-247X(71)90184-3.
   Web of Science ®Google Scholar
• Kingma, D. P. , and Ba, J. (2014), “Adam: A Method for Stochastic Optimization,” arXiv no. 1412.6980.
   Google Scholar
• Kunen, K. (1980), Set Theory: An Introduction to Independence Proofs, Mathematical Programming Study, Amsterdam: North-Holland Publishing Company.
   Google Scholar
• Lennard-Jones, J. E. (1924a), “On the Determination of Molecular Fields. I. From the Variation of the Viscosity of a Gas With Temperature,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences , 106, 441–462. DOI: 10.1098/rspa.1924.0081.
   Google Scholar
• Lennard-Jones, J. E. (1924b), “On the Determination of Molecular Fields. II. From the Equation of State of a Gas,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences , 106, 463–477. DOI: 10.1098/rspa.1924.0082.
   Google Scholar
• Morris, M. D. , and Mitchell, T. J. (1995), “Exploratory Designs for Computational Experiments,” Journal of Statistical Planning and Inference , 43, 381–402. DOI: 10.1016/0378-3758(94)00035-T.
   Web of Science ®Google Scholar
• Nguyen, T. T. , Székely, E. , Imbalzano, G. , Behler, J. , Csányi, G. , Ceriotti, M. , Götz, A. W. , and Paesani, F. (2018), “Comparison of Permutationally Invariant Polynomials, Neural Networks, and Gaussian Approximation Potentials in Representing Water Interactions Through Many-Body Expansions,” The Journal of Chemical Physics , 148, 241725. DOI: 10.1063/1.5024577.
   PubMed Web of Science ®Google Scholar
• Owen, A. B. (1992), “Orthogonal Arrays for Computer Experiments, Integration and Visualization,” Statistica Sinica , 2, 439–452.
   Web of Science ®Google Scholar
• Qian, P. Z. (2012), “Sliced Latin Hypercube Designs,” Journal of the American Statistical Association , 107, 393–399. DOI: 10.1080/01621459.2011.644132.
   Web of Science ®Google Scholar
• Sacks, J. , Welch, W. J. , Mitchell, T. J. , and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science , 4, 409–423. DOI: 10.1214/ss/1177012413.
   Google Scholar
• Saltelli, A. , Tarantola, S. , Campolongo, F. , and Ratto, M. (2004), Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , Chichester: Wiley.
   Google Scholar
• Santner, T. J. , Williams, B. J. , and Notz, W. I. (2013), The Design and Analysis of Computer Experiments , New York: Springer-Verlag.
   Google Scholar
• Schölkopf, B. , Herbrich, R. , and Smola, A. J. (2001), “A Generalized Representer Theorem,” in International Conference on Computational Learning Theory , pp. 416–426.
   Google Scholar
• Wahba, G. (1990), Spline Models for Observational Data (Vol. 59), Philadelphia, PA: SIAM.
   Google Scholar
• Wu, C. , and Hamada, M. (2009), Experiments: Planning, Analysis, and Parameter Design Optimization , New York: Wiley.
   Google Scholar