2020
DOI: 10.1007/978-3-030-40245-7_9
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Physical Extrapolation of Quantum Observables by Generalization with Gaussian Processes

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Cited by 3 publications
(5 citation statements)
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“…As illustrated in Ref. [48], the iterative kernel construction algorithm based on BIC optimization is critical for building models with low generalization error.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…As illustrated in Ref. [48], the iterative kernel construction algorithm based on BIC optimization is critical for building models with low generalization error.…”
Section: Discussionmentioning
confidence: 99%
“…As shown previously, complex kernel functions cannot be constructed as random combinations of simple kernels [48]. Instead, the kernel construction algorithm should be guided by a model selection metric.…”
Section: Complex Kernelsmentioning
confidence: 99%
“…We optimize the functional form of the kernel function using a greedy search algorithm that combines simple functions into linear combinations and products, as was described in [17,18] and used for various applications in [103,108,109,[113][114][115]. The kernel construction algorithm is illustrated in figure 4.…”
Section: Method: Gaussian Process Regression With Variable Kernelsmentioning
confidence: 99%
“…This methodology is commonly named as the Bayesian information criterion (BIC). These kernel structure discovery methods have been demonstrated to extrapolate physical observables accurately enough to detect phase transitions 34,35 . Additionally, GPs with complex kernels have shown the possibility to predict accurate energies for PES trained only with low energy points 17,18 .…”
Section: Gaussian Processesmentioning
confidence: 99%
“…The latter quantifies the similarity between a pair of points. If the kernel function can generalize a similarity metric, GPs are efficient regression algorithms that require less training data than NNs 1 , and are also capable of extrapolating functions beyond the training data regime 17,[34][35][36][37] . To achieve more robust kernel functions, once can simply combine different simple kernel functions 38,39 .…”
Section: Introductionmentioning
confidence: 99%