Gaussian Process Regression -- Neural Network Hybrid with Optimized Redundant Coordinates
Not on the map. Why?
Abstract (arXiv)
Recently, a Gaussian Process Regression - neural network (GPRNN) hybrid machine learning method was proposed, which is based on additive-kernel GPR in redundant coordinates constructed by rules [J. Phys. Chem. A 127 (2023) 7823]. The method combined the expressive power of an NN with the robustness of linear regression, in particular, with respect to overfitting when the number of neurons is increased beyond optimal. We introduce opt-GPRNN, in which the redundant coordinates of GPRNN are optimized with a Monte Carlo algorithm and show that when combined with optimization of redundant coordinates, GPRNN attains the lowest test set error with much fewer terms / neurons and retains the advantage of avoiding overfitting when the number of neurons is increased beyond optimal value. The method, opt-GPRNN possesses an expressive power closer to that of a multilayer NN and could obviate the need for deep NNs in some applications. With optimized redundant coordinates, a dimensionality reduction regime is also possible. Examples of application to machine learning an interatomic potential and materials informatics are given.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 10 of its 64 references that are in the map. First posted on arXiv 10 Sep 2025.
Builds on
10 of 64 references.
References · 10
- 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
- 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
- 2022A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledgecited by 31
- 2023Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regressioncited by 14
- 2021On the optimization of hyperparameters in Gaussian process regression with the help of low-order high-dimensional model representationcited by 6
- 2020Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general methodcited by 5
- 2023Neural network with optimal neuron activation functions based on additive Gaussian process regressioncited by 5
- 2023Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimensioncited by 3
- 2022The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfacescited by 2
- 2025Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theorycited by 2
Built on by
Not cited yet.