A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification

• URL: http://arxiv.org/abs/2205.06494v1
• Date: Fri, 13 May 2022 07:53:49 GMT
• Title: A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification
• Authors: Cheng Chang and Tieyong Zeng
• Abstract summary: We propose a hybrid data driven-physics constrained Gaussian process regression framework. We encode the physics knowledge with Boltzmann-Gibbs distribution and derive our model through maximum likelihood (ML) approach. The proposed model achieves good results in high-dimensional problem, and correctly propagate the uncertainty, with very limited labelled data provided.
• Score: 21.972192114861873
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset. If appropriate physics constraints (e.g. expressed in partial differential equations) can be incorporated, the amount of data can be greatly reduced and the accuracy further improved. In this work, we propose a hybrid data driven-physics constrained Gaussian process regression framework. We encode the physics knowledge with Boltzmann-Gibbs distribution and derive our model through maximum likelihood (ML) approach. We apply deep kernel learning method. The proposed model learns from both data and physics constraints through the training of a deep neural network, which serves as part of the covariance function in GPR. The proposed model achieves good results in high-dimensional problem, and correctly propagate the uncertainty, with very limited labelled data provided.

Related papers

• Sparse Variational Contaminated Noise Gaussian Process Regression with Applications in Geomagnetic Perturbations Forecasting [4.675221539472143]
  We propose a scalable inference algorithm for fitting sparse Gaussian process regression models with contaminated normal noise on large datasets. We show that our approach yields shorter prediction intervals for similar coverage and accuracy when compared to an artificial dense neural network baseline.
  arXiv  Detail & Related papers  (2024-02-27T15:08:57Z)
• Implicit Manifold Gaussian Process Regression [49.0787777751317]
  Gaussian process regression is widely used to provide well-calibrated uncertainty estimates. It struggles with high-dimensional data because of the implicit low-dimensional manifold upon which the data actually lies. In this paper we propose a technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way.
  arXiv  Detail & Related papers  (2023-10-30T09:52:48Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• Parallel and Limited Data Voice Conversion Using Stochastic Variational Deep Kernel Learning [2.5782420501870296]
  This paper proposes a voice conversion method that works with limited data. It is based on variational deep kernel learning (SVDKL) It is possible to estimate non-smooth and more complex functions.
  arXiv  Detail & Related papers  (2023-09-08T16:32:47Z)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• RMFGP: Rotated Multi-fidelity Gaussian process with Dimension Reduction for High-dimensional Uncertainty Quantification [12.826754199680474]
  Multi-fidelity modelling enables accurate inference even when only a small set of accurate data is available. By combining the realizations of the high-fidelity model with one or more low-fidelity models, the multi-fidelity method can make accurate predictions of quantities of interest. This paper proposes a new dimension reduction framework based on rotated multi-fidelity Gaussian process regression and a Bayesian active learning scheme.
  arXiv  Detail & Related papers  (2022-04-11T01:20:35Z)
• Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
  We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
  arXiv  Detail & Related papers  (2021-10-26T10:45:25Z)
• Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks [0.0]
  We show how to use local approximate process regression to predict stress outputs at particular strain space locations. A modified Newton-Raphson approach is proposed to accommodate for the local nature of the laGPR approximation when solving the global structural problem in a FE setting.
  arXiv  Detail & Related papers  (2021-05-07T14:49:28Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)
• Real-Time Regression with Dividing Local Gaussian Processes [62.01822866877782]
  Local Gaussian processes are a novel, computationally efficient modeling approach based on Gaussian process regression. Due to an iterative, data-driven division of the input space, they achieve a sublinear computational complexity in the total number of training points in practice. A numerical evaluation on real-world data sets shows their advantages over other state-of-the-art methods in terms of accuracy as well as prediction and update speed.
  arXiv  Detail & Related papers  (2020-06-16T18:43:31Z)
• Physics Informed Deep Kernel Learning [24.033468062984458]
  Physics Informed Deep Kernel Learning (PI-DKL) exploits physics knowledge represented by differential equations with latent sources. For efficient and effective inference, we marginalize out the latent variables and derive a collapsed model evidence lower bound (ELBO)
  arXiv  Detail & Related papers  (2020-06-08T22:43:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.