Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints

In this work, we propose a new Gaussian process (GP) regression framework that enforces the physical constraints in a probabilistic manner. Specifically, we focus on inequality and monotonicity constraints. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC) algorithm, wh...

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Main Authors: Didem Kochan, Xiu Yang
Format: Article
Language:English
Published: Frontiers Media S.A. 2025-01-01
Series:Frontiers in Mechanical Engineering
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Online Access:https://www.frontiersin.org/articles/10.3389/fmech.2024.1410190/full
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author Didem Kochan
Xiu Yang
author_facet Didem Kochan
Xiu Yang
author_sort Didem Kochan
collection DOAJ
description In this work, we propose a new Gaussian process (GP) regression framework that enforces the physical constraints in a probabilistic manner. Specifically, we focus on inequality and monotonicity constraints. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC) algorithm, which is an efficient way to sample from a broad class of distributions by allowing a particle to have a random mass matrix with a probability distribution. Integrating the QHMC into the inequality and monotonicity constrained GP regression in the probabilistic sense, our approach enhances the accuracy and reduces the variance in the resulting GP model. Additionally, the probabilistic aspect of the method leads to reduced computational expenses and execution time. Further, we present an adaptive learning algorithm that guides the selection of constraint locations. The accuracy and efficiency of the method are demonstrated in estimating the hyperparameter of high-dimensional GP models under noisy conditions, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.
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spelling doaj-art-687a9df4ebbb4ea495a85158e6155dd42025-01-23T06:56:37ZengFrontiers Media S.A.Frontiers in Mechanical Engineering2297-30792025-01-011010.3389/fmech.2024.14101901410190Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraintsDidem KochanXiu YangIn this work, we propose a new Gaussian process (GP) regression framework that enforces the physical constraints in a probabilistic manner. Specifically, we focus on inequality and monotonicity constraints. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC) algorithm, which is an efficient way to sample from a broad class of distributions by allowing a particle to have a random mass matrix with a probability distribution. Integrating the QHMC into the inequality and monotonicity constrained GP regression in the probabilistic sense, our approach enhances the accuracy and reduces the variance in the resulting GP model. Additionally, the probabilistic aspect of the method leads to reduced computational expenses and execution time. Further, we present an adaptive learning algorithm that guides the selection of constraint locations. The accuracy and efficiency of the method are demonstrated in estimating the hyperparameter of high-dimensional GP models under noisy conditions, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.https://www.frontiersin.org/articles/10.3389/fmech.2024.1410190/fullconstrained optimizationGaussian process regressionquantum-inspired Hamiltonian Monte Carloadaptive learningsoft constraints
spellingShingle Didem Kochan
Xiu Yang
Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints
Frontiers in Mechanical Engineering
constrained optimization
Gaussian process regression
quantum-inspired Hamiltonian Monte Carlo
adaptive learning
soft constraints
title Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints
title_full Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints
title_fullStr Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints
title_full_unstemmed Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints
title_short Blending physics with data using an efficient Gaussian process regression with soft inequality and monotonicity constraints
title_sort blending physics with data using an efficient gaussian process regression with soft inequality and monotonicity constraints
topic constrained optimization
Gaussian process regression
quantum-inspired Hamiltonian Monte Carlo
adaptive learning
soft constraints
url https://www.frontiersin.org/articles/10.3389/fmech.2024.1410190/full
work_keys_str_mv AT didemkochan blendingphysicswithdatausinganefficientgaussianprocessregressionwithsoftinequalityandmonotonicityconstraints
AT xiuyang blendingphysicswithdatausinganefficientgaussianprocessregressionwithsoftinequalityandmonotonicityconstraints