# Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence

arXiv: https://arxiv.org/abs/1811.09757 · HTML: https://mlsanity.com/paper/1811.09757/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2018.

## Built on by (most cited first, 16 of 16)

- [Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations](https://mlsanity.com/paper/2203.08501/) (2022)
- [Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation](https://mlsanity.com/paper/2106.13790/) (2021)
- [Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions](https://mlsanity.com/paper/2208.08635/) (2022)
- [Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems](https://mlsanity.com/paper/2108.00037/) (2021)
- [Failure-averse Active Learning for Physics-constrained Systems](https://mlsanity.com/paper/2110.14443/) (2021)
- [PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations](https://mlsanity.com/paper/2204.02583/) (2022)
- [Physics-informed CoKriging model of a redox flow battery](https://mlsanity.com/paper/2106.09188/) (2021)
- [A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification](https://mlsanity.com/paper/2205.06494/) (2022)
- [General multi-fidelity surrogate models: Framework and active learning strategies for efficient rare event simulation](https://mlsanity.com/paper/2212.03375/) (2022)
- [Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis](https://mlsanity.com/paper/2305.13879/) (2023)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Physics-informed solution reconstruction in elasticity and heat transfer using the explicit constraint force method](https://mlsanity.com/paper/2505.04875/) (2025)
- [Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression](https://mlsanity.com/paper/2403.09758/) (2024)
- [Gaussian Process Regression with Soft Inequality and Monotonicity Constraints](https://mlsanity.com/paper/2404.02873/) (2024)
- [Label Propagation for Physics-Informed Neural Networks and Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2404.05817/) (2024)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)

## Abstract (arXiv)

In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and high-fidelity data using a parameterized GP with hyperparameters identified via optimization. Our approach reduces the cost of optimization for inferring hyperparameters by incorporating partial physical knowledge. We prove that the physical constraints in the form of deterministic linear operators are satisfied up to an error bound. Furthermore, we combine CoPhIK with a greedy active learning algorithm for guiding the selection of additional observation locations. The efficiency and accuracy of CoPhIK are demonstrated for reconstructing the partially observed modified Branin function, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.