mlsanityData to 7 Oct 2026

Linearly constrained Gaussian processes

arXiv 1703.00787 ↗First posted 2 Mar 2017stat.MLcited by 41

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Abstract (arXiv)

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sample drawn or prediction made. We also propose a constructive procedure for designing the transformation operator and illustrate the result on both simulated and real-data examples.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Mar 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 12; 2023: 3; 2024: 7; 2025: 4; 2026: 6.

41 papers.

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  1. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  2. 2022Learning differentiable solvers for systems with hard constraintscited by 34
  3. 2024Physics-Informed Neural Networks with Hard Linear Equality Constraintscited by 30
  4. 2021A Probabilistic State Space Model for Joint Inference from Differential Equations and Datacited by 21
  5. 2022Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learningcited by 20
  6. 2022Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficientscited by 17
  7. 2021High-Dimensional Gaussian Process Inference with Derivativescited by 16
  8. 2021Bayesian Numerical Methods for Nonlinear Partial Differential Equationscited by 15
  9. 2022Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equationscited by 14
  10. 2022Constraining Gaussian processes for physics-informed acoustic emission mappingcited by 7
  11. 2022Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fieldscited by 7
  12. 2022A Kernel Approach for PDE Discovery and Operator Learningcited by 7
29 more
  1. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  2. 2023Learning thermodynamically constrained equations of state with uncertaintycited by 5
  3. 2022On boundary conditions parametrized by analytic functionscited by 4
  4. 2024Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Modelscited by 4
  5. 2026Conditioning Gaussian Processes on Almost Anythingcited by 3
  6. 2021Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guaranteescited by 2
  7. 2021Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priorscited by 2
  8. 2022Incorporating Sum Constraints into Multitask Gaussian Processescited by 2
  9. 2022Adjoint-aided inference of Gaussian process driven differential equationscited by 2
  10. 2022Monotonic Gaussian process for physics-constrained machine learning with materials science applicationscited by 2
  11. 2022A connection between probability, physics and neural networkscited by 2
  12. 2024Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equationscited by 2
  13. 2025Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Featurescited by 2
  14. 2026PHDME: Physics-Informed Diffusion Models without Explicit Governing Equationscited by 2
  15. 2021Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularizationcited by 1
  16. 2021Efficient methods for Gaussian Markov random fields under sparse linear constraintscited by 1
  17. 2021Distributional Gradient Matching for Learning Uncertain Neural Dynamics Modelscited by 1
  18. 2023Efficient Sensor Placement from Regression with Sparse Gaussian Processes in Continuous and Discrete Spacescited by 1
  19. 2023Gaussian Processes with State-Dependent Noise for Stochastic Controlcited by 1
  20. 2025Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Modelscited by 1
  21. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  22. 2024PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networkscited by 0
  23. 2024On the Laplace Approximation as Model Selection Criterion for Gaussian Processescited by 0
  24. 2024Physics-informed Gaussian Processes as Linear Model Predictive Controllercited by 0
  25. 2025Determination of Particle-Size Distributions from Light-Scattering Measurement Using Constrained Gaussian Process Regressioncited by 0
  26. 2025Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Paritycited by 0
  27. 2026Fast Reconstruction of Exact Maxwell Dynamics from Sparse Datacited by 0
  28. 2026Multi-output Gaussian process prediction of physical fields under linear equality constraintscited by 0
  29. 2026When Noise Estimation Hides Basis Misspecification in Repeated Bayesian Inverse Problemscited by 0