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Algorithmic Linearly Constrained Gaussian Processes

arXiv 1801.09197 ↗First posted 28 Jan 2018stat.ML cs.LG cs.SCcited by 20

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Abstract (arXiv)

We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr"obner bases. If successful, a push forward Gaussian process along the paramerization is the desired prior. We consider several examples from physics, geomathematics and control, among them the full inhomogeneous system of Maxwell's equations. By bringing together stochastic learning and computer algebra in a novel way, we combine noisy observations with precise algebraic computations.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jan 2018.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 1; 2024: 4; 2025: 2; 2026: 3.

20 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. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
  4. 2022Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficientscited by 17
  5. 2022Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equationscited by 14
  6. 2023Intrinsic Gaussian Vector Fields on Manifoldscited by 8
  7. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  8. 2022On boundary conditions parametrized by analytic functionscited by 4
  9. 2022Designing Robust Biotechnological Processes Regarding Variabilities using Multi-Objective Optimization Applied to a Biopharmaceutical Seed Train Designcited by 4
  10. 2024Neural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equationscited by 4
  11. 2022Incorporating Sum Constraints into Multitask Gaussian Processescited by 2
  12. 2024Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equationscited by 2
8 more
  1. 2025Gaussian Process Regression for Inverse Problems in Linear PDEscited by 2
  2. 2021Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularizationcited by 1
  3. 2021Efficient methods for Gaussian Markov random fields under sparse linear constraintscited by 1
  4. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  5. 2024Physics-informed Gaussian Processes as Linear Model Predictive Controllercited by 0
  6. 2025Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Paritycited by 0
  7. 2026Fast Reconstruction of Exact Maxwell Dynamics from Sparse Datacited by 0
  8. 2026Multi-output Gaussian process prediction of physical fields under linear equality constraintscited by 0