mlsanityData to 7 Oct 2026

A spectrum of physics-informed Gaussian processes for regression in engineering

arXiv 2309.10656 ↗First posted 19 Sep 2023cs.LGcited by 13

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Abstract (arXiv)

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as ``big,'' they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a spectrum of possible Gaussian process models are introduced that enable the incorporation of different levels of expert knowledge of a system. Examples illustrate how these approaches can significantly reduce reliance on data collection whilst also increasing the interpretability of the model, another important consideration in this context.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 30 of its 86 references that are in the map. First posted on arXiv 19 Sep 2023.

Builds on

30 of 86 references.

References · 30

  1. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  2. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  3. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 203
  4. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
  5. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 139
  6. 2013Gaussian Process Kernels for Pattern Discovery and Extrapolationcited by 131
  7. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  8. 2019Nonlinear System Identification: A User-Oriented Roadmapcited by 55
  9. 2020A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challengescited by 51
  10. 2017Bayesian Probabilistic Numerical Methodscited by 50
  11. 2017Convolutional Gaussian Processescited by 44
  12. 2022Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solverscited by 40
18 more
  1. 2016Inferring solutions of differential equations using noisy multi-fidelity datacited by 38
  2. 2017Spectral Mixture Kernels for Multi-Output Gaussian Processescited by 29
  3. 2015Modeling and interpolation of the ambient magnetic field by Gaussian processescited by 28
  4. 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processescited by 20
  5. 2019A Gaussian process latent force model for joint input-state estimation in linear structural systemscited by 18
  6. 2019Gaussian processes with linear operator inequality constraintscited by 16
  7. 2020Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocitycited by 13
  8. 2021Grey-box models for wave loading predictioncited by 13
  9. 2019Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Featurescited by 10
  10. 2019Black-Box Inference for Non-Linear Latent Force Modelscited by 9
  11. 2021Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Featurescited by 8
  12. 2022Constraining Gaussian processes for physics-informed acoustic emission mappingcited by 7
  13. 2020A Bayesian methodology for localising acoustic emission sources in complex structurescited by 6
  14. 2021Probabilistic Inference for Structural Health Monitoring: New Modes of Learning from Datacited by 5
  15. 2021Structured Machine Learning Tools for Modelling Characteristics of Guided Wavescited by 4
  16. 2021Learning Nonparametric Volterra Kernels with Gaussian Processescited by 4
  17. 2022Physically Meaningful Uncertainty Quantification in Probabilistic Wind Turbine Power Curve Models as a Damage Sensitive Featurecited by 4
  18. 2023Physics-enhanced Gaussian Process Variational Autoencodercited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 6.

13 papers.

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  1. 2024Physics-Enhanced Machine Learning: a position paper for dynamical systems investigationscited by 11
  2. 2024Co-orchestration of Multiple Instruments to Uncover Structure-Property Relationships in Combinatorial Librariescited by 4
  3. 2024Measurements with Noise: Bayesian Optimization for Co-optimizing Noise and Property Discovery in Automated Experimentscited by 3
  4. 2025Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processescited by 0
  5. 2025Physically-informed change-point kernels for structural dynamicscited by 0
  6. 2025Digital twin for virtual sensing of ferry quays via a Gaussian Process Latent Force Modelcited by 0
  7. 2025Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architecturescited by 0
  8. 2026Physics-Informed Framework for Impact Identification in Aerospace Compositescited by 0
  9. 2026Green Physics-Informed Machine Learning Models For Structural Health Monitoringcited by 0
  10. 2026Orthogonal Discrepancy Kernels for Learning with Partial Physicscited by 0
  11. 2026Synergizing Physically Constrained MCMC and Chemical-Informed Gaussian Processes for Reaction Network Discoverycited by 0
  12. 2026Physics-Informed Machine Learning Under Small-Data Constraints: Lessons from Abrasive Waterjet Millingcited by 0
1 more
  1. 2026From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?cited by 0