Equivalence between Gaussian processes and linear diffusion models enables general conditioning on arbitrary pointwise likelihoods via ODE dynamics and Monte Carlo guidance approximation.
Physics-informed Gaussian process regression generalizes linear PDE solvers
6 Pith papers cite this work. Polarity classification is still indexing.
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Lagrangian Gaussian Processes use discrete Euler-Lagrange equations to condition GPs, preserving geometric structure for stable dynamics learning from sparse position snapshots without velocities.
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
Gaussian process regression generalizes Green's function integration for pressure reconstruction from error-embedded gradients, matching or exceeding GFI performance on turbulence data while providing calibrated posterior uncertainty.
A regularization-based kernel ridge regression approach learns PDE solution operators from physical priors without paired data and provides convergence rates.
A finite-dimensional dynamical model is derived from an infinite-dimensional state-space representation of second-order SPDEs via Galerkin approximation, with space-time covariance and approximation error quantified and tested on wave and diffusion examples.
citing papers explorer
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Conditioning Gaussian Processes on Almost Anything
Equivalence between Gaussian processes and linear diffusion models enables general conditioning on arbitrary pointwise likelihoods via ODE dynamics and Monte Carlo guidance approximation.
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Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations
Lagrangian Gaussian Processes use discrete Euler-Lagrange equations to condition GPs, preserving geometric structure for stable dynamics learning from sparse position snapshots without velocities.
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Error bounds for approximate posteriors from likelihood-informed reduced-order models
Derives error bounds on the root prior-preconditioned Hessian, posterior covariance, and mean for a Petrov-Galerkin reduced-order model, with exact posterior recovery at the intrinsic dimension.
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Pressure reconstruction from error-embedded gradient measurements: a Gaussian-process generalization of Green's function integration
Gaussian process regression generalizes Green's function integration for pressure reconstruction from error-embedded gradients, matching or exceeding GFI performance on turbulence data while providing calibrated posterior uncertainty.
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Kernel Learning of PDE Solution Operators
A regularization-based kernel ridge regression approach learns PDE solution operators from physical priors without paired data and provides convergence rates.
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A Dynamical Model for Spatio-Temporal Processes Motivated by Second-Order Partial Differential Equations
A finite-dimensional dynamical model is derived from an infinite-dimensional state-space representation of second-order SPDEs via Galerkin approximation, with space-time covariance and approximation error quantified and tested on wave and diffusion examples.