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New Gaussian Process method solves complex wave problems with uncertainty quantification

By PulseAugur Editorial · [2 sources] ·

Researchers have developed a novel method for solving complex wave propagation problems governed by the Helmholtz equation, particularly in dissipative media where the squared wavenumber is complex. This new approach extends operator-informed Gaussian Process (GP) regression to handle complex-valued fields by transforming the problem into an equivalent real-valued system. The method demonstrates competitive performance against finite-difference and neural network baselines on benchmark problems, offering the advantage of quantifying uncertainty in its predictions. When applied to in vivo brain magnetic resonance elastography, the technique successfully reconstructed the shear curl field with a high correlation to measurements. AI

IMPACT This research advances probabilistic methods for complex physics simulations, potentially improving accuracy and uncertainty quantification in fields like medical imaging.

RANK_REASON The cluster contains an academic paper detailing a new method for solving complex physics problems using Gaussian Processes.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New Gaussian Process method solves complex wave problems with uncertainty quantification

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The cluster contains an academic paper detailing a new method for solving complex physics problems using Gaussian Processes.
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COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Boyuan Deng, Kshitiz Upadhyay, Michael Shields ·

    Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

    arXiv:2607.14193v1 Announce Type: new Abstract: The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also q…

  2. arXiv stat.ML TIER_1 English(EN) · Michael Shields ·

    Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

    The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $κ^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gauss…

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