arxivstat.MLcs.LGmath.NAphysics.med-ph2026-07-15
Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography
Boyuan Deng, Kshitiz Upadhyay, Michael Shields
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…