brain elastography 1complex-valued fields 1gaussian processes 1helmholtz equation 1physics-informed learning 1
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stat.ML2026
Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography
Boyuan Deng, Kshitiz Upadhyay, Michael Shields
The paper extends physics‑informed Gaussian‑process regression to complex‑valued Helmholtz wavefields by converting the complex operator into a coupled real system, allowing uncert…
stat.ML2026
Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
Cornelius Otchere, Michael Shields
Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundar…
stat.ML2025
Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators
Ponkrshnan Thiagarajan, Tamer A. Zaki, Michael D. Shields
Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demandi…