Michael D. Shields

works on

brain elastography 1 complex-valued fields 1 gaussian processes 1 helmholtz equation 1 physics-informed learning 1

From the 1 of 9 linked papers with an AI index.

activity

20242026

collaborators

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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…

cs.CE2026

$I ¨ -$ DeepONet: A Discontinuity Capturing Neural Operator

Sumanta Roy, Stephen T. Castonguay, Pratanu Roy +1

We present $I ¨ -$ DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Cla…

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

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks

I¨−DeepONet: A Discontinuity Capturing Neural Operator

$I ¨ -$ DeepONet: A Discontinuity Capturing Neural Operator