Author

Michael D. Shields

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#machine learning Preprint Oct 2026

Constrained Probabilistic Numerics: Gaussian Process Solvers for Linear PDEs under Linear Inequality Constraints

Gaussian process solvers for linear partial differential equations (PDEs) return posteriors rather than point estimates, but they condition only on equality information: the PDE residual, boundary data, and measurements. Many solutions of interest also obey inequality constraints, including nonnegativity, monotonicity,...

B. Deng, Kshitiz Upadhyay, Michael D. Shields · 0 citations

#machine learning Jul 2026

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

This work extends operator-informed GP regression to complex-valued Helmholtz problems by realifying the complex operator into an equivalent coupled real block, which enables inference with standard real-valued GP conditioning and identifies a low-frequency accuracy ceiling set by model mismatch and a posterior uncerta...

B. Deng, Kshitiz Upadhyay, Michael D. Shields · arXiv.org · 0 citations