A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
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Augmented Krylov subspaces jointly approximate quadratic forms and log-dets for faster MLE-based hyperparameter tuning in kernel-based linear system identification.
The paper provides sufficient conditions on parametric regularity for QMC error bounds in finite element discretizations of parametric PDEs with Gevrey-regular random fields, achieving faster-than-MC rates when the quantity of interest depends continuously on the solution, flux, or gradient.
Review chapter summarizing advances in parallel sparse direct solvers along communication reduction and data-sparse compression axes.
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Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
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Kernel-based linear system identification using augmented Krylov subspaces
Augmented Krylov subspaces jointly approximate quadratic forms and log-dets for faster MLE-based hyperparameter tuning in kernel-based linear system identification.
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Parallel Sparse and Data-Sparse Factorization-based Linear Solvers
Review chapter summarizing advances in parallel sparse direct solvers along communication reduction and data-sparse compression axes.