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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Sufficient conditions for QMC analysis of finite elements for parametric differential equations
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.
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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.
- A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold