Extends PIE representation inductively to multivariate PDEs via domain intersections, proves consistency condition for operator inverse, and enables SDP-based stability analysis with PIETOOLS software.
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Equivariant SGMs achieve improved Wasserstein-1 generalization bounds on group-invariant distributions and learn the symmetrized score via equivariant vector fields without augmentation, with non-equivariant models incurring a quantifiable model-form error.
Regularization of Fourier multipliers yields L^∞ stability for wave propagation and compact operator inversion in inverse problems.
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A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Extends PIE representation inductively to multivariate PDEs via domain intersections, proves consistency condition for operator inverse, and enables SDP-based stability analysis with PIETOOLS software.
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Equivariant score-based generative models provably learn distributions with symmetries efficiently
Equivariant SGMs achieve improved Wasserstein-1 generalization bounds on group-invariant distributions and learn the symmetrized score via equivariant vector fields without augmentation, with non-equivariant models incurring a quantifiable model-form error.
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On $L^\infty$ stability for wave propagation and for linear inverse problems
Regularization of Fourier multipliers yields L^∞ stability for wave propagation and compact operator inversion in inverse problems.