Global existence of weak solutions is established for 1D cross-diffusion systems with arbitrary advections via vanishing-viscosity limit and a three-entropy compensated-compactness argument that exploits oscillation correlation.
The Stein-log-Sobolev inequality and the exponential rate of convergence for the continuous Stein variational gradient descent method.arXiv preprint arXiv:2412.10295, 2024
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Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
Constructs multiple weak solutions to a cross-diffusion-advection system on the line, proving non-uniqueness by exhibiting both segregated and mixing behaviors from complementary half-line supports.
Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.
citing papers explorer
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Global solutions to cross-diffusion systems with independent advections in one dimension
Global existence of weak solutions is established for 1D cross-diffusion systems with arbitrary advections via vanishing-viscosity limit and a three-entropy compensated-compactness argument that exploits oscillation correlation.
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Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent
Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
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Non-uniqueness of weak solutions to cross-diffusion systems with advection
Constructs multiple weak solutions to a cross-diffusion-advection system on the line, proving non-uniqueness by exhibiting both segregated and mixing behaviors from complementary half-line supports.
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Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow
Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
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Stein Variational Gradient Descent dynamics for highly concentrated kernels
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.