Covariance-modulated optimal transport and gradient flows

DOI10.1007/s00205-024-02065-wMaRDI QIDQ6660122

André Schlichting, Daniel Matthes, Matthias Erbar, Martin Burger, Franca Hoffmann

Publication date: 10 January 2025

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Sub-Riemannian geometry (53C17) Fokker-Planck equations (35Q84) Optimal transportation (49Q22)

Cites Work

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• Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion
• The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances
• Optimal linear drift for the speed of convergence of an hypoelliptic diffusion
• The reconstruction problem for the Euler-Poisson system in cosmology
• Riemannian geometry and matrix geometric means
• Nonlinear mobility continuity equations and generalized displacement convexity
• Characterization of absolutely continuous curves in Wasserstein spaces
• On an inequality of Lieb and Thirring
• Mass transportation on sub-Riemannian manifolds
• On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals
• A new class of transport distances between measures
• On a constrained 2-D Navier-Stokes equation
• A class of Wasserstein metrics for probability distributions
• A convexity principle for interacting gases
• Constrained steepest descent in the 2-Wasserstein metric
• On generalized Csiszár-Kullback inequalities
• Ensemble preconditioning for Markov chain Monte Carlo simulation
• Wasserstein Riemannian geometry of Gaussian densities
• Convex functionals of probability measures and nonlinear diffusions on manifolds
• Online natural gradient as a Kalman filter
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium
• Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
• On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility
• Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativity
• Is affine-invariance well defined on SPD matrices? A principled continuum of metrics
• Procrustes metrics on covariance operators and optimal transportation of Gaussian processes
• On the Bures-Wasserstein distance between positive definite matrices
• Kinetic methods for inverse problems
• Well-posedness of evolution equations with time-dependent nonlinear mobility: a modified minimizing movement scheme
• Hessian transport gradient flows
• Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation
• Dualistic differential geometry of positive definite matrices and its applications to related problems
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• A Nonparametric Ensemble Transform Method for Bayesian Inference
• A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
• Positive Definite Matrices
• Information Geometry of the Gaussian Distribution in View of Stochastic Optimization
• On a Nonlinear, Nonlocal Parabolic Problem with Conservation of Mass, Mean and Variance
• Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering
• Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
• Optimal transportation under nonholonomic constraints
• Logarithmic Sobolev Inequalities
• Scaling Limit of the Stein Variational Gradient Descent: The Mean Field Regime
• Convergence analysis of ensemble Kalman inversion: the linear, noisy case
• Analysis and Geometry of Markov Diffusion Operators
• Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations
• Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler
• Tikhonov Regularization within Ensemble Kalman Inversion
• Probabilistic Forecasting and Bayesian Data Assimilation
• Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces
• Ensemble Kalman inversion: a derivative-free technique for machine learning tasks
• Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations
• Poisson's Equation in Nonlinear Filtering
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Analysis of the Ensemble Kalman Filter for Inverse Problems
• Information Geometry
• Sub-Riemannian Geometry and Optimal Transport
• Eulerian Calculus for the Contraction in the Wasserstein Distance
• An Extension of Kakutani's Theorem on Infinite Product Measures to the Tensor Product of Semifinite w ∗ -Algebras
• Ensemble Kalman Sampler: Mean-field Limit and Convergence Analysis
• Gradient flow structure and convergence analysis of the ensemble Kalman inversion for nonlinear forward models
• Optimal Whitening and Decorrelation
• Optimal Transport
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
• Transport distances and geodesic convexity for systems of degenerate diffusion equations
• Stein variational gradient descent: many-particle and long-time asymptotics
• On a novel gradient flow structure for the aggregation equation
• New results in linear filtering and prediction theory
• Information geometry of Wasserstein statistics on shapes and affine deformations

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