Search Results - "Li, Wuchen"

Transport information geometry: Riemannian calculus on probability simplex by Li, Wuchen

“…We formulate the Riemannian calculus of the probability set embedded with L 2 -Wasserstein metric. This is an initial work of transport information geometry…”
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A machine learning framework for solving high-dimensional mean field game and mean field control problems by Ruthotto, Lars, Osher, Stanley J., Li, Wuchen, Nurbekyan, Levon, Fung, Samy Wu

“…Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive populations of interacting…”
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Quantum Statistical Learning via Quantum Wasserstein Natural Gradient by Becker, Simon, Li, Wuchen

“…In this article, we introduce a new approach towards the statistical learning problem argmin ρ ( θ ) ∈ P θ W Q 2 ( ρ ⋆ , ρ ( θ ) ) to approximate a target…”
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Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations by Bayraktar, Erhan, Feng, Qi, Li, Wuchen

“…We study long-time dynamical behaviors of weakly self-consistent Vlasov–Fokker–Planck equations. We introduce Hessian matrix conditions on mean-field kernel…”
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Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games by Lin, Alex Tong, Fung, Samy Wu, Li, Wuchen, Nurbekyan, Levon, Osher, Stanley J.

“…We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean-field games (MFGs). Our algorithm is geared toward…”
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Entropy Dissipation for Degenerate Stochastic Differential Equations via Sub-Riemannian Density Manifold by Feng, Qi, Li, Wuchen

“…We studied the dynamical behaviors of degenerate stochastic differential equations (SDEs). We selected an auxiliary Fisher information functional as the…”
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A kernel formula for regularized Wasserstein proximal operators by Li, Wuchen, Liu, Siting, Osher, Stanley

“…We study a class of regularized proximal operators in Wasserstein-2 space. We derive their solutions by kernel integration formulas. We obtain the Wasserstein…”
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Mean field control problems for vaccine distribution by Lee, Wonjun, Liu, Siting, Li, Wuchen, Osher, Stanley

“…With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational…”
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Modeling COVID-19 with mean field evolutionary dynamics: Social distancing and seasonality by Gao, Hao, Li, Wuchen, Pan, Miao, Han, Zhu, Poor, H. Vincent

“…The coronavirus pandemic has been declared a world health emergency by the World Health Organization, which has raised the importance of an accurate…”
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Dynamical Schrödinger Bridge Problems on Graphs by Chow, Shui-Nee, Li, Wuchen, Mou, Chenchen, Zhou, Haomin

“…We study a discrete dynamical Schrödinger bridge problem (SBP) as a dynamical variational problem on a finite graph. We prove that the discrete SBP exists a…”
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Accelerated Information Gradient Flow by Wang, Yifei, Li, Wuchen

“…We present a framework for Nesterov’s accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo algorithms for…”
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Langevin dynamics for the probability of finite state Markov processes by Li, Wuchen

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Diffusion hypercontractivity via generalized density manifold by Li, Wuchen

“…We prove a one-parameter family of diffusion hypercontractivity from a class of drift-diffusion processes. We next derive the related log–Sobolev, Poincare,…”
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Transport information Bregman divergences by Li, Wuchen

“…We study Bregman divergences in probability density space embedded with the L 2 –Wasserstein metric. Several properties and dualities of transport Bregman…”
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Fisher information regularization schemes for Wasserstein gradient flows by Li, Wuchen, Lu, Jianfeng, Wang, Li

“…•Derive Fisher information regularization via energy splitting.•Reduce the dimension of inner dynamic formulation.•With the new regularization, the method is…”
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Natural gradient via optimal transport by Li, Wuchen, Montúfar, Guido

“…We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the…”
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Computational mean-field information dynamics associated with reaction-diffusion equations by Li, Wuchen, Lee, Wonjun, Osher, Stanley

“…We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations…”
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Wasserstein information matrix by Li, Wuchen, Zhao, Jiaxi

“…We study information matrices for statistical models by the L 2 -Wasserstein metric. We call them Wasserstein information matrices (WIMs), which are analogs of…”
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Controlling conservation laws I: Entropy–entropy flux by Li, Wuchen, Liu, Siting, Osher, Stanley

“…We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal…”
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Controlling conservation laws II: Compressible Navier–Stokes equations by Li, Wuchen, Liu, Siting, Osher, Stanley

“…We propose, study, and compute solutions to a class of optimal control problems for hyperbolic systems of conservation laws and their viscous regularization…”
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