Dynamics and Discretization: PDEs, Sampling, and Optimization

Program

Geometric Methods in Optimization and Sampling

Date

Monday, Oct. 25 – Friday, Oct. 29, 2021

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All times are listed in Pacific Time.

8:30 – 8:50 a.m.

Coffee and Check-In

8:50 – 9 a.m.

Opening Remarks

9 – 9:45 a.m.

Singular Limits for Vlasov Equations via Kinetic-Type Wasserstein Distances

Mikaela Iacobelli (ETH Zurich)

9:45 – 10:15 a.m.

The (Non-Convex) Optimal Uniform Quantization Problem

Quentin Mérigot (Université Paris-Saclay)

10:15 – 10:45 a.m.

Break

10:45 – 11:30 a.m.

Nonlocal Interaction Equation on Graphs: Gradient Flow Structure and Continuum Limit

Antonio Esposito (Friedrich-Alexander University Erlangen-Nürnberg)

11:30 a.m. – 12 p.m.

Nonlocal Wasserstein Distance and the Associated Gradient Flows

Dejan Slepčev (Carnegie Mellon Univeristy)

12 – 2 p.m.

Lunch

2 – 2:45 p.m.

A Duality Approach for Entropic-Regularized Optimal Transport: Sinkhorn Algorithm and Applications to Generative Models

Augusto Gerolin (University of Ottawa)

2:45 – 3:15 p.m.

The Most Likely Evolution of Diffusing and Vanishing Particles in the Spirit of E. Schroedinger: Constructing Bridges With Unbalanced Marginals

Tryphon Georgiou (UC Irvine)

3:15 – 3:45 p.m.

Break

3:45 – 4:30 p.m.

Training Wasserstein Generative Adversarial Networks Without Gradient Penalties

Dohyun Kwon (University of Wisconsin, Madison)

4:30 – 5:30 p.m.

Reception

8:30 – 9 a.m.

Coffee and Check-In

9 – 9:45 a.m.

An Optimal Transport Problem With Bulk/Interface Interactions

Léonard Monsaingeon (University of Lorraine and University of Lisbon)

9:45 – 10:15 a.m.

Dissipative Evolution of Probability Measures

Giuseppe Savaré (Bocconi University)

10:15 – 10:45 a.m.

Break

10:45 – 11:30 a.m.

Sampling via Birth-Death Dynamics

Yulong Lu (University of Massachusetts, Amherst)

11:30 a.m. – 12 p.m.

Latest Results on Birth-Death Dynamics

Lihan Wang (Carnegie Mellon University)

12 – 2 p.m.

Lunch

2 – 2:45 p.m.

Optimal Transport for Learning Chaotic Dynamics via Invariant Measures

Yunan Yang (Simons Institute)

2:45 – 3:15 p.m.

Hessian Informed Mirror Descent With Application in Gradient Flows

Li Wang (University of Minnesota)

3:15 – 3:45 p.m.

Break

3:45 – 4:30 p.m.

Uniform Convergence Rates for Lipschitz Learning Down to Graph Connectivity

Jeff Calder (University of Minnesota)

8:30 – 9 a.m.

Coffee and Check-In

9 – 9:45 a.m.

Optimal Transport With Stopping Times and the Stefan Problem

Inwon Kim (UCLA)

9:45 – 10:15 a.m.

The Singular Set in the Stefan Problem

Alessio Figalli (ETH Zurich)

10:15 – 10:45 a.m.

Break

10:45 – 11:30 a.m.

Global Well Posedness of Master Equations Mean Field Games

Wilfrid Gangbo (UCLA)

11:30 a.m. – 12 p.m.

Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)

Jan Stanczuk (University of Cambridge)

12 – 2 p.m.

Lunch

2 – 4 p.m.

Open Discussion (In-Person Only)

8:30 – 9 a.m.

Coffee and Check-In

9 – 9:45 a.m.

Linearised Optimal Transport Distances

Matthew Thorpe (University of Manchester)

9:45 – 10:15 a.m.

Archetypal Analysis

Braxton Osting (University of Utah)

10:15 – 10:45 a.m.

Break

10:45 – 11:30 a.m.

Mean-Field Theory of Two-Layers Neural Networks: Dimension Free Bounds and Example

Theodor Misiakiewicz (Stanford University)

11:30 a.m. – 12 p.m.

Continuous Time Stochastic Gradient Descent and Flat Minimum Selection

Stephan Wojtowytsch (Texas A&M)

12 – 2 p.m.

Lunch

2 – 2:45 p.m.

Consensus Based Sampling

Franca Hoffmann (University of Bonn)

2:45 – 3:15 p.m.

Sampling From Wasserstein Barycenter

Thibaut Le Gouic (Ecole Centrale de Marseille)

3:15 – 3:45 p.m.

Break

3:45 – 4:30 p.m.

Extending the JKO Scheme Beyond Wasserstein-2 Gradient Flows

Matthew Jacobs (UCLA)

8:30 – 9 a.m.

Coffee and Check-In

9 – 9:45 a.m.

Deterministic Particle Approximation for Nonlocal Transport Equations

Emanuela Radici (École Polytechnique Fédérale de Lausanne)

9:45 – 10:15 a.m.

A Particle Method for Degenerate Diffusion, and Applications to Robotic Swarming

Olga Turanova (Michigan State University)

10:15 – 10:45 a.m.

Break

10:45 – 11:30 a.m.

How to Train Better: Exploiting the Separability of DNNs

Lars Ruthotto (Emory University),
Elizabeth Newman (Emory University)

11:30 a.m. – 12 p.m.

Mirror Descent Algorithms for Minimizing Interacting Free Energy

Lexing Ying (Stanford University)

12 – 2 p.m.

Lunch

2 – 2:30 p.m.

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

Sui Tang (UC Santa Barbara)

2:30 – 3 p.m.

Discrete-To-Continuum Limits of Dynamical Optimal Transport Problems

Lorenzo Portinale (Hausdorff Center of Mathematics, Bonn)

3 – 3:30 p.m.

Density Control of Interacting Agent Systems

Yongxin Chen (Georgia Institute of Technology)