Oliver Tse

Eindhoven University of Technology (TU/e)

Here, you find information on research activities, publications, and members within the Vidi project:

Dynamical-variational transport costs and application to variational evolutions
Funded by Dutch Research Council

Project Summary

Evolution equations in spaces of measures describe a wide variety of natural phenomena. The theory for such evolutions has seen tremendous growth in the last decades, which resulted in (1) the metric space theory for gradient flows, and (2) the theory of rate-independent systems for analyzing variational evolutions—evolutions driven by one or more energies/entropies. While these theories have allowed for massive development of variational evolutions in a certain direction—gradient flows with homogeneous dissipation—physics and large-deviation theory suggest the study of generalized gradient flows—gradient flows with non-homogeneous dissipation—which are not covered in either theories.

In this project, we develop a theory of dynamical-variational transport costs (DVTs), a class of large-deviation-inspired functionals that provide a variational generalization of a zoo of existing transport distances. DVTs generate non-homogeneous generalizations of length spaces that will be used to extend metric-space techniques to general length spaces, thereby allowing a variational framework for (A) generalized gradient flows to be rigorously investigated, and (B) the multiscale analysis of such evolutions used in the development of numerical schemes.

Project Related Material

• Alberto Montefusco, Upanshu Sharma and Oliver Tse. Fourier-Cattaneo equation: stochastic origin, variational formulation, and asymptotic limits (arXiv:2211.07265)
• Jasper Hoeksema and Oliver Tse. Generalized gradient structures for measure-valued population dynamics and their large-population limit
  Calculus of Variations and Partial Differential Equations, 2023. (arXiv:2207.00853)
• Anastasiia Hraivoronska and Oliver Tse. Diffusive limit of random walks on tessellations via generalized gradient flows (arXiv:2202.06024)
• Simone Fagioli and Oliver Tse. On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility
  Nonlinear Analysis, 2022. (arXiv:2105.11389)
• Mark A. Peletier, Riccarda Rossi, Giuseppe Savaré and Oliver Tse. Jump processes as Generalized Gradient Flows
  Calculus of Variations and Partial Differential Equations, 2022. (arXiv:2006.10624)
• Bastian Hilder, Mark A. Peletier, Upanshu Sharma and Oliver Tse. An inequality connecting entropy distance, Fisher Information and large deviations
  Stochastic Processes and their Applications, 2019. (arXiv:1812.04358)

Collaborators

• Simone Fagioli, University of L'Aquila
• Bastian Hilder, University of Stuttgart
• Jasper Hoeksema, Eindhoven University of Technology
• Anastasiia Hraivoronska, Eindhoven University of Technology
• Alberto Montefusco, Zuse Institute Berlin
• Mark A. Peletier, Eindhoven University of Technology
• Riccarda Rossi, University of Brescia
• Giuseppe Savaré, Bocconi University
• André Schlichting, University of Münster
• Upanshu Sharma, Freie Universität Berlin