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