Related papers: Data-driven quasiconformal morphodynamic flows

Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…

A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…

Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations.…

We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. For this, we study the associated nonlocal quasilinear evolution equation satisfied by the family of graph functions. We establish, using an…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

We have found that the relation between the flow through campylotic (generically curved) media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system exhibits two distinct functional expressions…

We show the existence of a global unique and analytic solution for the mean curvature flow, the surface diffusion flow and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. We also show the existence…

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…

Remote sensing change detection is often challenged by spatial misalignment between bi-temporal images, especially when acquisitions are separated by long seasonal or multi-year gaps. While modern convolutional and transformer-based models…

We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space making statistical…

Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…

Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the…

Flow matching has emerged as a promising generative approach that addresses the lengthy sampling times associated with state-of-the-art diffusion models and enables a more flexible trajectory design, while maintaining high-quality image…

In this note, we give a diffeomorphism (to $\mathbb{R}^n$) criterion via long-time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in [Manifolds with small curvature concentration,…

In this paper we survey some results on Ricci flowing non-smooth initial data. Among other things, we give a non-exhaustive list of various weak initial data which can be evolved with the Ricci flow. We also survey results which show that…

Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…

We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three dimensional patterns. We experimentally demonstrate this theory by…

We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…

This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…