相关论文: On effective equidistribution for higher step nilf…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise.…
We study the asymptotic equidistribution of points with discrete energy close to Robin's constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of…
For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the…
The steady, asymmetric and two-dimensional flow of viscous, incompressible micropolar fluid through a rectangular channel with a splitter (parallel to walls) was formulated and simulated numerically. The plane Poiseuille flow was considered…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…
We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of $\R^n$ and their nondegenerate submanifolds.
The ability to learn multi-modal action distributions is indispensable for robotic manipulation policies to perform precise and robust control. Flow-based generative models have recently emerged as a promising solution to learning…
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We propose explicit forms for the steady state distributions governing fully developed turbulence in two and three spatial dimensions. We base our proposals on the crucial importance of the area and volume preserving diffeomorphisms in the…
Recent theoretical and experimental advances have shed light on the existence of so-called `perfectly transmitting' wavefronts with transmission coefficients close to 1 in strongly backscattering random media. These perfectly transmitting…
The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ…
We investigate small scale equidistribution of random orthonormal bases of eigenfunctions (i.e. eigenbases) on a compact manifold M. Assume that the group of isometries acts transitively on M and the multiplicity of eigenfrequency tends to…
Efficient particle sorting in microfluidic systems is vital for advancements in biomedical diagnostics and industrial applications. This study numerically investigates particle migration and passive sorting in symmetric serpentine…