Related papers: Homogenization of Enhancing Thin Layers
Metasurfaces composed of subwavelength unit cells usually require a large number of unit cells which leads to complicated design and optimization. Aggressive discretization in a metasurface can significantly reduce the number of unit cells…
Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditional distributions in the generative process and efficient computation of the loss as independent terms…
We present Deep Compression Autoencoder (DC-AE), a new family of autoencoder models for accelerating high-resolution diffusion models. Existing autoencoder models have demonstrated impressive results at a moderate spatial compression ratio…
End-to-end planning systems for autonomous driving are rapidly improving, especially in closed-loop simulation environments like CARLA. Many such driving systems either do not consider uncertainty as part of the plan itself or obtain it by…
For one dimensional homogeneous bistable diffusion equations, Fife-McLeod ([Arch. Ration. Mech. Anal., 65 (1977), 335-361]) gave a well-known theorem which says that spreading solutions starting from compactly supported initial data can be…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
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…
Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes…
The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
Diffusion transformers have been widely adopted for text-to-image synthesis. While scaling these models up to billions of parameters shows promise, the effectiveness of scaling beyond current sizes remains underexplored and challenging. By…
We compute the effective diffusion coefficient of a Brownian particle in a piece-wise linear periodic potential and subject of spatially inhomogeneous temperature, otherwise known as the B{\"u}ttiker-Landauer motor. We obtain analytical…
This paper develops a comprehensive Hamilton-Jacobi framework to analyze asymptotic propagation dynamics in a field-road system featuring unidirectional advection and Wentzell-type boundary conditions. We rigorously derive a Hamilton-Jacobi…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
We present an algorithm to estimate fast and accurate depth maps from light fields via a sparse set of depth edges and gradients. Our proposed approach is based around the idea that true depth edges are more sensitive than texture edges to…
We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…
We consider the dispersion properties of tracer particles moving in non-equilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local…
Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this…
Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {\em sticky} environments. Therefore, diffusing particles experience both…