相关论文: Notes on Perfectly Matched Layers (PMLs)

In the context of electromagnetic absorption, it is obvious that for an infinite planar periodic structure illuminated by a plane wave, the maximum attainable absorptance, i.e., perfect absorption, is theoretically limited to 100% of the…

Despite Contrastive Language-Image Pretraining (CLIP)'s remarkable capability to retrieve content across modalities, a substantial modality gap persists in its feature space. Intriguingly, we discover that off-the-shelf MLLMs (Multimodal…

Large Language Models (LLMs) have recently demonstrated remarkable capabilities in natural language processing tasks and beyond. This success of LLMs has led to a large influx of research contributions in this direction. These works…

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide…

Multinomial Logit (MNL) is one of the most popular discrete choice models and has been widely used to model ranking data. However, there is a long-standing technical challenge of learning MNL from many real-world ranking data: exact…

Unsupervised point cloud completion aims at estimating the corresponding complete point cloud of a partial point cloud in an unpaired manner. It is a crucial but challenging problem since there is no paired partial-complete supervision that…

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on the final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that…

In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…

We revisit the Universal Approximation Theorem(UAT) through the lens of the tropical geometry of neural networks and introduce a constructive, geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs). Tropical geometry…

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…

This paper studies the PML method for wave scattering in a half space of homogeneous medium bounded by a two-dimensional, perfectly conducting, and locally defected periodic surface, and develops a high-accuracy boundary-integral-equation…

Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…

Wave propagation through complex poroelastic multilayered media is difficult to model and invert because pronounced heterogeneity, scattering, mode conversion and fluid-solid coupling jointly distort acoustic signals during propagation.…

In this paper, theoretical and numerical studies of perfect/nearly-perfect conversion of a plane wave into a surface wave are presented. The problem of determining the electromagnetic properties of an inhomogeneous lossless boundary which…

This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory…

In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the…

For next-generation technology nodes, multiple patterning lithography (MPL) has emerged as a key solution, e.g., triple patterning lithography (TPL) for 14/11nm, and quadruple patterning lithography (QPL) for sub-10nm. In this paper, we…

Enforcing universal symmetries in machine learning (ML) models is a common strategy to mitigate data scarcity. We show that exploiting exact, as well as approximate, label symmetries can benefit scaling laws. We illustrate the idea for the…

Known coherent metasurfaces control interference of waves of a given frequency with other coherent waves at the same frequency, either illuminating from a different direction or created as intermodulation products. In this paper, we…