Related papers: Efficient rational approximation of optical respon…
We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, S\`{e}te, and Trefethen to approximate the nonlinear eigenvalue problem by a rational eigenvalue…
Accurate choroid segmentation in optical coherence tomography (OCT) image is vital because the choroid thickness is a major quantitative biomarker of many ocular diseases. Deep learning has shown its superiority in the segmentation of the…
Chiral photonic metasurfaces provide unique capabilities for tailoring light-matter interactions, which are essential for next-generation photonic devices. Here, we report an advanced optimization framework that combines deep learning and…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
Surrogate assisted evolutionary algorithms (EA) are rapidly gaining popularity where applications of EA in complex real world problem domains are concerned. Although EAs are powerful global optimizers, finding optimal solution to complex…
This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems,…
This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call "field amplification",…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…
Arbitrarily Applicable Relational Responding (AARR) is a cornerstone of human language and reasoning, referring to the learned ability to relate symbols in flexible, context-dependent ways. In this paper, we present a novel theoretical…
AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
In this paper we describe an adaptive and multi-scale algorithm for the parsimonious fit of the corneal surface data that allows to adapt the number of functions used in the reconstruction to the conditions of each cornea. The method…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Devices that detect angle-of-arrival (AoA) over a wide field of view are crucial for various applications such as wireless communication and navigation. They are often installed on platforms with challenging mechanical and stealth…
This paper describes MAIA, a Multimodal Automated Interpretability Agent. MAIA is a system that uses neural models to automate neural model understanding tasks like feature interpretation and failure mode discovery. It equips a pre-trained…
Many algorithms for approximating data with rational functions are built on interpolation or least-squares approximation. Inspired by the adaptive Antoulas-Anderson (AAA) algorithm for the univariate case, the parametric adaptive…