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Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
Many applications generate and consume temporal data and retrieval of time series is a key processing step in many application domains. Dynamic time warping (DTW) distance between time series of size N and M is computed relying on a dynamic…
Model discrepancy, defined as the difference between model predictions and reality, is ubiquitous in computational models for physical systems. It is common to derive partial differential equations (PDEs) from first principles physics, but…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this…
Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the…
Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this paper, we propose an iterative…
A Statistic Vectorial Complex Ray Model (SVCRM) is proposed for the scattering of a plane wave by a non-spherical dielectric particle in three dimensions. This method counts the complex amplitudes of all rays arriving in a tiny box in the…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…
Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$, the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that has the maximum weighted coverage by \emph{sampling only a few hyperedges} in…
A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous…
The digital telecommunications receiver is an important context for inference methodology, the key objective being to minimize the expected loss function in recovering the transmitted information. For that criterion, the optimal decision is…
In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard…
The inverse design of optical metasurfaces is a rapidly emerging field that has already shown great promise in miniaturizing conventional optics as well as developing completely new optical functionalities. Such a design process relies on…
Adaptive optics can be used to mitigate the effects of atmospheric turbulence on imaging systems, but the correction is only partial, and deconvolution is often required to improve the resolution. This results in entire optical/digital…
In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$.…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
The FTTH (Fiber To The Home) market currently needs new network maintenance technologies that can, economically and effectively, cope with massive fiber plants. However, operating these networks requires adequate means for an effective…
An analytical expression is given for the minimum of the time-delay induced wavefront error (also known as the servo-lag error) in Adaptive Optics systems under temporal prediction filtering. The analysis is based on the von K\'arm\'an…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…