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This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…
Traditional CNC technology mostly uses the method of increasing the degree of interpolation polynomial when constructing $C^2$ continuous NURBS curves, but this often leads to the appearance of Runge phenomenon in interpolation curves.…
Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…
In this paper a fourth order asymptotically optimal error bound for a new cubic interpolating spline function, denoted by Q-spline, is derived for the case that only function values at given points are used but not any derivative…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…
Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
Radio frequency transceivers operating in in-band full-duplex or frequency-division duplex mode experience strong transmitter leakage. Combined with receiver nonlinearities, this causes intermodulation products in the baseband, possibly…
6-DoF object pose estimation from a monocular image is challenging, and a post-refinement procedure is generally needed for high-precision estimation. In this paper, we propose a framework based on a recurrent neural network (RNN) for…
Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients. Short of designing new RNN architectures, previous methods for dealing…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…
Detecting slender, overlapping structures remains a challenge in computational microscopy. While recent coordinate-based approaches improve detection, they often produce less accurate splines than pixel-based methods. We introduce a…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…