相关论文: Data Denoising and Derivative Estimation for Data-…

Recent years have seen an increasing amount of research devoted to the development of so-called resonance-based methods for dispersive nonlinear partial differential equations. In many situations, this new class of methods allows for…

In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…

Generalizable implicit neural representation (INR) enables a single continuous function, i.e., a coordinate-based neural network, to represent multiple data instances by modulating its weights or intermediate features using latent codes.…

In this work, we explore the interplay between information and computation in non-linear transform-based compression for broad classes of modern information-processing tasks. We first investigate two emerging nonlinear data transformation…

The semi-airborne transient electromagnetic method (SATEM) is capable of conducting rapid surveys over large-scale and hard-to-reach areas. However, the acquired signals are often contaminated by complex noise, which can compromise the…

Implicit Neural Representations (INRs) are widely used to encode data as continuous functions, enabling the visualization of large-scale multivariate scientific simulation data with reduced memory usage. However, existing INR-based methods…

Numerical integrators could be used to form interpolation conditions when training neural networks to approximate the vector field of an ordinary differential equation (ODE) from data. When numerical one-step schemes such as the Runge-Kutta…

Deformable image registration (DIR) is a cornerstone of medical image analysis, enabling spatial alignment for tasks like comparative studies and multi-modal fusion. While learning-based methods (e.g., CNNs, transformers) offer fast…

Modern navigation solutions are largely dependent on the performances of the standalone inertial sensors, especially at times when no external sources are available. During these outages, the inertial navigation solution is likely to…

Decoding remote sensing images to achieve high perceptual quality, particularly at low bitrates, remains a significant challenge. To address this problem, we propose the invertible neural network-based remote sensing image compression…

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some…

We present the discriminative recurrent sparse auto-encoder model, comprising a recurrent encoder of rectified linear units, unrolled for a fixed number of iterations, and connected to two linear decoders that reconstruct the input and…

The non-differentiability of the singular nonlinearity (such as $f=\ln|u|^2$) at $u=0$ presents significant challenges in devising accurate and efficient numerical schemes for the logarithmic Schr\"{o}dinger equation (LogSE). To address…

Time series with missing data are signals encountered in important settings for machine learning. Some of the most successful prior approaches for modeling such time series are based on recurrent neural networks that transform the input and…

Next generation reservoir computing based on nonlinear vector autoregression (NVAR) is applied to emulate simple dynamical system models and compared to numerical integration schemes such as Euler and the $2^\text{nd}$ order Runge-Kutta. It…

This paper develops a data-driven time-limited h2 model reduction method for discrete-time linear time-invariant systems. Specifically, we formulate and solve a regularized time-limited h2 model reduction problem using only noisy impulse…

This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Runge-Kutta method with repeated randomized low-rank…

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…

Shape implicit neural representations (INRs) have recently shown to be effective in shape analysis and reconstruction tasks. Existing INRs require point coordinates to learn the implicit level sets of the shape. When a normal vector is…

Space discretization of some time-dependent partial differential equations gives rise to systems of ordinary differential equations in additive form whose terms have different stiffness properties. In these cases, implicit methods should be…