Related papers: Data Denoising and Derivative Estimation for Data-…

We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equations by means of Newton-like iterations. We pay particular…

Inversion of gravity data is an important method for investigating subsurface density variations relevant to mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here…

We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…

There is an emerging trend in applying deep learning methods to control complex nonlinear systems. This paper considers enhancing the runtime safety of nonlinear systems controlled by neural networks in the presence of disturbance and…

Given the recent surge of interest in data-driven control, this paper proposes a two-step method to study robust data-driven control for a parameter-unknown linear time-invariant (LTI) system that is affected by energy-bounded noises.…

This paper introduces the Raw Natural Image Noise Dataset (RawNIND), a diverse collection of paired raw images designed to support the development of denoising models that generalize across sensors, image development workflows, and styles.…

In this paper, discrete linear quadratic regulator (DLQR) and iterative linear quadratic regulator (ILQR) methods based on high-order Runge-Kutta (RK) discretization are proposed for solving linear and nonlinear quadratic optimal control…

Addressing the issues of severe noise and high frequency structural degradation in visible images under low-light conditions, this paper proposes a Near Infrared (NIR) aided low light image restoration method based on Frequency Decoupled…

Implicit neural representation (INR) embed various signals into neural networks. They have gained attention in recent years because of their versatility in handling diverse signal types. In the context of video, INR achieves video…

This study explores data-driven modeling techniques to capture the dynamics of a grid-forming converter-based infinite bus system, critical for renewable-integrated power grids. Using sparse identification of nonlinear dynamics and deep…

Healthcare data frequently contain a substantial proportion of missing values, necessitating effective time series imputation to support downstream disease diagnosis tasks. However, existing imputation methods focus on discrete data points…

We present a novel approach for super-resolution that utilizes implicit neural representation (INR) to effectively reconstruct and enhance low-resolution videos and images. By leveraging the capacity of neural networks to implicitly encode…

Runge-Kutta methods are affine equivariant: applying a method before or after an affine change of variables yields the same numerical trajectory. However, for some applications, one would like to perform numerical integration after a…

Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete…

This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned…

This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta…

Infrared dim and small target detection presents a significant challenge due to dynamic multi-frame scenarios and weak target signatures in the infrared modality. Traditional low-rank plus sparse models often fail to capture dynamic…

Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as…

Implicit neural representations (INRs) have emerged as a promising approach for video storage and processing, showing remarkable versatility across various video tasks. However, existing methods often fail to fully leverage their…

Symbolic regression (SR) has emerged as a pivotal technique for uncovering the intrinsic information within data and enhancing the interpretability of AI models. However, current state-of-the-art (sota) SR methods struggle to perform…