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

Implicit neural representation (INR) methods for video compression have recently achieved visual quality and compression ratios that are competitive with traditional pipelines. However, due to the need for per-sample network training, the…

System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…

A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, the solution of…

We construct eight implicit-explicit (IMEX) Runge-Kutta (RK) schemes up to third order of the type in which all stages are implicit so that they can be used in the zero relaxation limit in a unified and convenient manner. These…

In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined…

Implicit Neural Representations (INRs) have revolutionized signal processing and computer vision by modeling signals as continuous, differentiable functions parameterized by neural networks. However, INRs are prone to the spectral bias…

We present a perceptually-driven video compression framework integrating implicit neural representations (INRs) and pre-trained video diffusion models to address the extremely low bitrate regime (<0.05 bpp). Our approach exploits the…

This paper presents a tractable tube-based robust data-driven predictive control scheme that uses only a single finite noisy input-state trajectory of an unknown discrete-time linear time-invariant (LTI) system. A simplex constraint is…

We present the Minimally-Implicit Runge-Kutta (MIRK) methods for the numerical evolution of the resistive relativistic magnetohydrodynamic (RRMHD) equations, following the approach proposed by Komissarov (2007) of an augmented system of…

Tabular data builds the basis for a wide range of applications, yet real-world datasets are frequently incomplete due to collection errors, privacy restrictions, or sensor failures. As missing values degrade the performance or hinder the…

In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no…

We study the construction and convergence of semi-explicit and iterative decoupling schemes for an elliptic-parabolic problem using higher-order Runge-Kutta methods. For the semi-explicit schemes, which are constructed using a nearby delay…

We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…

We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…

Implicit neural representations (INRs) have emerged as a powerful paradigm for medical imaging via physics-informed unsupervised learning. Classical INRs optimize an entire network from scratch for each subject, leading to inefficient…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

Accurate state estimation is critical for optimal policy design in dynamic systems. However, obtaining true system states is often impractical or infeasible, complicating the policy learning process. This paper introduces a novel neural…

Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural network-based methods. However, the…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Rectified flow (RF) models have recently demonstrated superior generative performance compared to DDIM-based diffusion models. However, in real-world applications, they suffer from two major challenges: (1) low inversion accuracy that…