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

The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…

Supervised Deep-Learning (DL)-based reconstruction algorithms have shown state-of-the-art results for highly-undersampled dynamic Magnetic Resonance Imaging (MRI) reconstruction. However, the requirement of excessive high-quality…

In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work…

A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under the exact solution of their governing PDEs. However, standard temporal schemes,…

In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise. The proposed scheme converges with respect to the computational effort with a…

Measurements acquired from distributed physical systems are often sparse and noisy. Therefore, signal processing and system identification tools are required to mitigate noise effects and reconstruct unobserved dynamics from limited sensor…

In this work we present a new class of Runge-Kutta (RK) methods for solving systems of hyperbolic equations with a particular structure, generalization of a wave-equation. The new methods are {\it partially implicit} in the sense that a…

A mixed accuracy framework for Runge--Kutta methods presented in [Grant, JSC 2022] has been shown to speed up the computation in diagonally implicit Runge--Kutta (DIRK) methods by using less expensive low accuracy approaches for the…

In this paper we consider time-dependent PDEs discretized by a special class of Physics Informed Neural Networks whose design is based on the framework of Runge--Kutta and related time-Galerkin discretizations. The primary motivation for…

We consider the efficient numerical solution of coupled dynamical systems, consisting of a small nonlinear part and a large linear time invariant part, possibly stemming from spatial discretization of an underlying partial differential…

Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated…

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

We introduce a modality-agnostic neural compression algorithm based on a functional view of data and parameterised as an Implicit Neural Representation (INR). Bridging the gap between latent coding and sparsity, we obtain compact latent…

Learning the governing equations from time-series data has gained increasing attention due to its potential to extract useful dynamics from real-world data. Despite significant progress, it becomes challenging in the presence of noise,…

Signal compression based on implicit neural representation (INR) is an emerging technique to represent multimedia signals with a small number of bits. While INR-based signal compression achieves high-quality reconstruction for relatively…

This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and component-partitioned…

Implicit Neural Representations (INRs) are increasingly recognized as a versatile data modality for representing discretized signals, offering benefits such as infinite query resolution and reduced storage requirements. Existing signal…

Spatiotemporal prediction is important in solving natural problems and processing video frames, especially in weather forecasting and human action recognition. Recent advances attempt to incorporate prior physical knowledge into the deep…

We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is…