相关论文: Compressed Compressor

This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the…

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of Compressed Sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC AS, SPGL1, NestA,…

This study develops a unified Point Cloud Geometry (PCG) compression method through the processing of multiscale sparse tensor-based voxelized PCG. We call this compression method SparsePCGC. The proposed SparsePCGC is a low complexity…

There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…

We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…

In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…

In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…

Partial Differential Equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods like Sparse Identification of Nonlinear Dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and…

Recent research highlights frequent model communication as a significant bottleneck to the efficiency of decentralized machine learning (ML), especially for large-scale and over-parameterized neural networks (NNs). To address this, we…

Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

We propose sparse regression as an alternative to neural networks for the discovery of parsimonious constitutive models (CMs) from oscillatory shear experiments. Symmetry and frame-invariance are strictly imposed by using tensor basis…

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…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…