相关论文: On Higher Order Positive Differential Energy Opera…

Learning the mapping between two function spaces has garnered considerable research attention. However, learning the solution operator of partial differential equations (PDEs) remains a challenge in scientific computing. Fourier neural…

Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators…

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…

In this paper we present a complete classification scheme for kinetic energy operators (KEO's) describing a particle endowed with position-dependent mass (PDM). We first present a generalized formulation of KEO's with PDM and show that it…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Differential Evolution (DE) proved to be one of the most successful evolutionary algorithms for global optimization purposes in continuous problems. The core operator in DE is mutation which can provide the algorithm with both exploration…

Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to formulate first order dynamical systems in higher dimensions.…

We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary challenge of…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention,…

Described is a modification of the TKE operator from its usual `energy form'. The resulting `peak-tracker' (or peak-detector) is especially useful in studies that involve the frequency domain.

Recent advancements in data-driven approaches, such as Neural Operator (NO), have demonstrated their effectiveness in reducing the solving time of Partial Differential Equations (PDEs). However, one major challenge faced by these approaches…

Energy efficiency (EE) and spectral efficiency (SE) are two of the key performance metrics in future wireless networks, covering both design and operational requirements. For previous conventional resource allocation techniques, these two…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Traditional frequency based projection filters, or projection operators (PO), separate signal and noise through a series of transformations which remove frequencies where noise is present. However, this technique relies on a priori…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Spectrally and energy efficient orthogonal frequency division multiplexing (SEE-OFDM) is an optical OFDM technique based on combining multiple asymmetrically clipped optical OFDM (ACO-OFDM) signals into one OFDM signal. By summing different…

Recently the Dark Energy Spectroscopic Instrument (DESI) provided constraints on the expansion history from their Data Release 2 (DR2). The DESI baryon acoustic oscillation (BAO) measurements are well described by a flat $\Lambda$CDM model,…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

In wireless communication systems, the nonlinear effect and inefficiency of power amplifier (PA) have posed practical challenges for system designs to achieve high spectral efficiency (SE) and energy efficiency (EE). In this paper, we…