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The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models…

In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…

Entity Resolution concerns identifying co-referent entity pairs across datasets. A typical workflow comprises two steps. In the first step, a blocking method uses a one-many function called a blocking scheme to map entities to blocks. In…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

This paper introduces a novel method for human face detection with its orientation by using wavelet, principle component analysis (PCA) and redial basis networks. The input image is analyzed by two-dimensional wavelet and a two-dimensional…

We present adaptive finite difference ENO/WENO methods by adopting infinitely smooth radial basis functions (RBFs). This is a direct extension of the non-polynomial finite volume ENO/WENO method proposed by authors in \cite{GuoJung} to the…

Despite the recent popularity of deep generative state space models, few comparisons have been made between network architectures and the inference steps of the Bayesian filtering framework -- with most models simultaneously approximating…

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…

Time series forecasting is crucial in many fields, yet current deep learning models struggle with noise, data sparsity, and capturing complex multi-scale patterns. This paper presents MFF-FTNet, a novel framework addressing these challenges…

In MRI, deep neural networks have been proposed to reconstruct diffusion model parameters. However, the inputs of the networks were designed for a specific diffusion gradient scheme (i.e., diffusion gradient directions and numbers) and a…

It has become mainstream in computer vision and other machine learning domains to reuse backbone networks pre-trained on large datasets as preprocessors. Typically, the last layer is replaced by a shallow learning machine of sorts; the…

In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of…

While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…

In this paper, we address the intricate issue of RF signal separation by presenting a novel adaptation of the WaveNet architecture that introduces learnable dilation parameters, significantly enhancing signal separation in dense RF…