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Optical fringe patterns are often contaminated by speckle noise, making it difficult to accurately and robustly extract their phase fields. To deal with this problem, we propose a filtering method based on deep learning, called optical…

Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…

In this paper, we investigate the detection problem of binary faster-than-Nyquist (FTN) signaling and propose a novel sequence estimation technique that exploits its special structure. In particular, the proposed sequence estimation…

The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often…

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…

Building upon the mean p-power error (MPE) criterion, the normalized subband p-norm (NSPN) algorithm demonstrates superior robustness in $\alpha$-stable noise environments ($1 < \alpha \leq 2$) through effective utilization of low-order…

We propose a systematic analysis of deep neural networks (DNNs) based on a signal processing technique for network parameter removal, in the form of synaptic filters that identifies the fragility, robustness and antifragility…

In this paper, we propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT). Conventional black-box PINNs…

Using Physics-Informed Neural Networks (PINNs) to solve a specific boundary value problem is becoming more popular as an alternative to traditional methods. However, depending on the specific problem, they could be computationally expensive…

This study proposes a self-optimization physics-informed Fourier-features randomized neural network (SO-PIFRNN) framework, which significantly improves the numerical solving accuracy of PDEs through hyperparameter optimization mechanism.…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

Feedback particle filter (FPF) is a Monte-Carlo (MC) algorithm to approximate the solution of a stochastic filtering problem. In contrast to conventional particle filters, the Bayesian update step in FPF is implemented via a mean-field type…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features…

Physics-Informed Neural Networks (PINNs) are becoming a popular method for solving PDEs, due to their mesh-free nature and their ability to handle high-dimensional problems where traditional numerical solvers often struggle. Despite their…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…