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Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce…

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…

This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the…

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

Recent work showed that hybrid networks, which combine predefined and learnt filters within a single architecture, are more amenable to theoretical analysis and less prone to overfitting in data-limited scenarios. However, their performance…

A neural network targeting at unsupervised image anomaly localization, called the PEDENet, is proposed in this work. PEDENet contains a patch embedding (PE) network, a density estimation (DE) network, and an auxiliary network called the…

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…

Convolutional neural networks learns spatial features and are heavily interlinked within kernels. The SE module have broken the traditional route of neural networks passing the entire result to next layer. Instead SE only passes important…

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Large Foundation Models (LFMs) have demonstrated significant advantages in civil engineering, but they primarily focus on textual and visual data, overlooking the rich semantic, spatial, and topological features in BIM (Building Information…

Reliable real-time estimation of atmospheric turbulence intensity remains an open challenge for aircraft operating across diverse altitude bands, particularly over oceanic, polar, and data-sparse regions that lack operational nowcasting…

The ResNet and its variants have achieved remarkable successes in various computer vision tasks. Despite its success in making gradient flow through building blocks, the simple shortcut connection mechanism limits the ability of…

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

Knowledge distillation (KD) is a popular method for reducing the computational overhead of deep network inference, in which the output of a teacher model is used to train a smaller, faster student model. Hint training (i.e., FitNets)…

We investigate nonlinear prediction in an online setting and introduce a hybrid model that effectively mitigates, via an end-to-end architecture, the need for hand-designed features and manual model selection issues of conventional…