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PINNs enhance scientific computing by incorporating physical laws into neural network structures, leading to significant advancements in scientific computing. However, PINNs struggle with multi-scale and high-frequency problems due to…

Training deep neural networks (DNNs) using traditional backpropagation (BP) presents challenges in terms of computational complexity and energy consumption, particularly for on-device learning where computational resources are limited.…

Deep networks are vulnerable to adversarial examples. Adversarial Training (AT) has been a standard foundation of modern adversarial defense approaches due to its remarkable effectiveness. However, AT is extremely time-consuming, refraining…

We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to…

Deep learning methods have shown great promise in many practical applications, ranging from speech recognition, visual object recognition, to text processing. However, most of the current deep learning methods suffer from scalability…

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…

Recent breakthroughs in deep learning (DL) have led to the emergence of many intelligent mobile applications and services, but in the meanwhile also pose unprecedented computing challenges on resource-constrained mobile devices. This paper…

Understanding and controlling the informational complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving partial differential equations~(PDEs) in various scientific and engineering domains. However, traditional PINN architectures typically rely on large, fully…

Deep neural networks (DNNs) are known for extracting useful information from large amounts of data. However, the representations learned in DNNs are typically hard to interpret, especially in dense layers. One crucial issue of the classical…

Over the past years, inverse problems in partial differential equations have garnered increasing interest among scientists and engineers. However, due to the lack of conventional stability, nonlinearity and non-convexity, these problems are…

Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences, engineering or even finance. For example, in physical systems, the Allen-Cahn equation…

We introduce the Differentiable Weightless Neural Network (DWN), a model based on interconnected lookup tables. Training of DWNs is enabled by a novel Extended Finite Difference technique for approximate differentiation of binary values. We…

Defect detection is a basic and essential task in automatic parts production, especially for automotive engine precision parts. In this paper, we propose a new idea to construct a deep convolutional network combining related knowledge of…

In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…

Although deep learning has been applied to successfully address many data mining problems, relatively limited work has been done on deep learning for anomaly detection. Existing deep anomaly detection methods, which focus on learning new…

We propose a new approach for large-scale high-dynamic range computational imaging. Deep Neural Networks (DNNs) trained end-to-end can solve linear inverse imaging problems almost instantaneously. While unfolded architectures provide…

The prediction accuracy of the deep neural networks (DNNs) after deployment at the edge can suffer with time due to shifts in the distribution of the new data. To improve robustness of DNNs, they must be able to update themselves to enhance…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…