Related papers: PIAT: Physics Informed Adversarial Training for So…

Though deep neural networks exhibit superior performance on various tasks, they are still plagued by adversarial examples. Adversarial training has been demonstrated to be the most effective method to defend against adversarial attacks.…

Adversarial training has been demonstrated to be the most effective approach to defend against adversarial attacks. However, existing adversarial training methods show apparent oscillations and overfitting issue in the training process,…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Adversarial training (AT) refers to integrating adversarial examples -- inputs altered with imperceptible perturbations that can significantly impact model predictions -- into the training process. Recent studies have demonstrated the…

Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial…

Adversarial training is a defense technique that improves adversarial robustness of a deep neural network (DNN) by including adversarial examples in the training data. In this paper, we identify an overlooked problem of adversarial training…

The neural network (NN) becomes one of the most heated type of models in various signal processing applications. However, NNs are extremely vulnerable to adversarial examples (AEs). To defend AEs, adversarial training (AT) is believed to be…

Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information.…

Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…

Adversarial Training (AT), which is commonly accepted as one of the most effective approaches defending against adversarial examples, can largely harm the standard performance, thus has limited usefulness on industrial-scale production and…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Adversarial training can improve the robustness of neural networks. Previous methods focus on a single adversarial training strategy and do not consider the model property trained by different strategies. By revisiting the previous methods,…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Adversarial training (AT) is among the most effective techniques to improve model robustness by augmenting training data with adversarial examples. However, most existing AT methods adopt a specific attack to craft adversarial examples,…

Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…

Extensive research has demonstrated that deep neural networks (DNNs) are prone to adversarial attacks. Although various defense mechanisms have been proposed for image classification networks, fewer approaches exist for video-based models…

Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in…

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…

The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those…

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…