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

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and…

Adversarial training (AT) is widely considered as the most promising strategy to defend against adversarial attacks and has drawn increasing interest from researchers. However, the existing AT methods still suffer from two challenges.…

Adversarial Training (AT) with Projected Gradient Descent (PGD) is an effective approach for improving the robustness of the deep neural networks. However, PGD AT has been shown to suffer from two main limitations: i) high computational…

To mitigate the susceptibility of neural networks to adversarial attacks, adversarial training has emerged as a prevalent and effective defense strategy. Intrinsically, this countermeasure incurs a trade-off, as it sacrifices the model's…

Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to…

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Recent efforts show that neural networks are vulnerable to small but intentional perturbations on input features in visual classification tasks. Due to the additional consideration of connections between examples (\eg articles with citation…

Adversarial training has been empirically proven to be one of the most effective and reliable defense methods against adversarial attacks. However, almost all existing studies about adversarial training are focused on balanced datasets,…

Adversarial Training (AT) and Virtual Adversarial Training (VAT) are the regularization techniques that train Deep Neural Networks (DNNs) with adversarial examples generated by adding small but worst-case perturbations to input examples. In…

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

Deep neural networks (DNNs) have achieved remarkable performance in many tasks, yet they often behave as opaque black boxes. Explanation-guided learning (EGL) methods steer DNNs using human-provided explanations or supervision on model…

Ensemble Adversarial Training (EAT) attempts to enhance the robustness of models against adversarial attacks by leveraging multiple models. However, current EAT strategies tend to train the sub-models independently, ignoring the cooperative…

Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…

Recently proposed adversarial training methods show the robustness to both adversarial and original examples and achieve state-of-the-art results in supervised and semi-supervised learning. All the existing adversarial training methods…