Related papers: When and Why Adversarial Training Improves PINNs: …

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Multiple different approaches of generating adversarial examples have been proposed to attack deep neural networks. These approaches involve either directly computing gradients with respect to the image pixels, or directly solving an…

One of the most significant challenges in statistical signal processing and machine learning is how to obtain a generative model that can produce samples of large-scale data distribution, such as images and speeches. Generative Adversarial…

As neural networks become the tool of choice to solve an increasing variety of problems in our society, adversarial attacks become critical. The possibility of generating data instances deliberately designed to fool a network's analysis can…

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit…

Adversarial learning methods are a promising approach to training robust deep networks, and can generate complex samples across diverse domains. They also can improve recognition despite the presence of domain shift or dataset bias: several…

Physics-Informed Neural Networks have shown unique utility in parameterising the solution of a well-defined partial differential equation using automatic differentiation and residual losses. Though they provide theoretical guarantees of…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

It has been demonstrated that deep neural networks are prone to noisy examples particular adversarial samples during inference process. The gap between robust deep learning systems in real world applications and vulnerable neural networks…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

In recent years, Generative Adversarial Networks (GANs) have drawn a lot of attentions for learning the underlying distribution of data in various applications. Despite their wide applicability, training GANs is notoriously difficult. This…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

Physics-informed neural networks (PINNs) are at the forefront of scientific machine learning, making possible the creation of machine intelligence that is cognizant of physical laws and able to accurately simulate them. However, today's…

Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect…

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…

Although current deep learning techniques have yielded superior performance on various computer vision tasks, yet they are still vulnerable to adversarial examples. Adversarial training and its variants have been shown to be the most…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs). We focus on a pair of benchmarks: discretized partial differential equations and…

Generative Adversarial Networks (GANs) are a type of generative model which have received much attention due to their ability to model complex real-world data. Despite their recent successes, the process of training GANs remains…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…