English
Related papers

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

200 papers

Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that…

Machine Learning · Computer Science 2024-06-11 Franz M. Rohrhofer , Stefan Posch , Clemens Gößnitzer , Bernhard C. Geiger

The impressive success of Generative Adversarial Networks (GANs) is often overshadowed by the difficulties in their training. Despite the continuous efforts and improvements, there are still open issues regarding their convergence…

Machine Learning · Computer Science 2018-11-08 Yannis Pantazis , Dipjyoti Paul , Michail Fasoulakis , Yannis Stylianou

Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…

Computational Physics · Physics 2023-04-18 Hubert Baty

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We reveal a fundamental flaw of previous analyses which, by incorrectly modeling GANs' training scheme, are subject to ill-defined…

Deep neural networks (DNNs) are vulnerable to adversarial examples, which are crafted by adding imperceptible perturbations to inputs. Recently different attacks and strategies have been proposed, but how to generate adversarial examples…

Machine Learning · Computer Science 2021-01-13 Tao Bai , Jun Zhao , Jinlin Zhu , Shoudong Han , Jiefeng Chen , Bo Li , Alex Kot

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their…

Machine Learning · Computer Science 2023-08-25 Andrea Bonfanti , Roberto Santana , Marco Ellero , Babak Gholami

Generative adversarial networks (GAN) have been effective for learning generative models for real-world data. However, existing GANs (GAN and its variants) tend to suffer from training problems such as instability and mode collapse. In this…

Machine Learning · Computer Science 2018-03-05 Chaoyue Wang , Chang Xu , Xin Yao , Dacheng Tao

Generative Adversarial Networks (GANs) have proven to be a powerful framework for learning to draw samples from complex distributions. However, GANs are also notoriously difficult to train, with mode collapse and oscillations a common…

Machine Learning · Statistics 2018-11-28 Kevin J Liang , Chunyuan Li , Guoyin Wang , Lawrence Carin

Generative Adversarial Networks (GANs) are a powerful framework for deep generative modeling. Posed as a two-player minimax problem, GANs are typically trained end-to-end on real-valued data and can be used to train a generator of…

Machine Learning · Statistics 2017-11-15 Anirudh Goyal , Nan Rosemary Ke , Alex Lamb , R Devon Hjelm , Chris Pal , Joelle Pineau , Yoshua Bengio

Generative networks are fundamentally different in their aim and methods compared to CNNs for classification, segmentation, or object detection. They have initially not been meant to be an image analysis tool, but to produce naturally…

Computer Vision and Pattern Recognition · Computer Science 2022-07-11 Markus Wenzel

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Machine Learning · Computer Science 2024-10-11 Vineet Jagadeesan Nair

Although physics-informed neural networks(PINNs) have progressed a lot in many real applications recently, there remains problems to be further studied, such as achieving more accurate results, taking less training time, and quantifying the…

Machine Learning · Computer Science 2022-12-01 Bin Shan , Ye Li , Shengjun Huang

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…

Machine Learning · Computer Science 2019-10-11 Shixian Wen , Laurent Itti

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems. In this work, we present a new training paradigm…

Machine Learning · Computer Science 2024-03-27 Zhiwei Fang , Sifan Wang , Paris Perdikaris

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

Numerical Analysis · Mathematics 2026-03-09 Saad Qadeer , Panos Stinis

Deep neural networks are capable of training fast and generalizing well within many domains. Despite their promising performance, deep networks have shown sensitivities to perturbations of their inputs (e.g., adversarial examples) and their…

Machine Learning · Computer Science 2020-07-09 Justin Goodwin , Olivia Brown , Victoria Helus

Physics-informed neural networks (PINNs) numerically approximate the solution of a partial differential equation (PDE) by incorporating the residual of the PDE along with its initial/boundary conditions into the loss function. In spite of…

Computational Physics · Physics 2022-11-22 M. H. Saadat , B. Gjorgiev , L. Das , G. Sansavini

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Machine Learning · Computer Science 2023-04-12 Aleksandr Dekhovich , Marcel H. F. Sluiter , David M. J. Tax , Miguel A. Bessa