Related papers: Adversarial Learning for Neural PDE Solvers with S…
Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…
There has been great interest in enhancing the robustness of neural network classifiers to defend against adversarial perturbations through adversarial training, while balancing the trade-off between robust accuracy and standard accuracy.…
In contrast to SGD, adaptive gradient methods like Adam allow robust training of modern deep networks, especially large language models. However, the use of adaptivity not only comes at the cost of extra memory but also raises the…
Adversarial training (AT) and its variants have spearheaded progress in improving neural network robustness to adversarial perturbations and common corruptions in the last few years. Algorithm design of AT and its variants are focused on…
Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…
Deep neural networks are increasingly being used to detect and diagnose medical conditions using medical imaging. Despite their utility, these models are highly vulnerable to adversarial attacks and distribution shifts, which can affect…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. There is an emerging literature on tackling this problem by…
Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient…
PDE discovery shows promise for uncovering predictive models of complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a…
Adversarial training is a widely-applied approach to training deep neural networks to be robust against adversarial perturbation. However, although adversarial training has achieved empirical success in practice, it still remains unclear…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
Deep Learning has revolutionized machine learning and artificial intelligence, achieving superhuman performance in several standard benchmarks. It is well-known that deep learning models are inefficient to train; they learn by processing…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
Deep neural networks are highly vulnerable to adversarial examples, i.e.,small perturbations that can significantly degrade model performance. While adversarial training has become the primary defense strategy, most studies focus on…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Owing to security implications of adversarial vulnerability, adversarial robustness of deep metric learning models has to be improved. In order to avoid model collapse due to excessively hard examples, the existing defenses dismiss the…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to…