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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) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…

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…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Despite their overwhelming capacity to overfit, deep neural networks trained by specific optimization algorithms tend to generalize well to unseen data. Recently, researchers explained it by investigating the implicit regularization effect…

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical…

In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with…

In this work, we propose an optimization algorithm which we call norm-adapted gradient descent. This algorithm is similar to other gradient-based optimization algorithms like Adam or Adagrad in that it adapts the learning rate of stochastic…

We propose PRISM, an optimizer that enhances first-order spectral descent methods like Muon with partial second-order information. It constructs an efficient, low-rank quasi-second-order preconditioner via innovation-augmented polar…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…

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…

Adaptive gradient methods, such as Adam and LAMB, have demonstrated excellent performance in the training of large language models. Nevertheless, the need for adaptivity requires maintaining second-moment estimates of the per-parameter…

This work focuses on the behavior of stochastic gradient descent (SGD) in solving least-squares regression with physics-informed neural networks (PINNs). Past work on this topic has been based on the over-parameterization regime, whose…

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared…

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…

"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…

Optimizers that further adjust the scale of gradient, such as Adam, Natural Gradient (NG), etc., despite widely concerned and used by the community, are often found poor generalization performance, compared with Stochastic Gradient Descent…

We consider solving the forward and inverse PDEs which have sharp solutions using physics-informed neural networks (PINNs) in this work. In particular, to better capture the sharpness of the solution, we propose adaptive sampling methods…