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In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions…

State estimation is the cornerstone of the power system control center since it provides the operating condition of the system in consecutive time intervals. This work investigates the application of physics-informed neural networks (PINNs)…

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…

The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific…

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…

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…

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

This study introduces an accelerated training method for Vanilla Physics-Informed-Neural-Networks (PINN) addressing three factors that imbalance the loss function: initial weight state of a neural network, domain to boundary points ratio,…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Recently, deep neural networks (DNNs) have shown advantages in accelerating optimization algorithms. One approach is to unfold finite number of iterations of conventional optimization algorithms and to learn parameters in the algorithms.…

In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential…

Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs). However, they often fail to converge to desirable solutions when the target…

Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

This paper investigates a numerical solution of Allen-Cahn equation with constant and degenerate mobility, with polynomial and logarithmic energy functionals, with deterministic and random initial functions, and with advective term in one,…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…