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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…

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…

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optimizing the activation parameters, compleX-PINN achieves high…

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output…

Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…

Many neural network architectures rely on the choice of the activation function for each hidden layer. Given the activation function, the neural network is trained over the bias and the weight parameters. The bias catches the center of the…

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

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,…

Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…

Despite broad interest in applying deep learning techniques to scientific discovery, learning interpretable formulas that accurately describe scientific data is very challenging because of the vast landscape of possible functions and the…

We present a new active learning algorithm based on nonparametric estimators of the regression function. Our investigation provides probabilistic bounds for the rates of convergence of the generalization error achievable by proposed method…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) by approximating their solutions via neural networks and imposing physics-based constraints on the loss function.…