Related papers: Deep neural networks for smooth approximation of p…

The rise of Physics-Informed Neural Networks (PINNs) has popularized the concept of solving differential equations via residual minimization. However, neural networks are often viewed as ``black boxes" requiring significant computational…

Deep neural networks (DNNs) are powerful black-box function approximators which have been shown to yield improved performance compared to traditional neural network (NN) architectures. However, black-box algorithms do not incorporate known…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the…

Neural networks (NNs) accelerate simulations of quantum dissipative dynamics. Ensuring that these simulations adhere to fundamental physical laws is crucial, but has been largely ignored in the state-of-the-art NN approaches. We show that…

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…

Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…

We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in…

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

In this paper, we introduce the SPINNs (stochastic physics-informed neural networks) in a systematic manner. This provides a mathematical framework for approximating the solution of stochastic differential equations (SDEs) driven by Levy…

We introduce NeuroPINNs, a neuroscience-inspired extension of Physics-Informed Neural Networks (PINNs) that incorporates biologically motivated spiking neuron models to achieve energy-efficient PDE solving. Unlike conventional PINNs, which…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…