Related papers: fPINN-DeepONet: A Physics-Informed Operator Learni…

The multi-term time-fractional mixed diffusion-wave equations (TFMDWEs) are considered and the numerical method with its error analysis is presented in this paper. First, a $L2$ approximation is proved with first order accuracy to the…

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

We propose transformed Diffsuion-Wave fractional Physics-Informed Neural Networks (tDWfPINNs) for efficiently solving time-fractional diffusion-wave equations with fractional order $\alpha\in(1,2)$. Conventional numerical methods for these…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs). Our approach involves a non-uniform discretization of the fractional Caputo operator, facilitating…

We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the learning abilities of artificial neural networks with…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…

Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe relative errors of $10^{-3} \, \sim \, 10^{-4}$ for the…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…

Learning operators for parametric partial differential equations (PDEs) using neural networks has gained significant attention in recent years. However, standard approaches like Deep Operator Networks (DeepONets) require extensive labeled…

Fractional partial differential equations (FPDEs) can effectively represent anomalous transport and nonlocal interactions. However, inherent uncertainties arise naturally in real applications due to random forcing or unknown material…

In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful…