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Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…
Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However,…
Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in…
The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by…
The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional…
Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…
We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its…
We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
With the advantages of fast calculating speed and high precision, the physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. Based on conserved quantities, we devise…
Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…
The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…
Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…