Related papers: A rate of convergence of Physics Informed Neural N…
Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
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 recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…
Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…
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…
In this paper, we present a new framework how a PDE with constraints can be formulated into a sequence of PDEs with no constraints, whose solutions are convergent to the solution of the PDE with constraints. This framework is then used to…
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…
In this paper, local H\"older regularization is incorporated into a physics-informed neural networks (PINNs) framework for solving elliptic partial differential equations (PDEs). Motivated by the interior regularity properties of linear…
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…
In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…
This work compares the advantages and limitations of the Finite Difference Method with Physics-Informed Neural Networks, showing where each can best be applied for different problem scenarios. Analysis on the L2 relative error based on…
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…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…
Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…
Physics-Informed Neural Networks (PINNs) are a powerful deep learning method capable of providing solutions and parameter estimations of physical systems. Given the complexity of their neural network structure, the convergence speed is…
Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…
Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…
Physics-Informed Neural Networks (PINNs) have gained popularity in scientific computing in recent years. However, they often fail to achieve the same level of accuracy as classical methods in solving differential equations. In this paper,…