相关论文: A Green-Integral-Constrained Neural Solver with St…

Simulating nonlinear reaction-diffusion dynamics on complex, non-Euclidean manifolds remains a fundamental challenge in computational morphogenesis, constrained by high-fidelity mesh generation costs and symplectic drift in discrete…

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…

Sound field reconstruction (SFR) augments the information of a sound field captured by a microphone array. Conventional SFR methods using basis function decomposition are straightforward and computationally efficient, but may require more…

Partial Differential Equations (PDEs) are central to modeling complex systems across physical, biological, and engineering domains, yet traditional numerical methods often struggle with high-dimensional or complex problems. Physics-Informed…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

We develop an unsupervised physics-informed neural network to solve saddle-point equations (SPEs) governing direct above-threshold ionization (ATI) within the strong-field approximation. This setting provides a well-understood testbed in…

We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…

In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the…

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) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration.…

An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels…

Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…

Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between…

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN…

This study devised a physics-informed neural network (PINN) framework to solve the wave equation for acoustic resonance analysis. The proposed analytical model, ResoNet, minimizes the loss function for periodic solutions and conventional…

A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately…