相关论文: Fourier Domain Physics Informed Neural Network

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

Physics-informed neural network (PINN) has been a prevalent framework for solving PDEs since proposed. By incorporating the physical information into the neural network through loss functions, it can predict solutions to PDEs in an…

We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial derivative terms in the PINN loss functions via automatic…

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task…

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…

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,…

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

We propose a new approach to the solution of the wave propagation and full waveform inversions (FWIs) based on a recent advance in deep learning called Physics-Informed Neural Networks (PINNs). In this study, we present an algorithm for…

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…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…