Related papers: Cosmo-PINN: A Physics-Informed Neural Network for …
In recent years there has been an increased interest in neural networks, particularly with regard to their ability to approximate partial differential equations. In this regard, research has begun on so-called physics-informed neural…
Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…
We apply two variants of Physics-Informed Neural Networks (PINNs) to reconstruct the Type~Ia supernova absolute magnitude $M_B(z)$ from joint BAO and supernova data under four cosmological models ($\Lambda$CDM, CPL, GEDE, $\Lambda_s$CDM)…
We parameterize the equation of state of late-time dark energy as $w_{\mathrm{bin}}(z)$, with three redshift bins, characterized by a constant equation of state in each bin. Then, we constrain the parameters of the $w_{\mathrm{bin}}$CDM…
Physics-Informed Neural Networks (PINNs) solve forward PDEs by minimizing residual losses from the governing equations with initial and boundary conditions, but they often struggle with discontinuities such as shocks. In contrast, finite…
Cosmographic reconstructions provide a model-agnostic approach towards constraining cosmic evolution. In this work, we develop a semi-cosmographic framework that adopts a Pad\'e-rational fraction parametrization of the Luminosity distance,…
Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…
Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…
Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…
In this paper, we employ two model-independent approaches, including redshift binning method and polynomial interpolation method, to reconstruct dark energy (DE) equation of state (EoS) $w(z)$ and DE density function $f(z)$. Our analysis…
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), 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…
Physics-informed neural networks have emerged as a coherent framework for building predictive models that combine statistical patterns with domain knowledge. The underlying notion is to enrich the optimization loss function with known…
We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the…
The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific…
The paper proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations -- Variable Coefficient Physical Information Neural Network (VC-PINN). The shortcut…
Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…
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,…
Inverse problems are extensively studied in applied mathematics, with applications ranging from acoustic tomography for medical diagnosis to geophysical exploration. Physics informed neural networks (PINNs) have emerged as a powerful tool…