• DeepXDE

  • Referenced in 61 articles [sw32456]
  • overview of physics-informed neural networks (PINNs), which embed a PDE into the loss ... neural network using automatic differentiation. The PINN algorithm is simple, and it can be applied ... Moreover, from the implementation point of view, PINNs solve inverse problems as easily as forward ... method to improve the training efficiency of PINNs. For pedagogical reasons, we compare the PINN...
  • FPINNs

  • Referenced in 27 articles [sw40570]
  • Informed Neural Networks. Physics-informed neural networks (PINNs) are effective in solving integer-order partial ... PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with ... respect to the NN parameters. We extend PINNs to fractional PINNs (fPINNs) to solve space...
  • NSFnets

  • Referenced in 23 articles [sw42059]
  • equations. We employ physics-informed neural networks (PINNs) to simulate the incompressible flows ranging from ... laminar to turbulent flows. We perform PINN simulations by considering two different formulations ... formulation. We refer to these specific PINNs for the Navier-Stokes flow nets as NSFnets ... embedded into the loss function of the PINNs. No data is provided for the pressure...
  • NeuralPDE.jl

  • Referenced in 33 articles [sw39548]
  • techniques such as physics-informed neural networks (PINNs) and deep BSDE solvers. This package utilizes...
  • PINNsNTK

  • Referenced in 17 articles [sw42058]
  • When and why PINNs fail to train: a neural tangent kernel perspective. Physics-informed neural ... networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide ... descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions ... analyze the training dynamics of PINNs through the lens of their limiting NTK and find...
  • SciANN

  • Referenced in 10 articles [sw38344]
  • using the physics-informed neural networks (PINN) architecture, therefore providing the flexibility...
  • PINN

  • Referenced in 3 articles [sw38999]
  • developed both physis-driven and ML-driven (PINN) thermal multi-phase flow models to simulate...
  • PiNN

  • Referenced in 2 articles [sw30601]
  • PiNN: A Python Library for Building Atomic Neural Networks of Molecules and Materials. Atomic neural ... Here, we present a python library named PiNN as a solution toward this goal ... PiNN, we implemented an interpretable graph convolutional neural network variant, PiNet, as well ... liquid water and an aqueous alkaline electrolyte. PiNN comes with a visualizer called PiNNBoard...
  • Stiff-PINN

  • Referenced in 1 article [sw42094]
  • Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics. Recently developed physics-informed neural ... network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws ... This work first investigates the performance of PINN in solving stiff chemical kinetic problems with ... results elucidate the challenges of utilizing PINN in stiff ODE systems. Consequently, we employ Quasi...
  • IDRLnet

  • Referenced in 1 article [sw39547]
  • Neural Network Library. Physics Informed Neural Network (PINN) is a scientific computing framework used ... toolbox for modeling and solving problems through PINN systematically. IDRLnet constructs the framework ... wide range of PINN algorithms and applications. It provides a structured way to incorporate geometric ... variational minimization, and integral differential equations. New PINN variants can be integrated into the framework...
  • L-BFGS

  • Referenced in 806 articles [sw03229]
  • Algorithm 778: L-BFGS-B Fortran subroutines for...
  • CUDA

  • Referenced in 1325 articles [sw03258]
  • The NVIDIA® CUDA® Toolkit provides a comprehensive development...
  • COMSOL

  • Referenced in 458 articles [sw04091]
  • The COMSOL Multiphysics engineering simulation software environment facilitates...
  • FEniCS

  • Referenced in 840 articles [sw04314]
  • The FEniCS Project is a collaborative project for...
  • LBFGS-B

  • Referenced in 414 articles [sw05142]
  • Algorithm 778: L-BFGS-B Fortran subroutines for...
  • Theano

  • Referenced in 95 articles [sw05894]
  • Theano is a Python library that allows you...
  • SciPy

  • Referenced in 775 articles [sw06293]
  • SciPy (pronounced ”Sigh Pie”) is open-source software...
  • Python

  • Referenced in 2091 articles [sw14460]
  • Python is a widely used high-level, general...
  • TensorFlow

  • Referenced in 629 articles [sw15170]
  • TensorFlow™ is an open source software library for...
  • DiffSharp

  • Referenced in 95 articles [sw16033]
  • DiffSharp: Automatic differentiation library. DiffSharp is a functional...