Anti-derivatives approximator for enhancing physics-informed neural networks

Artificial neural networks and deep learning (68T07) Numerical mathematical programming methods (65K05) Algorithms for approximation of functions (65D15) Numerical integration (65D30)

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Cites Work

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\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
Self-adaptive physics-informed neural networks
NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation
Parallel physics-informed neural networks via domain decomposition
Physics-informed neural networks for the shallow-water equations on the sphere
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Physics-informed neural networks for inverse problems in supersonic flows
Scientific machine learning through physics-informed neural networks: where we are and what's next
Physics-informed neural networks for high-speed flows
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Bayesian physics informed neural networks for real-world nonlinear dynamical systems
Algorithm 778: L-BFGS-B
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions
Physics-informed neural networks with adaptive localized artificial viscosity
Adaptive task decomposition physics-informed neural networks
Spectral operator learning for parametric PDEs without data reliance
Physics-informed graph neural network emulation of soft-tissue mechanics

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