Search Results

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

lululxvi/deepxde 1 Nov 2021

We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems.

Physics-informed neural networks with hard constraints for inverse design

lululxvi/deepxde 9 Feb 2021

We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often simpler and smoother for problems whose solution is not unique.

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

lululxvi/deepxde 21 Jul 2022

Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling.

Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness

lululxvi/deepxde 26 May 2023

Here, we develop a Fourier-enhanced deep operator network (Fourier-DeepONet) for FWI with the generalization of seismic sources, including the frequencies and locations of sources.

Computational Efficiency

fPINNs: Fractional Physics-Informed Neural Networks

lululxvi/deepxde 20 Nov 2018

We observe that for the BB forcing fPINNs outperform FDM.

Computational Physics

DeepXDE: A deep learning library for solving differential equations

lululxvi/deepxde 10 Jul 2019

We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an education tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering.

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

lululxvi/deepxde 26 Feb 2019

It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data.

Computational Physics

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

lululxvi/deepxde 1 Nov 2020

We demonstrate the effectiveness of DeepONet by predicting five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields.

Computational Physics

Reliable extrapolation of deep neural operators informed by physics or sparse observations

lululxvi/deepxde 13 Dec 2022

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks.

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

lululxvi/deepxde 8 Mar 2023

Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media.