http://manuscript.elsevier.com/S0045782522001207/pdf/S0045782522001207.pdf

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

/pdf/a-comprehensive-study-of-non-adaptive-and-residual-based-3mhbc0qi.pdf

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

/pdf/a-mixed-formulation-for-physics-informed-neural-networks-as-15gxq840.pdf

A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method

/pdf/transfer-learning-based-physics-informed-neural-networks-for-11vjlzo4.pdf

Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios

Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here we address this challenge by using multifidelity learning, i.e., learning from multifidelity data sets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems. 

/pdf/multifidelity-deep-neural-operators-for-efficient-learning-e5co03j7.pdf

Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been successfully employed to solve diverse forward and inverse PDE problems. However, one disadvantage of the first generation of PINNs is that they usually have limited accuracy even with many training points. Here, we propose a new method, gradient-enhanced physics-informed neural networks (gPINNs), for improving the accuracy and training efficiency of PINNs. gPINNs leverage gradient information of the PDE residual and embed the gradient into the loss function. We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems. Our numerical results show that gPINN performs better than PINN with fewer training points. Furthermore, we combined gPINN with the method of residual-based adaptive refinement (RAR), a method for improving the distribution of training points adaptively during training, to further improve the performance of gPINN, especially in PDEs with solutions that have steep gradients.

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

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