Scientific machine learning through physics–informed neural networks: Where we are and what's next

S Cuomo, VS Di Cola, F Giampaolo, G Rozza… - Journal of Scientific …, 2022 - Springer
Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

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

L Lu, X Meng, S Cai, Z Mao, S Goswami… - Computer Methods in …, 2022 - Elsevier
Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …

Physics-informed machine learning: A survey on problems, methods and applications

Z Hao, S Liu, Y Zhang, C Ying, Y Feng, H Su… - arXiv preprint arXiv …, 2022 - arxiv.org
Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …

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

M Zhu, H Zhang, A Jiao, GE Karniadakis… - Computer Methods in …, 2023 - Elsevier
Deep neural operators can learn nonlinear mappings between infinite-dimensional function
spaces via deep neural networks. As promising surrogate solvers of partial differential …

Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems

T Tripura, S Chakraborty - Computer Methods in Applied Mechanics and …, 2023 - Elsevier
With massive advancements in sensor technologies and Internet-of-things (IoT), we now
have access to terabytes of historical data; however, there is a lack of clarity on how to best …

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

L Lu, R Pestourie, SG Johnson, G Romano - Physical Review Research, 2022 - APS
Deep neural operators can learn operators mapping between infinite-dimensional function
spaces via deep neural networks and have become an emerging paradigm of scientific …

Partial differential equations meet deep neural networks: A survey

S Huang, W Feng, C Tang, J Lv - arXiv preprint arXiv:2211.05567, 2022 - arxiv.org
Many problems in science and engineering can be represented by a set of partial differential
equations (PDEs) through mathematical modeling. Mechanism-based computation following …

Learning two-phase microstructure evolution using neural operators and autoencoder architectures

V Oommen, K Shukla, S Goswami… - npj Computational …, 2022 - nature.com
Phase-field modeling is an effective but computationally expensive method for capturing the
mesoscale morphological and microstructure evolution in materials. Hence, fast and …

Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems

M Yin, E Zhang, Y Yu, GE Karniadakis - Computer methods in applied …, 2022 - Elsevier
Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …

Wavelet neural operator: a neural operator for parametric partial differential equations

T Tripura, S Chakraborty - arXiv preprint arXiv:2205.02191, 2022 - arxiv.org
With massive advancements in sensor technologies and Internet-of-things, we now have
access to terabytes of historical data; however, there is a lack of clarity in how to best exploit …