Data‐Driven Design for Metamaterials and Multiscale Systems: A Review

D Lee, W Chen, L Wang, YC Chan… - Advanced …, 2024 - Wiley Online Library
Metamaterials are artificial materials designed to exhibit effective material parameters that
go beyond those found in nature. Composed of unit cells with rich designability that are …

Physics-informed deep neural operator networks

S Goswami, A Bora, Y Yu, GE Karniadakis - Machine Learning in …, 2023 - Springer
Standard neural networks can approximate general nonlinear operators, represented either
explicitly by a combination of mathematical operators, eg in an advection–diffusion reaction …

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 …

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 …

Review of multi-fidelity models

MG Fernández-Godino - arXiv preprint arXiv:1609.07196, 2016 - arxiv.org
This article provides an overview of multi-fidelity modeling trends. Fidelity in modeling refers
to the level of detail and accuracy provided by a predictive model or simulation. Generally …

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

M Zhu, S Feng, Y Lin, L Lu - Computer Methods in Applied Mechanics and …, 2023 - Elsevier
Full waveform inversion (FWI) infers the subsurface structure information from seismic
waveform data by solving a non-convex optimization problem. Data-driven FWI has been …

Neural operator-based surrogate solver for free-form electromagnetic inverse design

Y Augenstein, T Repan, C Rockstuhl - ACS Photonics, 2023 - ACS Publications
Neural operators have emerged as a powerful tool for solving partial differential equations in
the context of scientific machine learning. Here, we implement and train a modified Fourier …

Deep neural operators as accurate surrogates for shape optimization

K Shukla, V Oommen, A Peyvan, M Penwarden… - … Applications of Artificial …, 2024 - Elsevier
Deep neural operators, such as DeepONet, have changed the paradigm in high-
dimensional nonlinear regression, paving the way for significant generalization and speed …