Data‐Driven Design for Metamaterials and Multiscale Systems: A Review
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 …
go beyond those found in nature. Composed of unit cells with rich designability that are …
Physics-informed deep neural operator networks
Standard neural networks can approximate general nonlinear operators, represented either
explicitly by a combination of mathematical operators, eg in an advection–diffusion reaction …
explicitly by a combination of mathematical operators, eg in an advection–diffusion reaction …
Physics-informed machine learning: A survey on problems, methods and applications
Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …
vision, reinforcement learning, and many scientific and engineering domains. In many real …
Reliable extrapolation of deep neural operators informed by physics or sparse observations
Deep neural operators can learn nonlinear mappings between infinite-dimensional function
spaces via deep neural networks. As promising surrogate solvers of partial differential …
spaces via deep neural networks. As promising surrogate solvers of partial differential …
Partial differential equations meet deep neural networks: A survey
Many problems in science and engineering can be represented by a set of partial differential
equations (PDEs) through mathematical modeling. Mechanism-based computation following …
equations (PDEs) through mathematical modeling. Mechanism-based computation following …
Learning two-phase microstructure evolution using neural operators and autoencoder architectures
Phase-field modeling is an effective but computationally expensive method for capturing the
mesoscale morphological and microstructure evolution in materials. Hence, fast and …
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 …
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
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 …
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
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 …
the context of scientific machine learning. Here, we implement and train a modified Fourier …
Deep neural operators as accurate surrogates for shape optimization
Deep neural operators, such as DeepONet, have changed the paradigm in high-
dimensional nonlinear regression, paving the way for significant generalization and speed …
dimensional nonlinear regression, paving the way for significant generalization and speed …