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 …
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 …
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Deep neural operators can learn operators mapping between infinite-dimensional function
spaces via deep neural networks and have become an emerging paradigm of scientific …
spaces via deep neural networks and have become an emerging paradigm of scientific …
[HTML][HTML] 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 …
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 …
[HTML][HTML] Multifidelity deep operator networks for data-driven and physics-informed problems
Operator learning for complex nonlinear systems is increasingly common in modeling multi-
physics and multi-scale systems. However, training such high-dimensional operators …
physics and multi-scale systems. However, training such high-dimensional operators …
Deeponet-grid-uq: A trustworthy deep operator framework for predicting the power grid's post-fault trajectories
This paper proposes a novel data-driven method for the reliable prediction of the power
grid's post-fault trajectories, ie, the power grid's dynamic response after a disturbance or …
grid's post-fault trajectories, ie, the power grid's dynamic response after a disturbance or …
SVD perspectives for augmenting DeepONet flexibility and interpretability
Deep operator networks (DeepONets) are powerful and flexible architectures that are
attracting attention in multiple fields due to their utility for fast and accurate emulation of …
attracting attention in multiple fields due to their utility for fast and accurate emulation of …
[PDF][PDF] Multifidelity deep operator networks
AA Howard, M Perego… - arXiv preprint arXiv …, 2022 - app.icerm.brown.edu
Multifidelity Deep Operator Networks Page 1 Multifidelity Deep Operator Networks Amanda
Howard Mauro Perego, George Karniadakis, Panos Stinis Page 2 2 General framework u(x1) …
Howard Mauro Perego, George Karniadakis, Panos Stinis Page 2 2 General framework u(x1) …