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Found 7 papers, 4 papers with code
Learning in latent spaces improves the predictive accuracy of deep neural operators
Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems.
Deep transfer operator learning for partial differential equations under conditional shift
Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labeling, potential computational power limitations, and dataset distribution mismatches.
On the influence of over-parameterization in manifold based surrogates and deep neural operators
In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics.
A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e. g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges.
Grassmannian diffusion maps based surrogate modeling via geometric harmonics
Using this representation, geometric harmonics, an out-of-sample function extension technique, is employed to create a global map from the space of input parameters to a Grassmannian diffusion manifold.
Neural density estimation and uncertainty quantification for laser induced breakdown spectroscopy spectra
Constructing probability densities for inference in high-dimensional spectral data is often intractable.
Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models
For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner.
