REVIEW 5 cited by
The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential equations (PDEs). Surrogate modeling is an enabling methodology for many-query computations in science and engineering, which include iterative methods in optimization and sampling methods in uncertainty quantification. Over the last few years, several approaches to surrogate modeling for PDEs using neural networks have emerged, motivated by successes in using neural networks to approximate nonlinear maps in other areas. In principle, the relative merits of these different approaches can be evaluated by understanding, for each one, the cost required to achieve a given level of accuracy. However, the absence of a complete theory of approximation error for these approaches makes it difficult to assess this cost-accuracy trade-off. The purpose of the paper is to provide a careful numerical study of this issue, comparing a variety of different neural network architectures for operator approximation across a range of problems arising from PDE models in continuum mechanics.
Forward citations
Cited by 5 Pith papers
-
Can neural operators always be continuously discretized?
Neural operators that are diffeomorphisms generally cannot be continuously discretized, but strongly monotone neural operators can, and bilipschitz neural operators decompose into strongly monotone layers plus a singl...
-
Geometric Generalization of Neural Operators from a Kernel Integral Perspective
M-PCNO, a multiscale point cloud neural operator using Ewald-style long/short-range kernel splitting, approximates singular kernel integrals and PDE solution operators with generalization across variable geometries.
-
Modeling turbulent and self-gravitating fluids with Fourier neural operators
Fourier neural operators trained on 2D projected views of 3D astrophysical simulations can forecast subsequent projected density and velocity snapshots with 5-25% RMS error, though a constant hidden magnetic field mea...
-
Point Cloud Neural Operator for Parametric PDEs on Complex and Variable Geometries
A point cloud neural operator combining Fourier integral and least-squares gradient layers approximates PDE solution maps on variable geometries with reported test errors around 0.17 percent to 7 percent.
-
Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators
A stabilized FEM with POD and autoencoder compression plus a learned solution operator reconstructs PDE solutions in unique continuation problems, with a first-order H1 error estimate in the linear case and numerical ...
Discussion (0). Continue with ORCID to comment.