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info.json
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{
"abstract": "Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any continuous operator to desired accuracy. Moreover, we suggest a mechanism by which FNOs can approximate operators associated with PDEs efficiently. Explicit error bounds are derived to show that the size of the FNO, approximating operators associated with a Darcy type elliptic PDE and with the incompressible Navier-Stokes equations of fluid dynamics, only increases sub (log)-linearly in terms of the reciprocal of the error. Thus, FNOs are shown to efficiently approximate operators arising in a large class of PDEs.",
"authors": [
"Nikola Kovachki",
"Samuel Lanthaler",
"Siddhartha Mishra"
],
"emails": [
"nkovachki@caltech.edu",
"samuel.lanthaler@math.ethz.ch",
"siddhartha.mishra@math.ethz.ch"
],
"id": "21-0806",
"issue": 290,
"pages": [
1,
76
],
"title": "On Universal Approximation and Error Bounds for Fourier Neural Operators",
"volume": 22,
"year": 2021
}