FNO$^{\angle θ}$: Extended Fourier neural operator for learning state and optimal control of distributed parameter systems
We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle, we show that any state and optimal control of linear PDEs with constant coefficients can be represented as an integral in the complex domain. The integrand of this representation involves the same exponential term as in the inverse Fourier transform, where the latter is used to represent the convolution operator in FNO layer. Motivated by this observation, we modify the FNO layer by extending the frequency variable in the inverse Fourier transform from ...
| Authors | Zhexian Li, Ketan Savla |
|---|---|
| Primary category | cs.LG |
| Published | 6 April 2026 |
| Last updated at source | 6 April 2026 |
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