Approximate DFT Based Fourier Neural Operators for ML-Based PDE Solution at Linear Complexity
Conference
Lawrance, K, Madanayake, A, Hariharan, SI et al. (2025). Approximate DFT Based Fourier Neural Operators for ML-Based PDE Solution at Linear Complexity
. 00 449-452. 10.1109/MWSCAS53549.2025.11244515
Lawrance, K, Madanayake, A, Hariharan, SI et al. (2025). Approximate DFT Based Fourier Neural Operators for ML-Based PDE Solution at Linear Complexity
. 00 449-452. 10.1109/MWSCAS53549.2025.11244515
The FFT has taken physics-informed neural network (PINN) for advanced simulations by storm. FFT based Fourier Neural Operators (FNOs) have led to massive reductions in compute requirements for partial differential equation (PDE) based classical physics simulations with extensive applications in climate modeling, turbulent flow modeling, and magnetohydronamics, as well as other branches of classical physics. The use of FFT based FNO-PINN models has reduced the complexity of massively complicated physics simulations from O(N2) to O(Nlog N). In this work, we propose replacing FFTs with sparse factorized approximate DFT algorithms, which lead to the novel concept of approximate FNOs, which further reduce the compute requirements by a further log N factor resulting in linear complexity O(N) algorithms for PINNs. Early work from open source FNO examples shows promising results for both Darcy flow and Navier-Stokes PDE problems.
