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Factorized Fourier Neural Operators
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Factorized Fourier Neural Operators
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We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the performance gap between pure machine learning approaches to that of the best numerical or hybrid solvers. This is achieved with new representations - separable spectral layers and improved residual connections - and a combination of training strategies such as the Markov assumption, Gaussian noise, and cosine learning rate decay. On several challenging benchmark PDEs on regular grids, structured meshes, and point clouds, the F-FNO can scale to deeper networks and outperform both the FNO and the geo-FNO, reducing the error by 83% on the Navier-Stokes problem, 31% on the elasticity problem, 57% on the airfoil flow problem, and 60% on the plastic forging problem. Compared to the state-of-the-art pseudo-spectral method, the F-FNO can take a step size that is an order of magnitude larger in time and achieve an order of magnitude speedup to produce the same solution quality.
Forward citations
Cited by 28 Pith papers
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Hybrid Fourier Neural Operator-Lattice Boltzmann Method
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Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients
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Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence
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Local Linear Transformer learns PDE operators by combining linear global attention with local spatial mixing, achieving competitive accuracy and lower training-step cost than prior transformers.
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Structure-Informed Neural Operators for Long-Time Prediction of Parametric Hamiltonian PDEs
EP-FNO adds an invariant projection to residual FNO time-stepping to improve long-time stability and soliton accuracy for parametric Hamiltonian PDEs on Zakharov-Kuznetsov, Kadomtsev-Petviashvili, and sine-Gordon equations.
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Structure-Informed Neural Operators for Long-Time Prediction of Parametric Hamiltonian PDEs
An energy-projection Fourier neural operator (EP-FNO) reduces invariant drift and improves long-time soliton fidelity versus standard FNO on several Hamiltonian PDEs.
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Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
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Structure-Informed Neural Operators for Long-Time Prediction of Parametric Hamiltonian PDEs
EP-FNO, a residual Fourier neural operator with an invariant mass/energy projection, reduces long-time rollout error versus standard FNO on three 2D Hamiltonian soliton benchmarks.
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