SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators

• URL: http://arxiv.org/abs/2606.11518v1
• Date: Tue, 09 Jun 2026 23:37:49 GMT
• Title: SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators
• Abstract summary: Fourier neural operators (FNOs) are effective surrogates for approximating solutions of PDEs and generalize across discretizations.<n>We propose SirenFNO, a novel framework that leverages sinusoidal representation networks (SIRENs) to learn implicit neural representations and perform mode-wise kernel parameterization.<n>Our results show that our SirenFNO consistently outperforms FNO with approximately $4$ to $15$ times parameter reductions with preserved discretization invariance.
• Score: 30.12182897841357
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations. However, owing to the reliance on frequency truncation to maintain learning efficiency of FNOs, empirical studies suggest that FNOs exhibit spectral bias toward low-frequency information, which may hinder the learning capability especially for certain PDEs with strong high-frequency oscillations. To address this limitation, we propose SirenFNO, a novel framework that leverages sinusoidal representation networks (SIRENs) to learn implicit neural representations and performs mode-wise kernel parameterization. Our SIREN parameterization learns a full-grid spectrum with a constant and discretization-independent parameter count, thereby eliminating the need for frequency truncation. We further extend SirenFNO with functional tensor decompositions to enhance parameter and learning efficiency. Empirical results show that our SirenFNO consistently outperforms FNO with approximately $4$ to $15$ times parameter reductions with preserved discretization invariance, and our functional decomposition variants obtain performance improvements with a maximum of $73$ times fewer parameters across multiple PDE benchmarks.

Related papers

• FUTON: Fourier Tensor Network for Implicit Neural Representations [56.48739018255443]
  Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant-based designs often suffer from slow convergence, overfitting to noise, and poor extrapolation.<n>We introduce FUTON, which models signals as generalized Fourier series whose coefficients are parameterized by a low-rank tensor decomposition.
  arXiv  Detail & Related papers  (2026-02-13T19:31:44Z)
• Spectral Gating Networks [65.9496901693099]
  We introduce Spectral Gating Networks (SGN) to introduce frequency-rich expressivity in feed-forward networks.<n>SGN augments a standard activation pathway with a compact spectral pathway and learnable gates that allow the model to start from a stable base behavior.<n>It consistently improves accuracy-efficiency trade-offs under comparable computational budgets.
  arXiv  Detail & Related papers  (2026-02-07T20:00:49Z)
• Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators [1.315766151337659]
  We introduce DINOZAUR: a diffusion-based neural operator parametrization with uncertainty quantification.<n>Our method achieves competitive or superior performance across several PDE benchmarks.
  arXiv  Detail & Related papers  (2025-08-01T13:57:19Z)
• FreqMoE: Dynamic Frequency Enhancement for Neural PDE Solvers [33.5401363681771]
  We propose FreqMoE, an efficient and progressive training framework that exploits the dependency of high-frequency signals on low-frequency components.<n>Experiments on both regular and irregular grid PDEs demonstrate that FreqMoE achieves up to 16.6% accuracy improvement.
  arXiv  Detail & Related papers  (2025-05-11T06:06:32Z)
• LOGLO-FNO: Efficient Learning of Local and Global Features in Fourier Neural Operators [20.77877474840923]
  High-frequency information is a critical challenge in machine learning.<n>Deep neural nets exhibit the so-called spectral bias toward learning low-frequency components.<n>We propose a novel frequency-sensitive loss term based on radially binned spectral errors.
  arXiv  Detail & Related papers  (2025-04-05T19:35:04Z)
• Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective [4.315136713224842]
  SpecB-FNO achieves better prediction accuracy on diverse PDE applications, with an average improvement of 50%. This paper offers empirical insights into FNO's difficulty with large kernels through spectral analysis.
  arXiv  Detail & Related papers  (2024-04-10T17:58:04Z)
• FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation [60.706803227003995]
  We introduce the FC-PINO (Fourier-Continuation-based PINO) architecture which extends the accuracy and efficiency of PINO to non-periodic and non-smooth PDEs.<n>We demonstrate that standard PINO struggles to solve non-periodic and non-smooth PDEs with high precision, across challenging benchmarks.<n>In contrast, the proposed FC-PINO provides accurate, robust, and scalable solutions, substantially outperforming PINO alternatives.
  arXiv  Detail & Related papers  (2022-11-29T06:37:54Z)
• Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs [86.35471039808023]
  We introduce the Incremental Fourier Neural Operator (iFNO), which progressively increases the number of frequency modes used by the model. We show that iFNO reduces total training time while maintaining or improving generalization performance across various datasets. Our method demonstrates a 10% lower testing error, using 20% fewer frequency modes compared to the existing Fourier Neural Operator, while also achieving a 30% faster training.
  arXiv  Detail & Related papers  (2022-11-28T09:57:15Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• Factorized Fourier Neural Operators [77.47313102926017]
  The Factorized Fourier Neural Operator (F-FNO) is a learning-based method for simulating partial differential equations. We show that our model maintains an error rate of 2% while still running an order of magnitude faster than a numerical solver.
  arXiv  Detail & Related papers  (2021-11-27T03:34:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.