# Periodic Neural Mapping for Unsteady Rotor-Blade Pressure and Aeroelastic Load Prediction

arXiv: https://arxiv.org/abs/2609.21590 · HTML: https://mlsanity.com/paper/2609.21590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [Mitigating spectral bias for the multiscale operator learning](https://mlsanity.com/paper/2210.10890/) (2022)
- [Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective](https://mlsanity.com/paper/2404.07200/) (2024)
- [An operator learning perspective on parameter-to-observable maps](https://mlsanity.com/paper/2402.06031/) (2024)
- [Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders](https://mlsanity.com/paper/2307.15288/) (2023)
- [Fourier Neural Operators Explained: A Practical Perspective](https://mlsanity.com/paper/2512.01421/) (2025)
- [Reduced-order modeling of unsteady fluid flow using neural network ensembles](https://mlsanity.com/paper/2402.05372/) (2024)
- [Machine learning enhanced real-time aerodynamic forces prediction based on sparse pressure sensor inputs](https://mlsanity.com/paper/2305.09199/) (2023)
- [Fully Coupled Forced Response Analysis of Nonlinear Turbine Blade Vibrations in the Frequency Domain](https://mlsanity.com/paper/2307.07365/) (2023)
- [A panoramic aerodynamic performance prediction method for turbomachinery cascades using transformer-enhanced neural operator](https://mlsanity.com/paper/2609.16066/) (2026)

## Abstract (arXiv)

Accurate prediction of unsteady aerodynamic loads remains a major challenge in turbomachinery design. High-fidelity Computational Fluid Dynamics (CFD) simulations are expensive, while aeroelastic Quantities of Interest (QoI) depend sensitively on the temporal evolution of the pressure field. This work introduces periodic Fourier Neural Mapping (p-FNM), a neural-operator framework for predicting unsteady pressure distributions on turbine rotor blades simulated using the chorochronic numerical hypothesis. The architecture embeds temporal periodicity into the model and learns a continuous mapping from operating conditions and time to pressure fields. Unlike sequential latent-space approaches, p-FNM predicts pressure fields independently at any time, avoiding error accumulation while preserving temporal continuity. The model is evaluated on a database of unsteady rotor-blade simulations and compared with a reduced-order baseline based on a variational autoencoder and recurrent neural network, refered as the Temporal Prediction Model (TPM). Performance is assessed for pressure fields and Generalized Aerodynamic Forces (GAFs), the primary aeroelastic QoI. Across all training datasets, p-FNM consistently outperforms TPM. On the largest dataset, p-FNM achieves a pressure-field mean absolute percentage error of 0.46% and a GAF-magnitude prediction error of 4.42%, corresponding to improvements of 60.7% and 77.6%, respectively. The minimum weighted phase error reaches 0.060 rad, demonstrating accurate preservation of the temporal characteristics of the aerodynamic response. The results show that GAF prediction is more challenging than pressure-field prediction and that temporal coherence is critical for accurately predicting spectral aerodynamic quantities. These findings demonstrate the potential of periodic neural operators for reduced-order modeling and aeroelastic analysis in turbomachinery.