# Low-Order Flow Reconstruction and Uncertainty Quantification in Disturbed Aerodynamics Using Sparse Pressure Measurements

arXiv: https://arxiv.org/abs/2501.03406 · HTML: https://mlsanity.com/paper/2501.03406/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 6 Jan 2025.

## Builds on (most cited first, 11 of 11)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Grasping Extreme Aerodynamics on a Low-Dimensional Manifold](https://mlsanity.com/paper/2305.08024/) (2023)
- [Jacobian Descent for Multi-Objective Optimization](https://mlsanity.com/paper/2406.16232/) (2024)
- [Dropout as a Bayesian Approximation: Appendix](https://mlsanity.com/paper/1506.02157/) (2015)
- [Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations](https://mlsanity.com/paper/2007.09644/) (2020)
- [Uncertainty Quantification via Stable Distribution Propagation](https://mlsanity.com/paper/2402.08324/) (2024)
- [A low-rank ensemble Kalman filter for elliptic observations](https://mlsanity.com/paper/2203.05120/) (2022)

## Built on by (most cited first, 4 of 4)

- [Spatiotemporal wall pressure forecast of a rectangular cylinder with physics-aware DeepU-Fourier neural network](https://mlsanity.com/paper/2508.03183/) (2025)
- [Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling](https://mlsanity.com/paper/2510.00233/) (2025)
- [Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flows](https://mlsanity.com/paper/2512.06031/) (2025)
- [Attention on flow control: transformer-based reinforcement learning for lift regulation in highly disturbed flows](https://mlsanity.com/paper/2506.10153/) (2025)

## Abstract (arXiv)

This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying response of sensors to gust-airfoil interactions, uncovering valuable insights into optimal sensor placement. To address uncertainties in deep learning predictions, we implement probabilistic regression strategies to model both epistemic and aleatoric uncertainties. Epistemic uncertainty, reflecting the model's confidence in its predictions, is modeled using Monte Carlo dropout, as an approximation to the variational inference in the Bayesian framework, treating the neural network as a stochastic entity. On the other hand, aleatoric uncertainty, arising from noisy input measurements, is captured via learned statistical parameters, which propagates measurement noise through the network into the final predictions. Our results showcase the efficacy of this dual uncertainty quantification strategy in accurately predicting aerodynamic behavior under extreme conditions while maintaining computational efficiency, underscoring its potential to improve online sensor-based flow estimation in real-world applications.