# README File for Scripts Supporting Thesis

**Title:** *Data-Driven Modelling of Nonlinear Aerodynamics in High-Speed Aircraft Using Machine Learning*

**Dataset DOI:** 10.5258/SOTON/D3670
**Author:** Gabriele Immordino, University of Southampton
**ORCID ID:** 0000-0003-2718-0120

**Awarded by:** University of Southampton
**Date of Award:** 2025
**Data Collection Period:** September 2021 – September 2025
**Location:** Zurich University of Applied Sciences (ZHAW), Switzerland
**Licence:** Creative Commons Attribution (CC-BY)
**Funding:** Digitalization Initiative of the Zurich Higher Education Institutions (DIZH) from Zurich University of Applied Sciences (ZHAW), grant 9710.Z.12.P.0003.05

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## DATA & FILE OVERVIEW

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This repository provides the **scripts** used to generate the results of the thesis.

**Folder structure:**

* **Chapter\_4** – *Parametric Nonlinear Volterra Series*

  * Scripts for kernel extraction from CFD and synthetic systems.
  * ML-based kernel prediction (FCNN, GPR).
  * Flutter boundary estimation, including multi-fidelity co-Kriging.
  * Includes:

    * Synthetic test case.
    * 2D CFD test case.
    * 3D CFD test case.

* **Chapter\_5** – *Multi-Fidelity Bayesian Neural Network*

  * Scripts for probabilistic load prediction in the transonic regime.
  * Multi-fidelity integration (low, mid, high) with transfer learning.
  * Bayesian neural networks with uncertainty quantification.

* **Chapter\_6** – *Deep Learning for Steady Transonic Flowfields*

  * Fully connected neural networks for surface field prediction.
  * Applications to aeroelastic twist and uncertainty quantification.
  * Evaluation on BSCW, ONERA M6, NASA CRM.

* **Chapter\_7** – *Graph-Convolutional Autoencoder (Steady Flowfields)*

  * GCN-based autoencoder for steady aerodynamic fields on unstructured meshes.
  * Physics-informed loss and multi-resolution pooling.

* **Chapter\_8** – *Spatio-Temporal GCN (Unsteady Flowfields)*

  * Implements feedforward and ARMA-based STGCN architectures.
  * Predicts unsteady pressure fields from motion histories.
  * Includes preprocessing, dimensionality reduction, and autoencoder pretraining pipelines.

* **Chapter\_9** – *Graph-Convolutional Autoencoder for Modal Space*

  * GCN autoencoder for parametrically deformed wing shapes.
  * Incorporates structural mode amplitudes in the input.
  * Includes modal sampling, MWLS pooling, and physics-informed training.

**Relationship between files:**
Each folder corresponds to one thesis chapter and contains notebooks and Python modules to reproduce the relevant experiments.

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## METHODOLOGICAL INFORMATION

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**Approach per chapter:**

* *Chapter 4*: Volterra kernel identification (linear/quadratic), ML-based prediction, flutter analysis, and multi-fidelity fusion.
* *Chapter 5*: Bayesian neural networks with transfer learning, uncertainty quantification, and Co-Kriging comparison.
* *Chapter 6*: Dense FCNNs for steady aerodynamic field regression, with extensions to aeroelastic deformation and uncertainty propagation.
* *Chapter 7*: Autoencoder GCN with hierarchical pooling/unpooling, moment-regularised loss, and Bayesian hyperparameter optimisation.
* *Chapter 8*: Spatio-temporal GCNs (feedforward/ARMA) with windowed CFD data; integrates motion states with graph-encoded CP fields.
* *Chapter 9*: GCN autoencoder on modal-deformed geometries, with MWLS pooling and physics-informed objectives.

**Software requirements:**

* **General:** Python ≥ 3.9, NumPy, SciPy, Matplotlib, Pandas.
* **Machine Learning:** TensorFlow/Keras, PyTorch, PyTorch Geometric, Optuna, GPy.


**Workflow (generalised):**

1. **Data preparation:** Preprocessing of CFD outputs (normalisation, mesh connectivity, pressure gradients, modal coordinates).
2. **Model definition:** Notebooks and Python modules specify neural architectures and loss functions.
3. **Training:** Models trained with hyperparameter tuning (Optuna, Keras-tuner).
4. **Evaluation:** Predictions validated against reference CFD; results visualised with provided plotting utilities.

**Quality assurance:**

* CFD data checked for convergence; unstable snapshots excluded.
* ML models benchmarked against baselines (Proper Orthogonal Decomposition with Interpolation (POD+I), Dynamic Mode Decomposition with control (DMDc), Co-Kriging).
* Scripts tested on GPU-enabled environments (NVIDIA RTX A4000).