ME5311 Project 2: System Modeling and Prediction

Author: Yu Huize

A data-driven pipeline for modeling and predicting 2D vector field dynamics using dimensionality reduction and multiple forecasting methods.

This project applies five data-driven approaches to learn the temporal evolution of a 2D velocity field (×ばつ64 grid, 2 components) and compares their prediction performance:

All models operate in a POD-reduced space (20 modes capturing 92.84% of fluctuation energy), reducing the original 8192-dimensional system for computational efficiency.

System-Modeling-and-Prediction/
├── pyproject.toml # Project metadata and dependencies
├── main.py # Full pipeline script (run all steps)
├── notebooks/
│ └── notebook.ipynb # Interactive Jupyter notebook with visualizations
├── src/
│ ├── config.py # Hyperparameters and paths
│ ├── data_loader.py # Data loading and preprocessing
│ ├── svd_reduction.py # SVD/POD decomposition and reconstruction
│ ├── dmd_model.py # DMD model implementation
│ ├── sindy_model.py # SINDy model implementation
│ ├── ml_models.py # Ridge, MLP, and SVR models
│ ├── evaluation.py # Metrics (RMSE, relative error, correlation)
│ └── visualization.py # Plotting utilities
├── data/
│ └── vector_64.npy # Raw vector field data (15000 snapshots)
├── figures/ # Generated plots
├── results/
│ └── summary.txt # Evaluation summary
└── docs/ # Documentation

• Python 3.10+
• NumPy
• SciPy
• Matplotlib
• scikit-learn

pip install .

Or install with notebook support:

pip install .[notebook]

python main.py

This executes all steps sequentially: data loading → SVD/POD → model fitting (DMD, SINDy, Ridge, MLP, SVR) → evaluation → visualization. Results are saved to results/summary.txt and figures to figures/.

Open notebooks/notebook.ipynb in Jupyter for step-by-step exploration with inline plots and discussion.

1. Data Loading & Preprocessing — Load 15,000 snapshots of a ×ばつ2 velocity field; compute temporal mean and fluctuations
2. SVD/POD Decomposition — Extract dominant spatial modes; reduce from 8,192 to 20 dimensions
3. Model Fitting — Train five models on POD temporal coefficients (train set: 10,500 snapshots)
4. Evaluation — Predict on validation (2,250) and test (2,250) sets; compute RMSE, relative error, and Pearson correlation
5. Sliding Window Evaluation — Assess prediction accuracy at multiple horizons (1, 5, 10, 25, 50, 100, 200 steps)

• Ridge Regression achieves the best overall accuracy across all horizons
• DMD is the fastest to fit and produces bounded predictions but loses phase alignment
• SINDy provides the most interpretable model (explicit governing equations) but diverges long-term
• No model achieves reliable prediction beyond ~50 time steps for this chaotic system

Key parameters can be adjusted in src/config.py: