ME5311 Project 2: Data-Driven System Modeling and Prediction

This project studies a 2D spatio-temporal chaotic vector field with strong nonlinearity and high sensitivity to initial conditions, where small perturbations can quickly amplify over time. I build a compact pipeline to reduce the state with POD, train DMD, SINDy, and LSTM predictors, and compare their forecasting performance on a dataset of shape (15000, 64, 64, 2) split into train, validation, and test sets.

Algorithm Highlights

DMD is a fast and interpretable linear latent-dynamics model. It usually works well for dominant coherent structures, but its performance can degrade for strongly nonlinear long-horizon prediction. SINDy identifies sparse nonlinear equations in reduced coordinates, which improves physical interpretability, but it is sensitive to noise and to library or threshold settings. LSTM is a flexible sequence model that captures nonlinear temporal dependencies and is often stronger for short- to medium-horizon prediction, while requiring higher training cost and more hyperparameter tuning.

Project Files

• main.py: full analysis pipeline entry point
• load_data.py: data loading and frame indexing
• POD.py: proper orthogonal decomposition implementation
• DMD.py: delay-embedded DMD predictor
• SINDy.py: sparse identification of dynamics in reduced space
• LSTM.py: LSTM-based sequence predictor
• metrics.py: error and skill metrics (relative error, RMSE, correlation, R2, horizon)
• plot.py: consolidated publication-style figure generation
• analyze_dynamics.py: additional diagnostic script for dynamics behavior
• data/vector_64.npy: input dataset (not included; place it in data/)
• data/PLACEHOLDER.txt: placeholder file for dataset directory

Requirements

Install dependencies:

pip install -r requirements.txt

Run

From the project root:

python main.py

Outputs

• Figure: output/report_figure.png
• Text summary: output/results_summary.txt