PyPhysDisc: Autonomous Discovery of Physical Laws from Noisy Data via Co-evolutionary Symbolic Regression and Smoothing

This repository contains the complete source code, simulation datasets, and analysis scripts required to reproduce the findings presented in the associated Swarm and Evolutionary Computation (SWEC) manuscript. The study introduces PyPhysDisc, a co-evolutionary genetic-programming framework that couples the evolution of mathematical expression trees with the autonomous adaptation of signal-processing parameters (Savitzky-Golay smoothing window), resolving the derivative-noise dilemma in symbolic regression.

Repository Contents:

• code/pyphysdisc_core.py: The core DEAP-based library implementing the co-evolutionary algorithm. It encodes the smoothing window (w) as a co-evolving discrete gene within each individual, enabling synergistic adaptation under a single fitness pressure.
• code/experiment_suite.py & code/benchmark_convergence.py: Master execution scripts to reproduce all experiments:
  • Experiment 1: Noise Robustness Sweep (Lorenz, Van der Pol, Duffing, Lotka-Volterra).
  • Experiment 2: Window Ablation Study (Co-Evo vs. Fixed-Window Variance).
  • Experiment 3: Strategy Comparison (Benchmark D: Oracle vs. Co-Evo vs. Random/Fixed).
  • Experiment 4: Co-evolutionary Dynamics Evidence (Per-generation entropy collapse).
  • Experiment 5 & 6: Non-Polynomial Laws (Pendulum) and Runtime Scaling.
• code/gen*_fig.py: Plotting scripts to reproduce high-resolution publication figures (Fitness Landscape Shift, Convergence Curves, Ablation) following journal standards.
• data/: Folder containing the raw .csv outputs from the experiments (e.g., benchmark_results.csv, coevo_dynamics.csv), allowing for the reproduction of figures and statistical tests without re-running intensive evolutionary searches.
• requirements.txt: List of Python dependencies (DEAP, NumPy, SciPy, Pandas, Matplotlib) required to run the code.

Methodology Highlights:

• Benchmark Systems: Lorenz (Chaotic), Van der Pol (Limit-cycle), Duffing (Stiff/Nonlinear), Lotka-Volterra (Periodic predator-prey), and Spinning Pendulum.
• Technique: Co-evolutionary Symbolic Regression. Unlike standard sparse regression methods (e.g., SINDy) or standard GP that require external hyperparameter tuning, PyPhysDisc simultaneously evolves the equation structure and the smoothing window, resulting in complexity-aware filtering.

Key Results:

• Genuine Co-evolution: Shannon entropy of the window-gene distribution drops by 82% over 40 generations, with elite window fraction reaching 1.0, proving directed selection rather than drift.
• Near-Oracle Performance: Achieves R^2 = 0.961 on the Lorenz system at 20% noise without manual tuning, within 2.2 percentage points of an oracle holding the true optimal window, while variance is reduced by 95% compared to fixed-window GP.
• Generality: Successfully discovers transcendental functions (-sin(theta) in the pendulum) from an elementary operator set.

Usage:

To reproduce the full suite of experiments:

1. Install dependencies: pip install -r requirements.txt
2. Run the master scripts: python code/experiment_suite.py (or benchmark_convergence.py for per-generation metrics)
3. Select the desired experiment to run or generate figures via the plotting scripts.