The Invariant Discovery Engine: A Modular Framework for Closed-Loop Autonomous Discovery of Physical Laws

This repository contains the official Python reference implementation for the Invariant Discovery Engine (IDE), a modular computational architecture designed for the autonomous closed-loop recovery of compact, interpretable, and physically consistent governing equations from observational data. Unlike passive machine learning pipelines that focus solely on predictive accuracy, the IDE treats scientific model discovery as an active inference loop. The provided codebase instantiates a six-module loop:1. Scientific Data Engine (Noise smoothing via Savitzky–Golay filters)2. Representation Learning (Monomial-trigonometric feature libraries)3. Invariant Discovery (Lie-derivative null-space optimization via SVD)4. Symbolic Equation Generator (Sequentially Thresholded Least Squares - STLSQ)5. Information-Theoretic Evaluator (BIC and structural bootstrap stability scoring)6. Active Experiment Planner (Expected Information Gain optimization) The included end-to-end demonstration script (demo.py) validates the engine on a noisy planar pendulum system. The planner autonomously identifies that a high-amplitude, near-vertical swing is required to actively falsify a linear small-angle approximation, successfully driving the model weights toward the true exact non-linear governing laws. Dependencies: Python 3.10+, NumPy (>=1.24), SciPy (>=1.10), SymPy (>=1.12).