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Simulated Hybrid System Identification

This example runs a full HyDRA identification loop on simulated one-dimensional hybrid-system traces. The reference system starts in one affine mode and switches to another when the state crosses a threshold. HyDRA learns mode dynamics, trains a selector for mode assignment, simulates the learned model, and compares that learned trajectory with the reference trace.

Run it from the repository root:

uv run --directory ./examples/simulated_hybrid_system python run.py

The learner uses PySR for symbolic regression. PySR requires Julia, and the first run can take longer while Julia packages are resolved and compiled.

The script performs these steps:

  1. Build a two-location HybridSystem with affine continuous dynamics.
  2. Simulate the system with derivative capture enabled.
  3. Convert the trace to a Polars frame with trace_to_polars.
  4. Train a HyDRALearner with PySR regressors for mode dynamics.
  5. Train a HybridDecisionTreeLearner selector over the state feature x.
  6. Simulate the learned HyDRAModel on the reference time grid.
  7. Print selector diagnostics and state-trace comparison metrics.
  8. Save selector and comparison plot artifacts.

The example passes HyDRATraceSchema(time="t", state=("x",), derivative=("dx",)) to the learner. This records which learned input column is time, which column is state, and which output column is the derivative, so HyDRAModel.simulate() can reconstruct a Trace after training.

Options:

  • --output-dir PATH: write selector and comparison artifacts to PATH instead of outputs.
  • --verbose: show HyDRA learner progress logs.

Expected printed output includes a summary dictionary containing rows, locations, modes, input_features, and output_features. If a selector is learned, the script also prints selector_summary, selector_mode_summary, selector_leaf_summary, selector_tree, and selector_svg diagnostics. The comparison block starts with learned trace comparison and reports mae, rmse, and max_error.

By default, artifacts are written to examples/simulated_hybrid_system/outputs/selector_tree.svg and examples/simulated_hybrid_system/outputs/learned_vs_reference.png. Use --output-dir PATH to choose another output directory.