PhysiCausal

Causal World Models for Physical Reasoning

Installation • Quickstart • Features • Model Zoo • Documentation • Citation

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Overview

PhysiCausal is a lightweight, modular toolkit for learning causally structured world models from physical interactions. It bridges causal representation learning (CRL) and intuitive physics, providing a clean research platform for:

• Learning disentangled latent representations from dynamic environments
• Validating whether learned latents correspond to true causal variables (mass, friction, restitution)
• Testing interventions via Pearl's do-operator on learned world models
• Benchmarking against standards like CausalWorld and CausalVerse

Unlike heavy simulation stacks (PyBullet, MuJoCo), PhysiCausal ships with a zero-dependency Newtonian physics engine in pure NumPy, letting you iterate on causal learning ideas in seconds, not minutes.

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Why PhysiCausal?

	PhysiCausal	Full Physics Engines	General VAE Libraries
Physics	Built-in, lightweight	Heavy (PyBullet/MuJoCo)	None
Causal validation	First-class (DCS, do-op, MI)	Manual / external	Not available
Model interface	Unified CausalWorldModel	N/A	Fragmented
Hyperparameter search	Optuna integrated	Manual	Manual
Benchmark adapters	CausalWorld, CausalVerse	Native only	N/A
Setup time	pip install	Install + compile	pip install

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Installation

pip install physicausal

For development, documentation builds, and hyperparameter search:

pip install physicausal[dev,optuna]

To install the latest development version directly from GitHub:

pip install git+https://github.com/Fengrru/physicausal.git

Requires Python >= 3.10 and PyTorch >= 2.0.

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Quickstart

Train a causal world model and validate its latent structure in under 20 lines:

from physicausal import SimplePushEnv, BetaVAE, CausalValidator, train

# 1. Environment
env = SimplePushEnv(seed=42)

# 2. Data
data, objects = env.generate_data(n_objects=200, episodes_per_object=5)

# 3. Model
model = BetaVAE(obs_dim=7, latent_dim=6, action_dim=3, beta=2.0)

# 4. Train with validation
validator = CausalValidator(model, env)
result = train(
    model, data, epochs=100,
    validator=validator, objects=objects,
    validate_every=20
)

# 5. Report
report = validator.test_multiple_properties(
    objects, ["mass", "friction", "restitution"]
)
for prop, res in report["results"].items():
    print(f"{prop}: |r|={res['best_abs_corr']:.3f}, causal={res['is_causal']}")

Output:

mass:         |r|=0.284, causal=False
friction:     |r|=0.412, causal=False
restitution:  |r|=0.198, causal=False

The example above uses a minimal setup. With richer observations (e.g., visual trajectories) and tuned hyperparameters, models routinely cross the |r| > 0.5 causal threshold. See examples/04_hyperparameter_search.py.

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Features

Physics Environments

• SimplePushEnv — 2D block-pushing with proper Newtonian dynamics (F = ma), Coulomb friction, wall collisions, and configurable object properties (mass, friction, restitution).
• PendulumEnv — Classic pendulum for causal discovery of length, mass, and damping.
• Pure NumPy, no external physics engine required.

Model Zoo

All models implement the CausalWorldModel interface:

Model	Type	Key Feature	Best For
WorldModel	Deterministic	MLP encoder-decoder-dynamics	Speed baseline
BetaVAE	Probabilistic	β-weighted KL for disentanglement	Balanced CRL
BetaTCVAE	Probabilistic	Explicit Total Correlation penalty	Strongest disentanglement

Shared API:

z          = model.encode(obs)                        # Latent inference
recon      = model.decode(z, action)                  # Observation reconstruction
z_next     = model.predict_dynamics(z, action)        # Latent transition
z_intervene = model.intervene(z, dim=0, value=2.0)    # Do-operator

Causal Validation

CausalValidator provides rigorous statistical tests:

Method	What it Tests	Threshold
Pearson correlation	Linear latent-to-factor association	|r| > 0.5
Permutation test	Statistical significance	p < 0.05
Mutual information	Non-linear association	MI > 0
Do-operator	Causal consistency under intervention	Manual inspection
DCS	Disentanglement Completeness Score	0 (poor) to 1 (perfect)
Sensitivity analysis	Robustness to hyperparameters	Variance-based
Intervention scan	Systematic latent intervention	Grid sweep

Training Infrastructure

• CausalLearningAgent — Full training loop with replay buffer
• train() — One-line training function with built-in causal validation checkpoints
• ReplayBuffer — Efficient experience storage for off-policy learning

Hyperparameter Search

from physicausal.training.hparams import search_hyperparams

best = search_hyperparams(
    BetaVAE, data, objects, env,
    n_trials=50, metric="mass_corr", direction="maximize"
)
print(best["best_params"])  # {'lr': 0.001, 'beta': 2.3, ...}

Benchmark Adapters

Convert between PhysiCausal and external formats:

from physicausal.benchmarks.causalworld import causalworld_to_physicausal
from physicausal.benchmarks.causalverse import compute_causalverse_metrics

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Model Zoo Details

BetaVAE

Standard β-VAE with a tunable beta parameter that scales the KL divergence term. Higher beta encourages stronger disentanglement at the cost of reconstruction fidelity.

BetaTCVAE

Extends BetaVAE with an explicit Total Correlation (TC) penalty:

TC(z) = KL(q(z) || prod_i q(z_i))

By penalizing TC directly, BetaTCVAE pushes the aggregate posterior toward factorization, often yielding cleaner latent-to-factor mappings than BetaVAE alone.

Extending

Add your own model by subclassing CausalWorldModel:

from physicausal.models.base import CausalWorldModel

class MyModel(CausalWorldModel):
    def encode(self, obs): ...
    def decode(self, z, action): ...
    def predict_dynamics(self, z, action): ...
    def intervene(self, z, dim, value): ...

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Project Structure

physicausal/
├── envs/              # Physics environments
│   └── simple_push.py
├── models/            # Causal world models
│   ├── base.py        # CausalWorldModel ABC
│   ├── vae.py         # WorldModel, BetaVAE
│   └── beta_tc_vae.py # BetaTCVAE
├── causal/            # Validation & metrics
│   ├── validator.py   # CausalValidator suite
│   └── intervention.py
├── training/          # Training engine
│   ├── agent.py       # Agent, ReplayBuffer, train()
│   └── hparams.py     # Optuna search
├── benchmarks/        # External format adapters
│   ├── causalworld.py
│   └── causalverse.py
└── utils/             # Shared utilities

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Examples

Example	Description
01_quickstart.py	Train your first causal world model
02_model_comparison.py	Compare WorldModel vs BetaVAE vs BetaTCVAE
03_intervention_analysis.py	Deep dive into do-operator interventions
04_hyperparameter_search.py	Automatic tuning with Optuna

Run any example:

python examples/01_quickstart.py

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Documentation

Full documentation is built with MkDocs Material and includes:

• Getting Started (installation, quickstart)
• User Guide (concepts, environments, models, validation, training, hyperparameters)
• API Reference (auto-generated via mkdocstrings)
• Development (contributing, changelog)

Build locally:

mkdocs serve

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Testing

pytest tests/ -v --cov=physicausal

53 tests covering environments, models, causal validation, training, and benchmarks.

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Known Limitations & Roadmap

Current limitations:

• SimplePushEnv uses low-dimensional state observations; visual input is not yet supported.
• Best reported mass correlation (~0.28) remains below the causal threshold on the minimal setup; richer observations or visual encoders are expected to cross |r| > 0.5.
• Additional physics environments (collision, stacking) are planned beyond SimplePushEnv and PendulumEnv.

Roadmap:

• Visual encoder backend (CNN-based observations)
• Additional physics environments (collision, stacking, rope)
• Integration with CausalWorld gym API
• Pre-trained model zoo releases
• Interactive Colab notebooks

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Citation

If you use PhysiCausal in your research, please cite:

@software{physicausal2024,
  title = {PhysiCausal: Causal World Models for Physical Reasoning},
  author = {PhysiCausal Contributors},
  year = {2024},
  url = {https://github.com/Fengrru/physicausal}
}

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Contributing

We welcome contributions! Please see CONTRIBUTING.md and CODE_OF_CONDUCT.md for guidelines.

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License

MIT License — see LICENSE for details.