[Paper] Exoplanet formation inference using conditional invertible neural networks

Source: arXiv - 2512.05751v1

Overview

A team of astronomers and machine‑learning researchers have shown how conditional invertible neural networks (cINNs) can be trained on simulated planet‑formation data to reverse‑engineer the birth locations and early histories of observed exoplanets. By turning a forward model (dust → planet) into a fast, probabilistic inverse model, they move from qualitative storytelling to quantitative inference—opening the door for data‑driven planet‑formation studies at scale.

Key Contributions

• First application of cINNs to exoplanet formation: Demonstrates that invertible deep networks can learn the complex, many‑to‑one mapping from initial disk conditions to final planetary properties.
• Hybrid training set: Combines deterministic single‑planet formation runs with chaotic multi‑planet simulations, enabling the network to handle both isolated and interacting systems.
• Probabilistic inverse mapping: Generates full posterior distributions over initial conditions (e.g., birth radius, disk mass) rather than a single point estimate, capturing uncertainties inherent in planet formation.
• Scalable inference pipeline: Once trained, the cINN can infer a planet’s origin in milliseconds, orders of magnitude faster than running a full forward simulation.
• Benchmarking of data regimes: Shows that training on single‑planet data alone limits extrapolation, while multi‑planet data (treated as individual points) yields more robust predictions across a broader parameter space.

Methodology

1. Synthetic training data – The authors used a global planet‑formation code that follows dust growth, pebble accretion, migration, and gas accretion from the protoplanetary disk stage to mature giant planets. They generated two datasets:

   • Deterministic runs: One planet per simulation, covering a limited region of parameter space.
   • Multi‑planet runs: Systems with 2–3 planets that interact gravitationally, introducing chaotic dynamics.

2. Conditional Invertible Neural Network (cINN) – A type of normalizing flow that learns a bijective mapping between a latent Gaussian space and the observable planet properties conditioned on the target variables (e.g., final mass, orbital radius). During training, the network sees pairs (initial conditions → final planet) and learns to invert this mapping.

3. Training strategy –

   • The network is fed the final observable properties as conditions and learns to sample plausible initial conditions from the latent space.
   • For multi‑planet data, each planet is treated as an independent sample, allowing the network to learn from a higher‑dimensional distribution without explicitly modeling the full system dynamics.

4. Inference – Given a real exoplanet’s observed mass, radius, orbital distance, etc., the trained cINN draws many latent samples, maps them back to the initial‑condition space, and produces a posterior distribution over birth locations and disk properties.

Results & Findings

• Accuracy on test data – For planets drawn from the same distribution as the training set, the cINN recovered birth radii within ~10 % (median absolute error) and correctly captured the spread of plausible disk masses.
• Generalization – Networks trained only on single‑planet runs failed to extrapolate to planets with properties outside the training envelope (e.g., very massive or distant giants). Adding multi‑planet data dramatically improved coverage, allowing the model to handle a wider variety of observed exoplanets.
• Speed – Inference per planet took ≈ 5 ms on a consumer‑grade GPU, compared to hours or days for a full forward simulation.
• Uncertainty quantification – The posterior distributions reflected known degeneracies (e.g., similar final masses can arise from different birth locations combined with varying migration histories), giving developers a realistic sense of confidence.

Practical Implications

• Rapid “forensic” analysis of new exoplanet discoveries – Survey pipelines (e.g., TESS, PLATO, JWST) can feed observed planet catalogs into a pre‑trained cINN to obtain statistically sound formation histories in real time, aiding target prioritization for follow‑up observations.
• Integration into planet‑population synthesis tools – Developers can replace expensive Monte‑Carlo forward runs with a lightweight inference module, enabling interactive exploration of how changes in disk physics affect observable planet demographics.
• Data‑driven model calibration – By comparing inferred birth‑condition posteriors against independent disk observations (ALMA dust maps, stellar metallicities), researchers can iteratively refine physical prescriptions (e.g., pebble‑accretion efficiency) without rerunning the full formation code.
• Educational & outreach platforms – Interactive web apps can let users “drag” a planet’s mass and orbit and instantly see a distribution of possible birth locations, making planet formation concepts tangible for developers and hobbyists.

Limitations & Future Work

• Training data coverage – The current model still struggles with extreme outliers (e.g., ultra‑short‑period super‑Earths) because the synthetic dataset does not span the full observed exoplanet parameter space.
• System‑level dynamics – Treating each planet in a multi‑planet system independently ignores correlated migration and resonant locking; a full joint inference would require higher‑dimensional conditioning and more training samples.
• Physical model fidelity – The underlying forward simulation assumes specific prescriptions for pebble accretion, disk viscosity, and migration torques; biases in these assumptions propagate into the inferred posteriors.
• Scalability to larger surveys – While inference is fast, generating the massive, diverse training set needed for comprehensive coverage remains computationally intensive. Future work will explore active learning strategies to focus simulation effort on the most informative regions of parameter space.

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Bottom line: By marrying state‑of‑the‑art invertible neural networks with planet‑formation physics, this research provides a practical, fast, and probabilistic tool for turning exoplanet observations into quantitative formation histories—an advance that could become a standard component of next‑generation exoplanet data pipelines.

Authors

• Remo Burn
• Victor F. Ksoll
• Hubert Klahr
• Thomas Henning

Paper Information

• arXiv ID: 2512.05751v1
• Categories: astro-ph.EP, cs.NE, physics.data-an
• Published: December 5, 2025
• PDF: Download PDF