Self-supervised PINNs for Stellar Structure Equations

Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks

Summary: arXiv:2604.06255v1 Announce Type: cross

Abstract

Stellar astrophysics relies critically on accurate descriptions of the physical conditions inside stars. Traditional solvers such as MESA (Modules for Experiments in Stellar Astrophysics), which employ adaptive finite-difference methods, can become computationally expensive and challenging to scale for large stellar population synthesis (greater than 10⁹ stars).

In this work, we present a self-supervised physics-informed neural network (PINN) framework that provides a mesh-free and fully differentiable approach to solving the stellar structure equations under hydrostatic and thermal equilibrium.

Key Features of the Framework

• The model takes as input the stellar boundary conditions (at the center and surface) along with the chemical composition.
• It learns continuous radial profiles for mass M_r(r), pressure P(r), density ρ(r), temperature T(r), and luminosity L_r(r).
• The framework enforces governing structure equations through physics-based loss terms.

Incorporation of Microphysics

To incorporate realistic microphysics, we introduce auxiliary neural networks that approximate the equation of state and opacity tables as smooth, differentiable functions of the local thermodynamic state. These surrogates replace traditional tabulated inputs and enable end-to-end training.

Model Performance and Validation

Once trained for a given star, the model produces continuous solutions across the entire radial domain without requiring discretization or interpolation. Validation against benchmark MESA models across a range of stellar masses yields a Mean Relative Absolute Error of 3.06% and an average R² score of 99.98%.

Significance of the Study

To our knowledge, this is the first demonstration that the stellar structure equations can be solved in a fully self-supervised and data-free fashion employing PINNs. This work establishes a foundation for scalable, physics-informed emulation of stellar interiors and opens the door to future extensions toward time-dependent stellar evolution.

Conclusion

The introduction of self-supervised PINNs represents a significant advancement in the field of stellar astrophysics, providing researchers with a powerful tool to explore and simulate the complex internal structures of stars more efficiently than traditional methods.

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