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This research applies generative AI within a causal inference framework to validate the Stefan-Boltzmann law using Gaia stellar data, demonstrating significant performance gains in estimating heterogeneous treatment effects. By formalizing physical laws as unidirectional causal models, the study bridges advanced machine learning techniques with fundamental astrophysical principles to recover nonlinear relationships from observational data.
Generative AI for Validating Physics Laws
arXiv:2503.17894v3 Announce Type: replace-cross Abstract: We propose generative learner for estimating heterogeneous treatment effects and characterizing the full distribution of causal effects. The learner takes the form of a multi-head feed-forward neural network with three jointly estimated subnetworks, propensity score, baseline outcome, and heterogeneous treatment effects, where the treatment-effect subnetwork parameterizes the conditional quantile function via a compositional architecture in which covariate features and cosine quantile embeddings are combined through element-wise multiplication. This quantile-based formulation recovers the conditional average treatment effect as an integral over quantile treatment effects while additionally characterizing the entire effect distribution. Under the classical assumptions in a Neyman--Rubin causal model, we demonstrate that the performance gains of the proposed generative learner are consistent across experimental designs and frequently exceed 70% in out-of-sample mean squared error when compared to the generalized random forest, double machine learning, and generative adversarial networks. These gains are particularly pronounced in small samples. As an empirical application, we formalize the Stefan--Boltzmann law as a unidirectional causal model and apply the method to Gaia DR3 stellar data. The method recovers the expected nonlinear temperature--luminosity relationship and quantifies heterogeneous effects across stellar radius and absolute magnitude.
Abstract:We propose generative learner for estimating heterogeneous treatment effects and characterizing the full distribution of causal effects. The learner takes the form of a multi-head feed-forward neural network with three jointly estimated subnetworks, propensity score, baseline outcome, and heterogeneous treatment effects, where the treatment-effect subnetwork parameterizes the conditional quantile function via a compositional architecture in which covariate features and cosine quantile embeddings are combined through element-wise multiplication. This quantile-based formulation recovers the conditional average treatment effect as an integral over quantile treatment effects while additionally characterizing the entire effect distribution. Under the classical assumptions in a Neyman--Rubin causal model, we demonstrate that the performance gains of the proposed generative learner are consistent across experimental designs and frequently exceed 70% in out-of-sample mean squared error when compared to the generalized random forest, double machine learning, and generative adversarial networks. These gains are particularly pronounced in small samples. As an empirical application, we formalize the Stefan--Boltzmann law as a unidirectional causal model and apply the method to Gaia DR3 stellar data. The method recovers the expected nonlinear temperature--luminosity relationship and quantifies heterogeneous effects across stellar radius and absolute magnitude.
Solar and Stellar Astrophysics (astro-ph.SR); Astrophysics of Galaxies (astro-ph.GA); Artificial Intelligence (cs.AI)
arXiv:2503.17894 [astro-ph.SR]
(or arXiv:2503.17894v3 [astro-ph.SR] for this version)
https://doi.org/10.48550/arXiv.2503.17894 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 288 words
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