Generative AI for Validating Physics Laws

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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.

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