arXiv:2604.11929v1 Announce Type: new
Abstract: Our ability to predict, control, and ultimately understand complex systems rests on discovering the equations that govern their dynamics. Identifying these equations directly from noisy, limited observations has therefore become a central challenge in data-driven science, yet existing library-based sparse regression methods force a compromise between automation, statistical rigor, and computational efficiency. Here we develop Bayesian-ARGOS, a hybrid framework that reconciles these demands by combining rapid frequentist screening with focused Bayesian inference, enabling automated equation discovery with principled uncertainty quantification at a fraction of the computational cost of existing methods. Tested on seven chaotic systems under varying data scarcity and noise levels, Bayesian-ARGOS outperforms two state-of-the-art methods in most scenarios. It surpasses SINDy in data efficiency for all systems and noise tolerance for six out of the seven, with a two-order-of-magnitude reduction in computational cost compared to bootstrap-based ARGOS. The probabilistic formulation additionally enables a suite of standard statistical diagnostics, including influence analysis and multicollinearity detection that expose failure modes otherwise opaque. When integrated with representation learning (SINDy-SHRED) for high dimensional sea surface temperature reconstruction, Bayesian-ARGOS increases the yield of valid latent equations with significantly improved long horizon stability. Bayesian-ARGOS thus provides a principled, automated, and computationally efficient route from scarce and noisy observations to interpretable governing equations, offering a practical framework for equation discovery across scales, from benchmark chaotic systems to the latent dynamics underlying global climate patterns.