Physics-Informed Machine Learning
Authors: Christian Findenig (Materials Center Leoben Forschung GmbH) , Manfred Mücke (Materials Center Leoben Forschung GmbH)
For many scientific and engineering problems, equations based on applicable laws of physics can be used to link observable physical quantities. Analytic expressions, however, provide only point estimates and therefore cannot express uncertainty. This limits trustworthiness of predictions, especially in setups with limited data, noisy observations or when extrapolating. Bayesian probabilistic models address this limitation by treating unknown model parameters as random variables initialized by prior distributions and yielding - through inference - posterior (predictive) distributions. Constructing Bayesian models and convergence of inference, however, still requires specialized knowledge in probabilistic programming and inference algorithms, hindering the broader adoption of Bayesian models and uncertainty quantification in many domains. To make uncertainty-aware equation modeling more accessible, we present Equayes (Equation to Bayesian Model), a scikit-learn-style estimator that converts a user-provided symbolic expression into a probabilistic model and performs posterior inference over its numerical constants. The core value of the method and tool to construction of hybrid models is that it implements a principled approach to hybrid model evaluation, linking laws of physics, random variables and inference in an accessible manner.
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How to Cite: Findenig, C. & Mücke, M. (2026) “Equayes - Democratizing Probabilistic Model Construction and Exploration with automatic Equation to Bayesian Model transformation”, Proceedings of the Austrian Symposium on AI, Robotics, and Vision. 3(1).