Machine learning discovers hidden thermodynamic laws from mixed data
Blind Thermodynamic Ontology Discovery from Anonymous Experiments
Machine LearningArtificial Intelligence
Summary
Sometimes machines get data that mixes up important scientific measurements, making it hard to understand real physical patterns. This paper shows how to unravel those hidden measurements from experiments where the data is scrambled without labels. The authors developed a fast method to find the true physical quantities and check the laws they follow, even when experiments only give mixed signals. Their approach works well with both simulated models and real fluid data, separating real states from noise.
What this means in practice
- •For industrial physicists: Automatically extract underlying thermodynamic variables and relations from complex experimental sensor data without prior labeling.
- •For chemical engineers: Improve interpretation of thermodynamic measurements from experiments with mixed or anonymous sensor channels in process development and optimization.
Authors
Linzhe Zhang, Changming Xu
Abstract
Before a machine learning model can learn a thermodynamic equation of state, it must discover what its measurements represent: which channels scale with system size, which are intensive conjugates, how sectors pair through contact, and which potential governs stability. When sensors expose only an unknown linear mixture of extensive states and intensive responses, passive observations cannot disentangle physical quantities from coordinate artifacts. We formulate the problem of discovering this hidden thermodynamic ontology directly from anonymous controlled experiments. We present an operational identifiability theory and a constructive polynomial-time algorithm that extracts extensive and intensive scaling sectors from replication contrasts, recovers their dual cotangent pairing from thermal contact and reciprocity, verifies a globally admissible concave potential via discrete cyclic concavity, and determines an invariant matroid of reservoir ensembles. We prove that the residual observational equivalence is strictly (x, lambda) ~ (A x, a A^{-T} lambda + beta), establishing the sharp observational limit that no permitted experiment can break. Blind evaluations on van der Waals fluids and Curie-Weiss magnets confirm robust recovery under ill-conditioned mixing, correctly resolving anonymous Maxwell tie-lines while rejecting non-equilibrium continuations. External validation across six real fluids from the NIST WebBook demonstrates that operational ontology discovery transfers across real physical substances without coordinate leakage.