Blind Thermodynamic Ontology Discovery from Anonymous Experiments

Before a machine can discover a physical law, it must discover what its measurements are: which observations live on cells, which are intensive or extensive, which sectors are dual, and which distinctions are merely gauge. We introduce physical representation-language discovery, the problem of recovering this hidden ontology directly from anonymous controlled experiments. We give an identifiability theory and constructive polynomial-time procedure that recovers a carrier and differential sequence, measurement types and orientation twist, noninvertible refinement semantics, primal-dual Maxwell diagrams, and the residual equivalences that no permitted experiment can break. The theory turns material nuisance into a commutant, uses refinement to separate quantities from coordinates, and selects physics only after its representation has been recovered. For a certified finite experiment family, we prove an end-to-end two-stage measurement bound and a matching minimax rate in dimension, accuracy, and confidence. Blind Maxwell experiments recover complete primal/relative-dual ontologies on regular and unstructured carriers under jointly corrupted observations; an independent unstructured RLC system demonstrates that the result is not specific to Maxwell. The framework scales to tens of thousands of cells per carrier, while stress audits demonstrate robustness across severe physical regimes - including non-Markovian memory, nonlinearities, nonlocality, and complex constitutive hysteresis. A public FDTD audit demonstrates the emergence of anonymous curl structure from incomplete field data, while characterizing the informational prerequisites for complete recovery. The goal is to move scientific ML from learning laws in a human-supplied language to discovering the language in which laws become expressible, establishing exact theoretical limits on observational identifiability.

Constitutive laws for inelastic materials must satisfy strict thermodynamic admissibility requirements, yet current data-driven approaches sacrifice interpretability, even when formal guarantees are provided by physics-encoded architectures. We propose a symbolic regression framework for the data-driven discovery of dissipation potentials governing the evolution of internal variables within the Generalized Standard Materials (GSM) formalism. Starting from the Clausius--Duhem inequality, we enforce the thermodynamic requirements, convexity and non-negativity, that the dual dissipation potential must satisfy to guarantee non-negative mechanical dissipation. These requirements are formulated in the general subdifferential setting, encompassing rate-dependent (viscoelastic) and viscoplastic dissipative mechanisms, including potentials with genuine elastic domains, within a unified framework. Candidate potentials are generated by a composition-extended convexity-preserving grammar that guarantees thermodynamic admissibility \emph{by construction}. The framework is validated on synthetic datasets spanning Newtonian, power-law, and Bingham viscoplastic ground truths under process and measurement noise, and on experimental oscillatory shear measurements of a synthetic elastomer across multiple strain amplitudes and frequencies, where the discovered potentials reproduce the amplitude-dependent softening of the dynamic moduli and outperform a calibrated linear Zener baseline.

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.