A thermodynamically-consistent data-analytics framework that naturally incorporates the free energy contributions of thermochemical, structural, mechanical, and electrical fields is developed to infer equilibrium state functions related phase stability. The state function formulation is first presented to describe the space charge layer and their effect on transport properties of polycrystalline ionic ceramics, enabling the design of microstructure under different external fields such as temperature, stress, electrical, magnetic, and chemical stimuli. The formulation is also shown to reproduce ideal and strong solution models while simultaneously demonstrating the need for physics-based model selection, as millivolt adjustments to the interfacial voltage in gadolinium-doped ceria decreases the cumulative error associated to experimental electrical conductivity values for all models, regardless of their relevance to the material system. In order to solve this need, the physical phenomena underlying phase stability were incorporated into thermodynamic modeling by creating practical distance metrics based on model parameters and invariant reaction to create a holistic view of phase diagram (PD) spaces rather than a material-centric one. PD spaces are then visualized and systematically explored without bias to infer model limitations and guide the integration of machine learning methods to model optimizations.

 

Building on this foundation, a physics-informed machine learning framework is developed to infer free energy models directly from experimental- and ab initio-determined PDs through an efficient explore-exploit k-nearest neighbor strategy, achieving 1000X to 100,000X faster than currently available approaches. The developed methodology is validated with the most widely used thermodynamic models – the regular solution, Redlich-Kister, and sublattice formalisms – to recover the properties of materials for lithium-ion battery applications in a matter of hours, reconstructing without human bias, well-established CALPHAD formulations while identifying previously missed stable and metastable phases and associated properties. The framework culminates with a scalable, thermodynamically-consistent data-analytics pipeline that infers material state functions directly from an image of a PD, using a human-in-the-loop machine learning architecture centered around residual convolutional neural networks that have been trained to enforce state-function uniqueness through tailored physics-informed loss functions. Automated image extraction, uncertainty-aware perturbation, and physics-based verification during preprocessing combined with stochastic optimization, model selection and iterative physics-based validation during postprocessing results in near real time identification and optimization of accurate CALPHAD-compatible free energy models for the generality of material systems.

 

The framework is shown to reliably reproduce or exceed the accuracy of published CALPHAD models across 52 metallic, ceramic, and polymer systems. Its predictive fidelity, even with reduced parameterization, reveals when additional thermodynamic complexity is necessary and when it can be safely avoided, mitigating overfitting and reducing human bias. Across all tested systems, the entire process achieves convergence from minutes to 3.5 hours on a single standalone GPU, enabling rapid iterative refinement on the physical understanding of material properties, while avoiding numerical issues. Collectively, the methodologies presented herein demonstrate a data-driven paradigm for thermodynamic modeling, enabling rapid, scalable, and interpretable discovery and design of materials for the next generation of materials.