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Wang et al. J. Mater. Inf. 2026, 6, 1 Page 7 of 9

stability or kinetic formation barriers. For instance, some compositions may satisfy geometric T f criteria yet
remain unrealizable due to unfavorable formation energies. Similarly, metastable phases with promising
properties might be overlooked because their synthesis requires non-equilibrium conditions that geometric
parameters cannot predict.

Solution: A closed-loop diffusion framework can be developed to explore thermodynamically and kinetically
stable compositions guided by geometric constraints. The diffusion model is conditioned on geometric
priors and thermodynamic parameters (temperature and pressure), enabling the generation of compositions
with structural feasibility. These candidates are filtered using AIMD simulations to assess kinetic stability.
Feedback from AIMD trajectories, such as mean square displacements, can be incorporated to refine the
diffusion model via reinforcement or reweighting, allowing the generation process to gradually shift toward
kinetically robust chemical space. This iterative scheme bridges composition generation and atomistic
validation, enabling efficient discovery of stable materials.

CONCLUSION
Recent progress in both T f and AI has laid a solid groundwork for evaluating materials stability. Nevertheless,
key obstacles persist, such as the lack of universally applicable and accurate tolerance descriptors. Addressing
these limitations will require integrated strategies such as data-driven estimation of effective ionic radii, and
the deployment of closed-loop AI models under realistic constraints. Furthermore, with the rise of non-ideal,
disordered, and dynamically evolving systems, extending T f to geodesic/probabilistic metrics open new
frontiers for predictive modeling in 2D materials and flexible framework materials, where atomic deviations
follow non-Euclidean pathways. With the continued convergence of AI methodologies, we foresee a
transformative shift: T f-informed AI frameworks will unlock new opportunities in diverse domains including
energy storage, sustainable systems, and optoelectronics, paving the way toward accelerated discovery and
design of stable, high-performance materials.

DECLARATIONS
Acknowledgments
The authors acknowledge members of the PEESE group for discussions related to the preparation of this
work.

Authors’ contributions
Conceptualization, methodology, visualization, data curation, writing - original draft: Wang, Z.
Conceptualization, methodology, supervision, resources, writing - original draft, review and editing: You, F.

Availability of data and materials
Not applicable.

Financial support and sponsorship
This project is partially supported by the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship, a
program of Schmidt Sciences, LLC.

Conflicts of interest
Both authors declared that there are no conflicts of interest.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.