The proposal outlined five key approaches, each novel in itself, but their combination in TEC1p led to a true breakthrough:
1) Ab initio theory of TC (advanced density-functional theory, seamlessly linked to size- and time-converged statistical mechanics).
2) Ab initio theory of EC (advanced density-functional theory, seamlessly linked to size- and time-converged statistical mechanics).
3) Compressed sensing to identify a set of physical parameters that describe the TC and EC behavior and to derive predictive equations that work for all materials.
4) Active learning to build a systematic big-data database of materials, their TCs and ECs.
5) Subgroup discovery to recognize trends and anomalies in the big data, enhance the active learning, and elucidate the underlying physical mechanisms.
All proposal objectives were met, with some methods significantly refined during the project, and several new, important, and unexpected concepts and methods were developed.
Items 1 & 2: New computational methods for thermal (TC) and electrical conductivity (EC) were developed using Green-Kubo and Kubo-Greenwood theories, validated on multiple materials. In particular, we studied strongly anharmonic materials for which previous theories break down.
Item 3: Existing machine-learning methods showed instabilities and unreliable descriptions. This led to the development of SISSO, a breakthrough method rapidly adopted by the community. We also pioneered AI-derived materials property maps, a novel concept for exploring diverse materials (Figs. 1 and 2).
Item 4: Active learning requires reliable uncertainty estimates, but standard ensemble-methods proved unreliable. Our work on trustworthy AI addresses this urgent challenge, with still ongoing and needed refinements.
Subgroup discovery was advanced via Pareto analysis and SISSO integration. (item 5)
Exploitation & Dissemination:
The ERC TEC1p work gained rapid traction as, for example reflected that its publications attracted more than 6,000 citations, so far. Researchers of the group were also invited to numerous international conferences to present the ERC-TEC1p work in invited, keynote and plenary talks. Last but not least, 3 ERC-TEC1p co-workers are now professors in Germany, the USA, and Japan.
The σ_A parameter, a new and urgently needed metric for material anharmonicity, is widely adopted.
The advancements of the efficiency of DFT-hybrid calculations and the demonstration for 30,000 atoms represents another breakthrough that was not expected when the proposal was written.
We also organized hands-on webinars on the ERC-TEC1p developed methods, in particular TC, EC, and SISSO. At an upcoming international workshop in Shanghai one full day is devoted to the ERC-TEC1p developed TC and EC methods, and another day to AI-driven workflows, which is mostly the ERC-TEC1p developed SISSO method.
All these developments are highly interesting to industry, e.g. pharmaceutical, chemistry, lighting/optoelectronics, semiconductors, ceramics and glass, steel. Bringing these ERC-TEC1p developed concepts to the level of “commercial readiness” is still a big step, and we submitted an “ERC Proof of Concept” proposal in order to reach this level, together with colleagues from the mentioned industries.
