Learning Optimal Forms of Constitutive Relations Characterizing Ion Intercalation from Data in Mathematical Models of Lithium-Ion Batteries
Bibliographic record
Abstract
Most mathematical models of the transport of charged species in battery electrodes require a constitutive relation describing the intercalation of lithium, which is a reversible process taking place on the interface between the electrolyte and the active particle. The most commonly used model is the Butler–Volmer relation, which gives the current density as a product of two expressions: one expression, the exchange current, depends on lithium concentration only, whereas the other expression depends on both lithium concentration and overpotential. We consider an inverse problem where an optimal form of the exchange current density is inferred, subject to minimum assumptions, from experimental voltage curves. This inverse problem is recast as an optimization problem in which the least-squares error functional is minimized with a suitable Sobolev gradient approach. The proposed method is thoroughly validated, and we also quantify the reconstruction uncertainty. Finally, we identify the universal features in the constitutive relations inferred from the data obtained during charging and discharging at different C-rates and discuss how these features differ from the behavior predicted by the standard Butler–Volmer relation. We also identify possible limitations of the proposed approach, mostly related to uncertainties inherent in the material properties assumed to be known in the inverse problem. Our approach can be used to systematically improve the accuracy of mathematical models employed to describe Li-ion batteries as well as other systems relying on the Butler–Volmer relation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".