Title : Target-driven inverse design of battery cathodes via constraint-prioritised cross-entropy search

The discovery of high-performing battery cathodes is constrained by an enormous and sparsely sampled composition space, in which candidate materials must satisfy several coupled chemical and electrochemical requirements. Conventional machine-learning workflows can rapidly predict the properties of proposed materials, but they do not directly solve the inverse problem of generating chemically meaningful compositions for specified performance targets. This work introduces a physics-aware, chemically type-conditioned cross-entropy method (CEM) for target-driven cathode inverse design.

The framework searches oxide-fluoride, phosphate, and sulphate composition spaces across target voltages from 2.5 to 4.5 V. Structured chemical blueprints specify the mobile ion, redox-active elements, spectator cations, framework family, and stoichiometric coefficients. A deterministic feasibility solver converts these blueprints into charge-balanced formulas and limits theoretical capacity according to both mobile-ion transfer and the accessible redox reservoir. Composition-based surrogate models trained on density-functional-theory data predict voltage, redox-limited capacity, formation-energy-related stability, relative volume change, band gap, and predictive uncertainty. Rather than combining these criteria through a manually weighted scalar objective, candidates are ranked using a constraint-prioritised lexicographic hierarchy, ensuring that favourable lower-priority properties cannot compensate for failure on essential feasibility constraints.

The structured blueprint space contains approximately 4.28 × 10^10 possible sampled compositions before charge-balance filtering, of which about 5.5 × 10^9 satisfy the formal charge-balance and redox-feasibility rules. Across three independent seeds, the chemically type-conditioned CEM identified 4,315 ± 42 unique candidates satisfying all imposed constraints. It achieved sample-efficiency gains of 38.6-292 times relative to uniform random search, with a mean gain of 174.5 times, while retaining a wall-clock advantage after accounting for optimisation overhead. The final archive contained oxide-fluoride and phosphate candidates, with enrichment in selected mobile-ion/framework combinations and vanadium-based redox chemistry.

These findings demonstrate that embedding chemical feasibility and explicit constraint priorities within population-based search can efficiently identify diverse candidate cathode compositions in rare, multi-constraint regions. The generated materials remain candidates for subsequent structure generation, higher-fidelity calculations, synthesis assessment, and experimental validation.

Ali Badakhshan is a PhD researcher in the Department of Engineering at Durham University. His research focuses on machine-learning-driven materials discovery, inverse design, and battery cathode development. He combines physics-aware machine learning, optimisation, and computational materials science to identify chemically feasible candidate materials under coupled electrochemical and physical constraints.