Data-driven approach to parameterize <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>SCAN</mml:mi><mml:mo>+</mml:mo><mml:mi>U</mml:mi></mml:math> for an accurate description of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>3</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math> transition metal oxide thermochemistry

Semilocal density-functional theory (DFT) methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description molecular oxygen and large self-interaction error in materials with strongly localized electronic orbitals. Empirical semiempirical corrections based on $\mathrm{DFT}+U$ method can reduce these errors, but parameterization validation correction terms remains on-going challenge. We develop a systematic methodology to determine parameters statistically assess results considering interlinked thermochemical data across set transition metal compounds. consider three interconnected levels terms: (1) constant binding correction, (2) Hubbard-$U$ (3) $\mathrm{DFT}/\mathrm{DFT}+U$ compatibility correction. The is expressed as unified optimization problem. demonstrate this approach $3d$ oxides, target binary ternary oxides. With total 37 measured formation enthalpies taken from literature, dataset augmented reaction energies 1710 unique reactions were derived enumeration. To ensure balanced available data, grouped their similarity using clustering suitably weighted. validated leave-one-out cross (CV), standard technique statistical models. apply constrained appropriately normed (SCAN) density functional. Based CV score, (ternary) oxide reduced 40% (75%) 0.10 (0.03) eV/atom. A simplified scheme does not involve $\mathrm{SCAN}/\mathrm{SCAN}+U$ still achieves reduction 30% (25%). tools demonstrated here be applied other classes or parameterize optimize performance physical properties.