Validation and low-cost schemes’ performance on key and major molecules. The plots illustrate the performance of our method on key molecules for HD 209458b (a) and HD 189733b (b). Left: molar fractions of key molecules as a function of pressure in the atmosphere. The full V20 model is represented by a solid line, DARWEN’s validation scheme by a dashed-dotted line, low-cost schemes by a dashed line, and the reduced scheme (R20) by a dotted line. Right: maximal percentage changes in the molar fractions of the key molecules compared to the full model. The full model’s line is not shown because it serves as the reference model. Lines close to zero indicate that the predictions are nearly identical to those of the full model for that molecule. We only show changes bigger than 1%.