Fig. 2: Explaining the fidelity of artificial neural networks (ANNs) from the perspective of interpretable machine learning.

a, b Critical regions for estimating El Niño-Southern Oscillation (ENSO) sea surface temperature (SST) amplitude, identified via occlusion sensitivity (shading). The six best-performing ANNs (BEST6) consistently highlight the central and eastern equatorial Pacific (boxes, 5°S-5°N, 160°E-140°W and 120°W-95°W), while the remaining five ANNs (REM5) fail to identify coherent critical regions. c Under a high-emission scenario, critical regions shift eastward as the tropical Pacific warms. Averaged occlusion sensitivity in the eastern box increases with greenhouse warming, indicating a growing influence of eastern Pacific warming on future ENSO SST variability. d, e Observed and simulated SST trends in the two critical regions. Observed SST trends are from three observational datasets, and simulated SST trends are from 11 Coupled Model Intercomparison Project (CMIP) models. Although the observed (La Niña-like) and modeled (El Niño-like) warming patterns appear to be opposite, the differential warming rate between the two critical regions is similar, shown by the faster warming in the east and a weakening zonal SST gradient. These two critical regions are physically recognized as the regions where multiple feedbacks controlling ENSO SST variability occur. The ANN sensitivity to these areas aligns with established ENSO physics.