You can try the 'traditional' correlation methods like Pearson, or Spearman's rank correlation for nonlinear relationships. As Arijit mentioned, ML regressions, decision trees, or ANNs (like in the paper provided), can give you deeper insights. For instance, I have see some interesting applications with Random Forest or Support Vector Machines for capturing complex NDVI-meteorological/hydrological interactions.
But your goal, and how deep you want to delve into this, as well as the nature of your data (quality, linearity, distribution), and the validation results you get from each test you will try, will guide you to chose th most appropriate method.
Apart from the good answers posted, a good starting point is to map your data (e.g., in QGIS) and check visually for areas of possible correlations (either positive or negative). Then try to create scatter plots between your response variable and the predictors you think you are going to use in your regression. After that try to create some bar plots or box plots of your data to get a sense of their distributions.
This exploratory analysis can guide you to which algorithm you might want to use. For example, if your data are skewed (but not heavily) then XGBoost might be a good solution. Or, if there extreme values GWR (or some of its variations) might help you.
But the algorithm you will choose depends on your data, so it's always good to know them.