How can a complex function be approximated using deep learning?

The insurance company I work for has a computationally intensive process to estimate future earnings based on tables of assumptions regarding price and probability of cancelation. I would like to train a model to approximate this process. I have tried a number of models, including xgboost and various configurations of neutral networks. The problem is that even when the model shows good performance on both training and test sets, it doesn't succeed in estimating the effect of a change in the assumptions that are inputted. For example, if the probability of cancelation goes up, the value of the future earnings should decrease - but not in a simple linear fashion. Understanding the sensitivity of the calculations to various assumptions is one of the goals of the proxy model. What is the best way forward? Is this even a reasonable problem to try to tackle with machine learning?