Theoretical predictions and simulations from first principles are a crucial ingredient of LHC analyses. The upcoming LHC runs require a significant improvement of these simulations to match the precision required to identify hints to physics beyond the Standard Model in the data. A recent technical development which could play a key role in achieving this task is machine learning. We propose to study potential benefits of deep regression and generative networks in 1-loop and 2-loop calculations for the LHC, specifically Higgs production in association with hard jets. Given that numerical integrations are often the bottleneck in these calculations we aim to overcome this by using modern machine learning techniques.