This paper focuses on active learning methods for training neural networks from synthetic input samples that can be generated on demand. This includes Physics Informed Neural Networks (PINNs), simulation-based inference, deep surrogates and deep reinforcement learning. An adaptive process observes the training progress and steers the data generation with the goal of speeding up and increasing the quality of training. We propose a novel adaptive sampling method that concentrates samples close to the areas showing high loss values. Compared to the state-of-the-art R3 sampling our algorithm converges to a validation loss of 0.5 in 6000 iterations, while it takes 25000 iterations to reach a loss of 0.7 for the R3 algorithm when training a PINN with the Allen Cahn equation.