Iterative surrogate model optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks

We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained problems. This algorithm is based on deep neural networks its key feature the selection training data through feedback loop between any underlying standard algorithm. Under suitable hypotheses, we show that resulting optimizers converge exponentially fast (and with decaying variance), respect to increasing number samples. Numerical examples optimal control, parameter identification shape problems PDEs are provided validate proposed theory illustrate ISMO significantly outperforms network