Deep learning (DL) is revolutionizing the scientific computing community. To reduce the data gap caused by usually expensive simulations or experimentation, active learning has been identified as a promising solution for the scientific computing community. However, the deep active learning (DAL) literature is currently dominated by image classification problems and pool-based methods, which are not directly transferrable to scientific computing problems, dominated by regression problems with no pre-defined 'pool' of unlabeled data. Here for the first time, we investigate the robustness of DAL methods for scientific computing problems using ten state-of-the-art DAL methods and eight benchmark problems. We show that, to our surprise, the majority of the DAL methods are not robust even compared to random sampling when the ideal pool size is unknown. We further analyze the effectiveness and robustness of DAL methods and suggest that diversity is necessary for a robust DAL for scientific computing problems.

In the past decade, deep active learning (DAL) has heavily focused upon classification problems, or problems that have some 'valid' data manifolds, such as natural languages or images. As a result, existing DAL methods are not applicable to a wide variety of important problems -- such as many scientific computing problems -- that involve regression on relatively unstructured input spaces. In this work we propose the first DAL query-synthesis approach for regression problems. We frame query synthesis as an inverse problem and use the recently-proposed neural-adjoint (NA) solver to efficiently find points in the continuous input domain that optimize the query-by-committee (QBC) criterion. Crucially, the resulting NA-QBC approach removes the one sensitive hyperparameter of the classical QBC active learning approach - the "pool size"- making NA-QBC effectively hyperparameter free. This is significant because DAL methods can be detrimental, even compared to random sampling, if the wrong hyperparameters are chosen. We evaluate Random, QBC and NA-QBC sampling strategies on four regression problems, including two contemporary scientific computing problems. We find that NA-QBC achieves better average performance than random sampling on every benchmark problem, while QBC can be detrimental if the wrong hyperparameters are chosen.

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning have arisen generating impressive results. We conceptualize these models as different schemes for efficiently, but randomly, exploring the space of possible inverse solutions. As a result, the accuracy of each approach should be evaluated as a function of time rather than a single estimated solution, as is often done now. Using this metric, we compare several state-of-the-art inverse modeling approaches on four benchmark tasks: two existing tasks, one simple task for visualization and one new task from metamaterial design. Finally, inspired by our conception of the inverse problem, we explore a solution that uses a deep learning model to approximate the forward model, and then uses backpropagation to search for good inverse solutions. This approach, termed the neural-adjoint, achieves the best performance in many scenarios.