An information-matching approach to optimal experimental design and active learning

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher Information Matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. We demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an Active Learning loop for material science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly active learning in large machine learning models.

Learning dislocation dynamics mobility laws from large-scale MD simulations

The computational method of discrete dislocation dynamics (DDD), used as a coarse-grained model of true atomistic dynamics of lattice dislocations, has become of powerful tool to study metal plasticity arising from the collective behavior of dislocations. As a mesoscale approach, motion of dislocations in the DDD model is prescribed via the mobility law; a function which specifies how dislocation lines should respond to the driving force. However, the development of traditional hand-crafted mobility laws can be a cumbersome task and may involve detrimental simplifications. Here we introduce a machine-learning (ML) framework to streamline the development of data-driven mobility laws which are modeled as graph neural networks (GNN) trained on large-scale Molecular Dynamics (MD) simulations of crystal plasticity. We illustrate our approach on BCC tungsten and demonstrate that our GNN mobility implemented in large-scale DDD simulations accurately reproduces the challenging tension/compression asymmetry observed in ground-truth MD simulations while correctly predicting the flow stress at lower straining rate conditions unseen during training, thereby demonstrating the ability of our method to learn relevant dislocation physics. Our DDD+ML approach opens new promising avenues to improve fidelity of the DDD model and to incorporate more complex dislocation motion behaviors in an automated way, providing a faithful proxy for dislocation dynamics several orders of magnitude faster than ground-truth MD simulations.