The availability of tera-byte scale experiment data calls for AI driven approaches which automatically discover scientific models from data. Nonetheless, significant challenges present in AI-driven scientific discovery: (i) The annotation of large scale datasets requires fundamental re-thinking in developing scalable crowdsourcing tools. (ii) The learning of scientific models from data calls for innovations beyond black-box neural nets. (iii) Novel visualization & diagnosis tools are needed for the collaboration of experimental and theoretical physicists, and computer scientists. We present Phase-Field-Lab platform for end-to-end phase field model discovery, which automatically discovers phase field physics models from experiment data, integrating experimentation, crowdsourcing, simulation and learning. Phase-Field-Lab combines (i) a streamlined annotation tool which reduces the annotation time (by ~50-75%), while increasing annotation accuracy compared to baseline; (ii) an end-to-end neural model which automatically learns phase field models from data by embedding phase field simulation and existing domain knowledge into learning; and (iii) novel interfaces and visualizations to integrate our platform into the scientific discovery cycle of domain scientists. Our platform is deployed in the analysis of nano-structure evolution in materials under extreme conditions (high temperature and irradiation). Our approach reveals new properties of nano-void defects, which otherwise cannot be detected via manual analysis.

Learning physics models in the form of Partial Differential Equations (PDEs) is carried out through back-propagation to match the simulations of the physics model with experimental observations. Nevertheless, such matching involves computation over billions of elements, presenting a significant computational overhead. We notice many PDEs in real world problems are sparse and decomposable, where the temporal updates and the spatial features are sparsely concentrated on small interface regions. We propose RAPID-PDE, an algorithm to expedite the learning of sparse and decomposable PDEs. Our RAPID-PDE first uses random projection to compress the high dimensional sparse updates and features into low dimensional representations and then use these compressed signals during learning. Crucially, such a conversion is only carried out once prior to learning and the entire learning process is conducted in the compressed space. Theoretically, we derive a constant factor approximation between the projected loss function and the original one with logarithmic number of projected dimensions. Empirically, we demonstrate RAPID-PDE with data compressed to 0.05% of its original size learns similar models compared with uncompressed algorithms in learning a set of phase-field models which govern the spatial-temporal dynamics of nano-scale structures in metallic materials.