LSH-SMILE: Locality Sensitive Hashing Accelerated Simulation and Learning

The advancement of deep neural networks over the last decade has enabled progress in scientific knowledge discovery in the form of learning Partial Differential Equations (PDEs) directly from experiment data. Nevertheless, forward simulation and backward learning of large-scale dynamic systems require handling billions of mutually interacting elements, the scale of which overwhelms current computing architectures. We propose Locality Sensitive Hashing Accelerated Simulation and Learning (LSH-SMILE), a unified framework to scale up both forward simulation and backward learning of physics systems. LSH-SMILE takes advantage of (i) the locality of PDE updates, (ii) similar temporal dynamics shared by multiple elements. LSH-SMILE hashes elements with similar dynamics into a single hash bucket and handles their updates at once.