Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems

TL;DR

This paper introduces HEAP, a hierarchical autoencoder architecture that efficiently models long-term evolution in complex multi-scale physical systems by encoding structures at multiple spatial resolutions, significantly improving prediction accuracy.

Contribution

The paper presents a novel hierarchical autoencoder with a multi-layer embedding approach for better long-term predictions in multi-scale physical systems, outperforming traditional models.

Findings

Multifold improvement in long-term prediction accuracy.

Effective modeling of multi-scale interactions.

Superior performance over ResNet variants in turbulence prediction.

Abstract

We propose a novel efficient architecture for learning long-term evolution in complex multi-scale physical systems which is based on the idea of separation of scales. Structures of various scales that dynamically emerge in the system interact with each other only locally. Structures of similar scale can interact directly when they are in contact and indirectly when they are parts of larger structures that interact directly. This enables modeling a multi-scale system in an efficient way, where interactions between small-scale features that are apart from each other do not need to be modeled. The hierarchical fully-convolutional autoencoder transforms the state of a physical system not just into a single embedding layer, as it is done conventionally, but into a series of embedding layers which encode structures of various scales preserving spatial information at a corresponding resolution level. Shallower layers embed smaller structures on a finer grid, while deeper layers embed larger structures on a coarser grid. The predictor advances all embedding layers in sync. Interactions between features of various scales are modeled using a combination of convolutional operators. We compare the performance of our model to variations of a conventional ResNet architecture in application to the Hasegawa-Wakatani turbulence. A multifold improvement in long-term prediction accuracy was observed for crucial statistical characteristics of this system.