Spatio-temporal Fourier Transformer (StFT) for Long-term Dynamics Prediction

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales and the interplay of diverse physical processes. Neural operators have emerged as promising models for predicting such dynamics due to their flexibility and computational efficiency. However, they often fail to effectively capture multi-scale interactions or quantify the uncertainties inherent in the predictions. These limitations lead to rapid error accumulation, particularly in long-term forecasting of systems characterized by complex and coupled dynamics. To address these challenges, we propose a spatio-temporal Fourier transformer (StFT), in which each transformer block is designed to learn dynamics at a specific scale. By leveraging a structured hierarchy of StFT blocks, the model explicitly captures dynamics across both macro- and micro- spatial scales. Furthermore, a generative residual correction mechanism is integrated to estimate and mitigate predictive uncertainties, enhancing both the accuracy and reliability of long-term forecasts. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.

FTL: Transfer Learning Nonlinear Plasma Dynamic Transitions in Low Dimensional Embeddings via Deep Neural Networks

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma physics, opens a unique opportunity for building efficient models to identify plasma instabilities for real-time control. Our Fusion Transfer Learning (FTL) model demonstrates success in reconstructing nonlinear kink mode structures by learning from a limited amount of nonlinear simulation data. The knowledge transfer process leverages a pre-trained neural encoder-decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL's capacity to capture transitional behaviors and dynamical features in plasma dynamics -- a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics (MHD) modes.

Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation

Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle the sizes of modern high-dimensional data sets (often on the order of terabytes), and assume Gaussian samples. To address these deficiencies, we introduce HP-CONCORD, a highly scalable optimization method for estimating a sparse inverse covariance matrix based on a regularized pseudolikelihood framework, without assuming Gaussianity. Our parallel proximal gradient method uses a novel communication-avoiding linear algebra algorithm and runs across a multi-node cluster with up to 1k nodes (24k cores), achieving parallel scalability on problems with up to ~819 billion parameters (1.28 million dimensions); even on a single node, HP-CONCORD demonstrates scalability, outperforming a state-of-the-art method. We also use HP-CONCORD to estimate the underlying dependency structure of the brain from fMRI data, and use the result to identify functional regions automatically. The results show good agreement with a clustering from the neuroscience literature.