CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations

Accurate and concise governing equations are crucial for understanding system dynamics. Recently, data-driven methods such as sparse regression have been employed to automatically uncover governing equations from data, representing a significant shift from traditional first-principles modeling. However, most existing methods focus on scalar equations, limiting their applicability to simple, low-dimensional scenarios, and failing to ensure rotation and reflection invariance without incurring significant computational cost or requiring additional prior knowledge. This paper proposes a Cartesian tensor-based sparse regression (CTSR) technique to accurately and efficiently uncover complex, high-dimensional governing equations while ensuring invariance. Evaluations on two two-dimensional (2D) and two three-dimensional (3D) test cases demonstrate that the proposed method achieves superior accuracy and efficiency compared to the conventional technique.

Highly Efficient Direct Analytics on Semantic-aware Time Series Data Compression

Semantic communication has emerged as a promising paradigm to tackle the challenges of massive growing data traffic and sustainable data communication. It shifts the focus from data fidelity to goal-oriented or task-oriented semantic transmission. While deep learning-based methods are commonly used for semantic encoding and decoding, they struggle with the sequential nature of time series data and high computation cost, particularly in resource-constrained IoT environments. Data compression plays a crucial role in reducing transmission and storage costs, yet traditional data compression methods fall short of the demands of goal-oriented communication systems. In this paper, we propose a novel method for direct analytics on time series data compressed by the SHRINK compression algorithm. Through experimentation using outlier detection as a case study, we show that our method outperforms baselines running on uncompressed data in multiple cases, with merely 1% difference in the worst case. Additionally, it achieves four times lower runtime on average and accesses approximately 10% of the data volume, which enables edge analytics with limited storage and computation power. These results demonstrate that our approach offers reliable, high-speed outlier detection analytics for diverse IoT applications while extracting semantics from time-series data, achieving high compression, and reducing data transmission.