Streaming Compression of Scientific Data via weak-SINDy

In this paper a streaming weak-SINDy algorithm is developed specifically for compressing streaming scientific data. The production of scientific data, either via simulation or experiments, is undergoing an stage of exponential growth, which makes data compression important and often necessary for storing and utilizing large scientific data sets. As opposed to classical ``offline" compression algorithms that perform compression on a readily available data set, streaming compression algorithms compress data ``online" while the data generated from simulation or experiments is still flowing through the system. This feature makes streaming compression algorithms well-suited for scientific data compression, where storing the full data set offline is often infeasible. This work proposes a new streaming compression algorithm, streaming weak-SINDy, which takes advantage of the underlying data characteristics during compression. The streaming weak-SINDy algorithm constructs feature matrices and target vectors in the online stage via a streaming integration method in a memory efficient manner. The feature matrices and target vectors are then used in the offline stage to build a model through a regression process that aims to recover equations that govern the evolution of the data. For compressing high-dimensional streaming data, we adopt a streaming proper orthogonal decomposition (POD) process to reduce the data dimension and then use the streaming weak-SINDy algorithm to compress the temporal data of the POD expansion. We propose modifications to the streaming weak-SINDy algorithm to accommodate the dynamically updated POD basis. By combining the built model from the streaming weak-SINDy algorithm and a small amount of data samples, the full data flow could be reconstructed accurately at a low memory cost, as shown in the numerical tests.

Fault Detection via Occupation Kernel Principal Component Analysis

The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this paper, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.