Clustering analysis of sequence data continues to address many applications in engineering design, aided with the rapid growth of machine learning in applied science. This paper presents an unsupervised machine learning algorithm to extract defining characteristics of earthquake ground‐motion spectra, also called latent features, to aid in ground‐motion selection (GMS). In this context, a latent feature is a low‐dimensional machine‐discovered spectral characteristic learned through nonlinear relationships of a neural network autoencoder. Machine discovered latent features can be combined with traditionally defined intensity measures and clustering can be performed to select a representative subgroup from a large ground‐motion suite. The objective of efficient GMS is to choose characteristic records representative of what the structure will probabilistically experience in its lifetime. Three examples are presented to validate this approach, including the use of synthetic and field recorded ground‐motion datasets. The presented deep embedding clustering of ground‐motion spectra has three main advantages: (1) defining characteristics that represent the sparse spectral content of ground motions are discovered efficiently through training of the autoencoder, (2) domain knowledge is incorporated into the machine learning framework with conditional variables in the deep embedding scheme, and (3) the method results in a ground‐motion subgroup that is more representative of the original ground‐motion suite compared to traditional GMS techniques.

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.