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Abstract 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. 

Abstract Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.