Disentangling complex data to its latent factors of variation is a fundamental task in
representation learning. Existing work on sequential disentanglement mostly provides two …

Fluctuating velocity plays an essential role in tornadic winds and the induced transient
loads, while its characteristics are rarely considered in existing tornado models. Based on …

Training of neural networks is a computationally intensive task. The significance of
understanding and modeling the training dynamics is growing as increasingly larger …

In this work we analyze the Total Variation (TV) flow applied to one dimensional signals. We
formulate a relation between Dynamic Mode Decomposition (DMD), a dimensionality …

This work presents the general form solution of Koopman Partial Differential Equation and
shows that its functional dimensionality is finite. The dimensionality is as the dimensionality …

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is
essential for their analysis and modeling. In this Element the authors attempt to provide a …

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine
learning. Existing work provides limited analysis or it depends on local theories, such as …

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is
essential for their analysis and modeling. In this work, we attempt to provide a consistent …

Research on Koopman operator theory has focused on three key areas for several decades:
the mathematical structure of the Koopman eigenfunction space, the basis of this space, and …

This work binds the existence of Koopman Eigenfunction (KEF), the geometric of the
dynamics, and the validity of Dynamic Mode Decomposition (DMD) to one coherent theory …