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This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Most neural network pruning methods, such as filter-level and layer-level prunings, prune the network model along one dimension (depth, width, or resolution) solely to meet a computational budget. However, such a pruning policy often leads…

This work builds on the models and concepts presented in part 1 to learn approximate dictionary representations of Koopman operators from data. Part I of this paper presented a methodology for arguing the subspace invariance of a Koopman…

Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…

This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space $(X,d_X)$. Approximations are constructed in terms…

This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an…

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on…

Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for…

In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is…

Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…

State Space Models (SSMs) have the advantage of keeping linear computational complexity compared to attention modules in transformers, and have been applied to vision tasks as a new type of powerful vision foundation model. Inspired by the…

For the class of continuous, measure-preserving automorphisms on compact metric spaces, a procedure is proposed for constructing a sequence of finite-dimensional approximations to the associated Koopman operator on a Hilbert space. These…