Related papers: Estimating Koopman operators with sketching to pro…
Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…
This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…
Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…
Mechanistic dynamic process models may be too computationally expensive to be usable as part of a real-time capable predictive controller. We present a method for end-to-end learning of Koopman surrogate models for optimal performance in a…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…
We propose to adopt statistical regression as the projection operator to enable data-driven learning of the operators in the Mori--Zwanzig formalism. We present a principled method to extract the Markov and memory operators for any…
This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
This article considers "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is…
Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…
This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from…
Learning dexterous manipulation skills presents significant challenges due to complex nonlinear dynamics that underlie the interactions between objects and multi-fingered hands. Koopman operators have emerged as a robust method for modeling…
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning…
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…