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Bioprocesses are often characterised by nonlinear and uncertain dynamics, posing particular challenges for model predictive control (MPC) algorithms due to their computational demands when applied to nonlinear systems. Recent advances in…
Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem,…
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…
Periodic dynamical systems, distinguished by their repetitive behavior over time, are prevalent across various engineering disciplines. In numerous applications, particularly within industrial contexts, the implementation of model…
The rapidly growing use of lithium-ion batteries across various industries highlights the pressing issue of optimal charging control, as charging plays a crucial role in the health, safety and life of batteries. The literature increasingly…
This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
Advanced autonomous driving systems require accurate vehicle dynamics modeling. However, identifying a precise dynamics model remains challenging due to strong nonlinearities and the coupled longitudinal and lateral dynamic characteristics.…
Reinforcement learning in partially observed Markov decision processes (POMDPs) faces two challenges. (i) It often takes the full history to predict the future, which induces a sample complexity that scales exponentially with the horizon.…
Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…
The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems. Estimators such as principal component regression (PCR) or reduced rank regression (RRR) in kernel…
The emergence of large language models (LLMs) like GPT-4 has revolutionized natural language processing (NLP), enabling diverse, complex tasks. However, extensive token counts lead to high computational and financial burdens. To address…
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is linear and encompasses full information on the (expected…
Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…
We propose a new quantum dynamics method called the effective potential analytic continuation (EPAC) to calculate the real time quantum correlation functions at finite temperature. The method is based on the effective action formalism which…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
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…
Accurate exploration of protein conformational ensembles is essential for uncovering function but remains hard because molecular-dynamics (MD) simulations suffer from high computational costs and energy-barrier trapping. This paper presents…
Markov Decision Processes (MDPs) offer a fairly generic and powerful framework to discuss the notion of optimal policies for dynamic systems, in particular when the dynamics are stochastic. However, computing the optimal policy of an MDP…