Related papers: Efficient Dynamics Modeling in Interactive Environ…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal…

Forecasting physical systems over long horizons from irregularly sampled observations demands models that are stable, computationally efficient, and free of fixed-timestep assumptions. We address this with a continuous-time Koopman…

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…

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In…

This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization…

Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…

Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current…

Imitation learning (IL) enables efficient skill acquisition from demonstrations but often struggles with long-horizon tasks and high-precision control due to compounding errors. Residual policy learning offers a promising, model-agnostic…

We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However,…

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…

This paper presents an examination of State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Through experiments with datasets generated under different…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…

We propose a novel framework for safe navigation in dynamic environments by integrating Koopman operator theory with conformal prediction. Our approach leverages data-driven Koopman approximation to learn nonlinear dynamics and employs…

The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…

Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…