Related papers: Operator-theoretic framework for forecasting nonli…

Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image…

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,…

Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…

Modeling of nonlinear behaviors with physical-based models poses challenges. However, Koopman operator maps the original nonlinear system into an infinite-dimensional linear space to achieve global linearization of the nonlinear system…

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,…

We present a kernel-based stochastic approximation (KBSA) framework for solving contextual stochastic optimization problems with differentiable objective functions. The framework only relies on system output estimates and can be applied to…

Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long…

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing…

Approaches based on Koopman operators have shown great promise in forecasting time series data generated by complex nonlinear dynamical systems (NLDS). Although such approaches are able to capture the latent state representation of a NLDS,…

The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…

In this work, we propose a meta-learning-based Koopman modeling and predictive control approach for nonlinear systems with parametric uncertainties. An adaptive deep meta-learning-based modeling approach, called Meta Adaptive Koopman…

This work presents a hybrid physics-informed and data-driven modeling framework for predictive control of autonomous off-road vehicles operating on deformable terrain. Traditional high-fidelity terramechanics models are often too…

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…

The Koopman Operator (KO) is a mathematical construct that maps nonlinear (state space) dynamics to corresponding linear dynamics in an infinite-dimensional functional space. For practical applications, finite-dimensional approximations can…

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…

When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…

The problem of prediction of behavior of dynamical systems has undergone a paradigm shift in the second half of the 20th century with the discovery of the possibility of chaotic dynamics in simple, physical, dynamical systems for which the…

Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…

Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of…

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…