Related papers: Koopman Theory-Inspired Method for Learning Time A…

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…

Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural…

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical…

Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand,…

Extended Kalman Filtering (EKF) can be used to propagate and quantify input uncertainty through a Deep Neural Network (DNN) assuming mild hypotheses on the input distribution. This methodology yields results comparable to existing methods…

Fourier Neural Operators (FNOs) have emerged as promising surrogates for partial differential equation solvers. In this work, we extensively tested FNOs on a variety of systems with non-linear and non-stationary properties, using a wide…

We address the problem of learning a neural Koopman operator model that provides dissipativity guarantees for an unknown nonlinear dynamical system that is known to be dissipative. We propose a two-stage approach. First, we learn an…

We have trained a fully convolutional spatio-temporal model for fast and accurate representation learning in the challenging exemplar application area of fusion energy plasma science. The onset of major disruptions is a critically important…

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…

This paper investigates the temporal evolution of high-speed compressible fluids in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

This paper demonstrates the benefits of imposing stability on data-driven Koopman operators. The data-driven identification of stable Koopman operators (DISKO) is implemented using an algorithm \cite{mamakoukas_stableLDS2020} that computes…

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which is resulted from the Koopman operator and deep neural networks. Analysis of the…

Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while…

Solving partial differential equations (PDEs) efficiently is essential for analyzing complex physical systems. Recent advancements in leveraging deep learning for solving PDE have shown significant promise. However, machine learning…

This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for…

In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…