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

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…

The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…

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…

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we…

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a…

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid…

Phase-field models have been widely used to investigate the phase transformation phenomena. However, it is difficult to solve the problems numerically due to their strong nonlinearities and higher-order terms. This work is devoted to…

We study numerical algorithms to solve a specific Partial Differential Equation (PDE), namely the Stefan problem, using Physics Informed Neural Networks (PINNs). This problem describes the heat propagation in a liquid-solid phase change…

Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of…

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function…

Time series forecasting plays a vital role across scientific, industrial, and environmental domains, especially when dealing with high-dimensional and nonlinear systems. While Transformer-based models have recently achieved state-of-the-art…

Optimal Power Flow (OPF) is a fundamental problem in power systems. It is computationally challenging and a recent line of research has proposed the use of Deep Neural Networks (DNNs) to find OPF approximations at vastly reduced runtimes…

This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…

This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…

We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…

This study presents an innovative approach to Model Predictive Control (MPC) by leveraging the powerful combination of Koopman theory and Deep Reinforcement Learning (DRL). By transforming nonlinear dynamical systems into a…

We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

This paper proposes a new method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the…