Related papers: Finite Time Lyapunov Exponent Analysis of Model Pr…

Autoregressive learning of time-stepping operators provides an effective approach to data-driven partial differential equation (PDE) simulation, yet for conservation laws, they face a fundamental challenge: learned updates may violate…

We consider several non-local models for traffic flow, including both microscopic ODE models and macroscopic PDE models. The ODE models describe the movement of individual cars, where each driver adjusts the speed according to the road…

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…

Deep learning surrogates for CFD flow-field prediction often rely on large, complex models, which can be slow and fragile when data are noisy or incomplete. We introduce FlowForge, a staged local rollout engine that predicts future flow…

We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…

Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…

In this work, we address the motion planning problem for autonomous vehicles through a new lattice planning approach, called Feedback Enhanced Lattice Planner (FELP). Existing lattice planners have two major limitations, namely the high…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable…

Deep-learning based traffic prediction models require vast amounts of data to learn embedded spatial and temporal dependencies. The inherent privacy and commercial sensitivity of such data has encouraged a shift towards decentralised…

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually…

A pinned-free beam in axial fluid flow, subjected to feedback-based actuation at the pinned end, is investigated. The actuation may be a moment or a prescribed angle and it is proportional to the state (curvature, slope, or displacement) of…

The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steady-state flow in a duct is considered under the condition that the turbulent…

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective…

Ridges of the Finite-Size Lyapunov Exponent (FSLE) field have been used as indicators of hyperbolic Lagrangian Coherent Structures (LCSs). A rigorous mathematical link between the FSLE and LCSs, however, has been missing. Here we prove that…

Traffic flow forecasting aims to predict future traffic flows based on the historical traffic conditions and the road network. It is an important problem in intelligent transportation systems, with a plethora of methods been proposed.…

Spreading of liquid droplets on solid substrates constitutes a classic multiphysics problem with widespread applications ranging from inkjet printing, spray cooling, to biomedical microfluidic systems. Yet, accurate computational fluid…

Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and…

We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…