Related papers: Using "AI Poincare" to analyze non-linear integrab…

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of…

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical…

We propose a method using supervised machine learning to estimate velocity fields from particle images having missing regions due to experimental limitations. As a first example, a velocity field around a square cylinder at Reynolds number…

We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a piecewise dynamical system with piecewise defined conserved…

We demonstrate a microfabricated optomechanical accelerometer that is capable of percent-level accuracy without external calibration. To achieve this capability, we use a mechanical model of the device behavior that can be characterized by…

Inspection of insulators is important to ensure reliable operation of the power system. Deep learning is being increasingly exploited to automate the inspection process by leveraging object detection models to analyse aerial images captured…

This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…

Artificial intelligence and machine learning is enhancing electric grids by offering data analysis tools that can be used to operate the power grid more reliably. However, the complex nonlinear dynamics, particularly when coupled with…

This paper presents a novel approach for optical flow control of Micro Air Vehicles (MAVs). The task is challenging due to the nonlinearity of optical flow observables. Our proposed Incremental Nonlinear Dynamic Inversion (INDI) control…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

We present the first experimental validation of the Deep Lie Map Network (DLMN) approach for recovering both linear and non-linear optics in a synchrotron. The DLMN facilitates the construction of a detailed accelerator model by integrating…

We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive)…

A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…

Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there…

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

We propose a real-time dynamic LiDAR odometry pipeline for mobile robots in Urban Search and Rescue (USAR) scenarios. Existing approaches to dynamic object detection often rely on pretrained learned networks or computationally expensive…

Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…

Recently, the study of integrable Hamiltonian systems has led to nonlinear accelerator lattices with one or two transverse invariants and wide stable tune spreads. These lattices may drastically improve the performance of high-intensity…

We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…