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The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…

A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

Equivariant neural networks require explicit knowledge of the symmetry group. Automatic symmetry discovery methods aim to relax this constraint and learn invariance and equivariance from data. However, existing symmetry discovery methods…

Detecting Internet routing instability is a critical yet challenging task, particularly when relying solely on endpoint active measurements. This study introduces TRACE, a MachineLearning (ML)pipeline designed to identify route changes…

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a…

The vast amount of design freedom in disordered systems expands the parameter space for signal processing, allowing for unique signal flows that are distinguished from those in regular systems. However, this large degree of freedom has…

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…

Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based…

We design a Convolutional Neural Network (CNN) which studies correlation between discretized inverse temperature and spin configuration of 2D Ising model and show that it can find a feature of the phase transition without teaching any a…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

Despite pre-trained language models have proven useful for learning high-quality semantic representations, these models are still vulnerable to simple perturbations. Recent works aimed to improve the robustness of pre-trained models mainly…

Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to the co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial…

Recently, a system identification method based on center manifold is proposed to identify polynomial nonlinear systems with uncontrollable linearization. This note presents a numerical example to show the effectiveness of this method.

Line detection is widely used in many robotic tasks such as scene recognition, 3D reconstruction, and simultaneous localization and mapping (SLAM). Compared to points, lines can provide both low-level and high-level geometrical information…

Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in…

Localization of unknown faults in industrial systems is a difficult task for data-driven diagnosis methods. The classification performance of many machine learning methods relies on the quality of training data. Unknown faults, for example…

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis,…