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Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

Estimating consistent parameters of a structured state-space representation requires a reliable initialization when the vector of parameters is computed by using a gradient-based algorithm. In the eponymous companion paper accepted for…

We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a…

The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…

Gear box dynamics is characterised by a periodically changing stiffness and a backlash which can lead to a loss of the contact between the teeth. Due to backlash, the gear system has piecewise linear stiffness characteristics and, in…

Computer models are widely used to study complex real world physical systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; and long evaluation times.…

We study the suppression of nonlinear interactions in resonant macroscopic quantum devices in the case of the solid-state ring laser gyroscope. These nonlinear interactions are tuned by vibrating the gain medium along the cavity axis. Beat…

Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets.…

In an effort to provide an alternative method to represent a quantum spin, a precise 3D nonlinear dynamics method is used. A two-sided torque function is created to mimic the unique behavior of the quantum spin. A full 3D representation of…

While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…

We examine the performance of a nonlinear fiber gyroscope for improved signal detection beating the quantum limits of its linear counterparts. The performance is examined when the nonlinear gyroscope is illuminated by practical field…

Operating complex real-world systems, such as soft robots, can benefit from precise predictive control schemes that require accurate state and model knowledge. This knowledge is typically not available in practical settings and must be…

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…

This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system…

The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of…

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based…

Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian…

An open question in the field of non-equilibrium statistical physics is whether there exists a unique way through which non-equilibrium systems equilibrate irrespective of how far they are away from equilibrium. To answer this question we…

We investigate the nonlinear vibration of a fractional viscoelastic cantilever beam, subject to base excitation, where the viscoelasticity takes the general form of a distributed-order fractional model, and the beam curvature introduces…