Related papers: The AAA framework for modeling linear dynamical sy…
The Airy process is characterized by its finite-dimensional distribution functions. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.
This note presents a numerical example worked out in order to illustrate the solution to the output regulation problem with quadratic stability for linear switching systems derived in [1].
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
A multi-factor extension of the Hobson and Rogers (HR) model, incorporating a quadratic variance function (QHR model), is proposed and analysed. The QHR model allows for greater flexibility in defining the moving average filter while…
The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Recent literature has shown how linear time-invariant (LTI) systems can be represented by trajectories features, that is relying on a single input-output (IO) data dictionary to span all possible system trajectories, as long as the input is…
Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes much more computationally demanding, and new algorithms are needed to efficiently…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…
This paper describes MAIA, a Multimodal Automated Interpretability Agent. MAIA is a system that uses neural models to automate neural model understanding tasks like feature interpretation and failure mode discovery. It equips a pre-trained…
Several applications of the QR-AAA algorithm, a greedy scheme for vector-valued rational approximation, are presented. The focus is on demonstrating the flexibility and practical effectiveness of QR-AAA in a variety of computational…