Related papers: Dissipative SymODEN: Encoding Hamiltonian Dynamics…
This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed…
In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
We present a framework that leverages the Discrete Empirical Interpolation Method (DEIM) for interpretable deep learning and dynamical system analysis. Although DEIM efficiently approximates nonlinear terms in projection-based reduced-order…
We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The…
Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many 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…
We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form…
Real-world control systems require policies that are not only high-performing but also interpretable and robust. A promising direction toward this goal is model-based control, which learns system dynamics and cost functions from historical…
Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow…
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
A well-specified parametrization for single-input/single-output (SISO) linear port-Hamiltonian systems amenable to structure-preserving supervised learning is provided. The construction is based on controllable and observable normal form…
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…
We investigate the dissipative adaptation hypothesis in a quantum regime using a system-reservoir approach. This hypothesis proposes that self-organization arises from a system's ability to dissipate the work transiently absorbed from an…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…