Related papers: Learning strange attractors with reservoir systems

The dissipative dynamics anticipated in the proof of 't Hooft's existence theorem -- "For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization" -- is constructed here…

Machine learning recently proved efficient in learning differential equations and dynamical systems from data. However, the data is commonly assumed to originate from a single never-changing system. In contrast, when modeling real-world…

We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which…

In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on learning a useful discretization of the phase space of a…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

The global push to advance Carbon Capture and Sequestration initiatives and green energy solutions, such as geothermal, have thrust new demands upon the current state-of-the-art subsurface fluid simulators. The requirement to be able to…

This paper proposes a general interpretable predictive system with shared information. The system is able to perform predictions in a multi-task setting where distinct tasks are not bound to have the same input/output structure. Embeddings…

With the advent of Joint Embedding Predictive Architectures (JEPAs), which appear to be more capable than reconstruction-based methods, this paper introduces a novel technique for creating world models using continuous-time dynamic systems…

We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…

Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…

A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability…