Related papers: Towards a Scientific Method for Dynamical Systems

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…

This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…

The whole complex process to obtain a protein encoded by a gene is difficult to include in a mathematical model. There are many models for describing different aspects of a genetic network. Finding a better model is one of the most…

Predicting dynamic behaviors is one of the goals of science in general as well as essential to many specific applications of human knowledge to real world systems. Here we introduce an analytic approach using the sigmoid growth curve to…

We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…

Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the…

We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

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…

A model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. This paper presents an extension to the Petri nets formalism suitable for describing information systems…

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…

In complex processes, various events can happen in different sequences. The prediction of the next event given an a-priori process state is of importance in such processes. Recent methods have proposed deep learning techniques such as…

The aim of this work is to learn models of population dynamics of physical systems that feature stochastic and mean-field effects and that depend on physics parameters. The learned models can act as surrogates of classical numerical models…

This paper introduces a general approach for synthesizing procedural models of the state-transitions of a given discrete system. The approach is general in that it accepts different target languages for modeling the state-transitions of a…

A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…

Deep learning models are widely used across computer vision and other domains. When working on the model induction, selecting the right architecture for a given dataset often relies on repetitive trial-and-error procedures. This procedure…

This paper develops a dynamical-systems framework for modeling influence propagation in product adoption networks, formulated as a positive linear system with Metzler interaction matrices and utility-based decay. Exact solutions are derived…

Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…

Threshold models and their dynamics may be used to model the spread of `behaviors' in social networks. Regarding such from a modal logical perspective, it is shown how standard update mechanisms may be emulated using action models -- graphs…