Related papers: Deep learning approach for predicting the replicat…
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…
Complex networks serve as abstract models for understanding real-world complex systems and provide frameworks for studying structured dynamical systems. This article addresses limitations in current studies on the exploration of individual…
Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi-agent systems. In particular, it has been proven to be a successful tool to describe multi-agent…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
The replicator equation in evolutionary game theory describes the change in a population's behaviors over time given suitable incentives. It arises when individuals make decisions using a simple learning process - imitation. A recent…
Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…
We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…
We extend the data-driven method of Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton et al, Proc. Natl. Acad. Sci USA 113 (2016) to the case of delay differential equations (DDEs). This is achieved in a bilevel…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
Although learning has found wide application in multi-agent systems, its effects on the temporal evolution of a system are far from understood. This paper focuses on the dynamics of Q-learning in large-scale multi-agent systems modeled as…
This paper develops a novel deep learning approach for solving evolutionary equations, which integrates sequential learning strategies with an enhanced hard constraint strategy featuring trainable parameters, addressing the low…
We propose using deep reinforcement learning to solve dynamic stochastic general equilibrium models. Agents are represented by deep artificial neural networks and learn to solve their dynamic optimisation problem by interacting with the…
People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
Deep reinforcement learning has shown remarkable success in the past few years. Highly complex sequential decision making problems have been solved in tasks such as game playing and robotics. Unfortunately, the sample complexity of most…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
Deep learning is used in computer vision problems with important applications in several scientific fields. In ecology for example, there is a growing interest in deep learning for automatizing repetitive analyses on large amounts of…
In this paper we present a new modelling framework combining replicator dynamics (which is the standard model of frequency dependent selection) with the model of an age-structured population. The new framework allows for the modelling of…