Machine Learning-Based Coarse-Scale Identification and Bifurcation Analysis for Modelling Tipping Points: a Financial Market Agent-Based Illustration

Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Cristina Martinez-Linares, Constantinos Siettos, Yannis Kevrekidis

Keywords: tipping points, bifurcation analysis, system identification, agent-based models, machine learning, neural network

Abstract:

We present a machine learning framework that targets the
systematic identification and bifurcation analysis of effective
coarse-grained dynamical laws describing the emergent
abrupt changing behavior of agent-based models near tipping
points. In particular, based on high-fidelity spatio-temporal
data, obtained in correspondence of different initial condition
and different value of a tracked parameter, we solve the
inverse problem to learn reduced effective low-dimensional
macroscopic laws in the form of (a) Integro-Partial differential
Equation for coarse-scale space-dependent fields and/or
(b) Stochastic differential equation (SDE) for global variables.
We illustrate and compare the two approaches through
an event-driven agent-based financial model describing the
mimetic behavior of many interacting investors. Specifically,
employing Diffusion Maps and Gaussian Processes for discovering
low-dimensional manifold embeddings and Deep
feedforward neural networks (DFNN) and single-layer Random
Projection Neural Networks(RPNNs) for learning effective
coarse-scale differential operators. Based on the learned
black-box Integro or StochasticDifferential model, we construct
the corresponding bifurcation diagram, thus we investigate
the stability of its multiple solution branches exploiting
the numerical bifurcation analysis tools. Finally, close to
the tipping point we compute the escaping time exploiting
Monte-Carlo simulation and a quadrature approach.