Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example
This work addresses the challenge of analyzing phase transitions in complex systems for researchers in statistical physics and computational modeling, representing an incremental improvement by applying existing machine learning techniques to a specific model.
The authors tackled the problem of identifying phase transitions in agent-based models by developing a data-driven framework that uses manifold learning and deep learning to derive a single parameter-dependent ODE, enabling the construction of a bifurcation diagram for the Desai-Zwanzig model with fewer variables than traditional closed-form approaches.
Deriving closed-form, analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM- the Desai-Zwanzig model in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ODE in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE - enabled through an odd symmetry transformation - to construct the bifurcation diagram exhibiting the phase transition.