# SKM 2023 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# TT: Fachverband Tiefe Temperaturen

## TT 43: Poster: Correlated Electrons II

### TT 43.33: Poster

### Mittwoch, 29. März 2023, 15:00–18:00, P2/OG3

Machine learning stochastic dynamics of order parameters — •Francesco Carnazza^{1}, Federico Carollo^{1}, Igor Lesanovsky^{1}, Georg Martius^{2}, Sabine Andergassen^{1}, and Miriam Klopotek^{3} — ^{1}University of Tuebingen — ^{2}Max Planck Institute for Intelligent Systems — ^{3}University of Stuttgart

The dynamics of coarse-grained observables, or of order-parameters, in many-body systems is usually rather intricate due to emergent nonlinearities and collective effects. In fact, except for few exactly solvable models, it is typically not possible to find the form of the differential equation describing the dynamics of these observables. Here, we address this problem exploiting a machine learning approach. We consider single trajectories of the thermal dynamics of a two-dimensional Ising model and feed these to a neural network. These trajectories, simulated by Monte Carlo methods, are intrinsically stochastic. Their dynamics can be approximated by a stochastic differential equation parametrised by a smooth term, the drift, and one multiplied by the differential of a Wiener process, that is, the diffusion.

In [1] a neural solver for stochastic differential equation was introduced, by means of which the drift and diffusion terms are approximated by neural networks. A classical integration method, e.g., Euler-Maruyama, is then adopted to recover full trajectories. We adopt this method to learn the drift and diffusion terms and infer the properties of the Ising model.

[1] Li et al., PMLR 108:3870-3882,2020.