SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 37: Data Analytics of Complex Dynamical Systems (joint session DY/SOE)

DY 37.3: Vortrag

Donnerstag, 30. März 2023, 10:00–10:15, MOL 213

Inferring partial differential equations from molecular dynamics simulations — •Oliver Mai, Tim Kroll, Uwe Thiele, and Oliver Kamps — Institute of Theoretical Physics and Center for Nonlinear Science, University of Münster

Although integral to scientific or engineering applications, deriving partial differential equations (PDEs) solely from experimental data proves quite challenging and in most cases relies on physical principles in addition to qualitative behaviour of the system. In the last decade various efforts based on empirical data have been put forth to supplement first-principle derivations in theoretical sciences. That is in place of or in addition to typical conservation laws or phenomenological observations, time series data has been used to yield analytic expressions to describe the spatio-temporal evolution of a given dynamical system. While there have been various improvements in the sparsity and interpretability of the results, we provide another approach to optimization using the predictive power of the estimation when integrating it. Additionally aggregated small scale behaviour in macro- or mesoscopic experiments may exhibit unknown governing laws and as such a way for comparing data more directly to models derived in statistical physics may prove critical in furthering our understanding. To this end we study the application of system identification methods on molecular dynamics (MD) simulations.