Learning Lagrangian dynamics to determine the anisotropic dust-dust interaction potential in a microgravity dusty plasma*

Arrangements of filamentary dust structures have been observed to form under external electric fields in the microgravity dusty plasma generated in the Plasmakristall-4 (PK-4) facility on board the International Space Station. Of particular interest is the investigation of the form of the anisotropic dust-dust interaction potential, which can reveal whether the observed filamentary structures are reminiscent of an electrorheological or a liquid crystal state. We present an analysis of dust particle dynamics with the novel statistical learning algorithm, the Sparse Identification of Nonlinear Dynamics (SINDy) [1], which exploits sparse regression to deduce parsimonious and interpretable models from data. To improve SINDy’s robustness to noisy data, recent developments use SINDy to deduce the form of the Lagrangian from data. We test the “extended Lagrangian” SINDy (xL-SINDy) method [2] on a simulated two-dust-particle system which interacts via a pure Yukawa potential, and discuss different results generated from training data with different magnitudes of Gaussian-distributed random noise added. Perspectives on the application of this method to experimental PK-4 data are presented and preliminary results are shown.

[1] Brunton, S.L., Proctor, J.L. and Kutz, J.N. (2016). Proc. Natl Acad. Sci. 113 3932–7. https://doi.org/10.1073/pnas.1517384113

[2] Purnomo, A. and Hayashibe, M. (2023). Sci. Reports 19 7919. https://doi.org/10.1038/s41598-023-34931-0