Abstract:
Lagrangian data assimilation (DA) aims to reconstruct flow fields from particle trajectories, but its nonlinear and high-dimensional nature often limits efficiency and accuracy. In this talk, we will introduce LEMDA, a Lagrangian–Eulerian multiscale data assimilation framework that bridges particle-based and continuum-based perspectives. We begin with a brief overview of our recent work on the multiscale modeling of sea-ice floe particles, developed within the conceptual framework of Hilbert’s sixth problem. Starting from a Boltzmann kinetic formulation of particle dynamics, we employ the BBGKY hierarchy to derive Eulerian continuum equations that capture the statistical behavior and large-scale evolution of the particle system. Building upon this particle–continuum multiscale model, we introduce the LEMDA (Lagrangian–Eulerian Multiscale Data Assimilation) framework, which integrates both Lagrangian and Eulerian observational data. By incorporating a stochastic surrogate model for the dynamics of both particles and continuum fields, the posterior distribution of the system can be expressed in closed analytic form, thereby avoiding ensemble-based approximations and empirical tuning. The resulting framework consists of two complementary components: a Lagrangian DA module suited for sparse particle data and an Eulerian DA module designed for the large-scale behavior of dense, colliding, or multiscale particle systems. We will show numerical experiments to illustrate LEMDA’s accuracy, robustness, and computational efficiency.
About the Speaker:
Dr. Quanling Deng is an Assistant Professor at the Yau Mathematical Sciences Center (YMSC), Tsinghua University. Before joining YMSC, he held positions at Curtin University (Research Associate, 2016–2020), the University of Wisconsin–Madison (Van Vleck Visiting Assistant Professor, 2020–2022), and the Australian National University (Lecturer, 2022–2025). He got his PhD in Mathematics at the University of Wyoming in 2016. He has a broad interest in Computational and Applied Mathematics and AI. Inspired by Hilbert’s Sixth Problem, he pioneered a particle–continuum multiscale modeling paradigm for sea ice floes and developed the LEMDA framework that unifies multiscale observations. He also introduced SoftFEM, SoftIGA, and high-order boundary penalty techniques, resolving long-standing challenges in finite elements and isogeometric analysis. His research has been published in leading venues, including MCOM, CMAME, JAMES, ICLR, and the SIAM journals, with over 45 peer-reviewed publications to date.
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