8 papers
Wasserstein Moment Nudging for Vlasov-Poisson Data Assimilation
Liyao Lyu, Xinyue Yu, David Schneidinger +1
We introduce a continuous data assimilation method for particle-in-cell simulations of the Vlasov-Poisson equation when only hydrodynamic moments are observed. The forecast state i…
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
Liyao Lyu, Xinyue Yu, Hayden Schaeffer
We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation m…
Consensus-based adaptive sampling and approximation for high-dimensional energy landscapes
Liyao Lyu, Huan Lei
We present a consensus-based framework that unifies phase space exploration with posterior-residual-based adaptive sampling for surrogate construction in high-dimensional energy la…
High-Dimensional Enhanced Sampling via Regularized Path-Dependent McKean--Vlasov Dynamics using Tensor Density Approximation
Liyao Lyu, Siyu Guo, Huan Lei
Sampling from high-dimensional Gibbs measures poses a challenge when the energy landscape consists of multiple metastable states. Enhanced-sampling methods mitigate this difficulty…
MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
Liyao Lyu, Xinyue Yu, Hayden Schaeffer
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued…
A stochastic branching particle method for solving non-conservative reaction-diffusion equations
Liyao Lyu, Huan Lei
We propose a stochastic branching particle-based method for solving nonlinear non-conservative advection-diffusion-reaction equations. The method splits the evolution into an advec…