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Reduced order model for parametric Boltzmann equation and its application to inverse problems
Shanyin Tong, Jingwei Hu, Fengyan Li +3
The Boltzmann equation plays an important role in modeling mesoscopic behavior in a wide range of scientific and engineering applications. However, its numerical solution is comput…
Two Adjoint Perspectives on Fokker-Planck Optimization: A Microscopic-Macroscopic Correspondence
Kathrin Hellmuth, Qin Li, Yunan Yang
The Fokker-Planck equation admits both a macroscopic Eulerian description through probability densities and a microscopic Lagrangian description through stochastic trajectories. Co…
Structure-Preserving Reduced-Order Modeling via Low-Rank Transport Signatures
Jiajia Yu, Jingwei Hu, Fengyan Li +3
Parametrized PDEs with density-valued solutions are often difficult to approximate with classical linear reduced-order models, especially in transport-dominated regimes. We introdu…
Data-Adaptive Learning of Dynamical Systems by Matching Transfer Operators and Invariant Measures
Yinong Huang, Jonah Botvinick-Greenhouse, Yunan Yang
Trajectory-based learning of dynamical systems is often fragile in the presence of noise, chaos, or sparse observations, as small pointwise errors can rapidly amplify. We introduce…
Inference of interacting kernel in the mean-field regime
Peiyi Chen, Qin Li, Li Wang +1
We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction…