1 citations · 1 across the 10 of their papers we have counts for
11 papers
Stochastic Gradient Descent over P2
Maria Oprea, Qin Li, Yunan Yang
Stochastic gradient descent (SGD) admits diffusion approximations that replace the complicated randomness of stochastic gradients by Gaussian noise, providing a powerful tool for u…
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…
Inverse Problems Over Probability Measure Space
Qin Li, Maria Oprea, Li Wang +1
Define a forward problem as , where the probability distribution is mapped to another distribution using the forward operator . In this work, we inves…
Least-Squares Problem Over Probability Measure Space
Qin Li, Li Wang, Yunan Yang
In this work, we investigate the variational problem where quantifies the difference between two probability measures, and…
Invariant Measures in Time-Delay Coordinates for Unique Dynamical System Identification
Jonah Botvinick-Greenhouse, Robert Martin, Yunan Yang
While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniq…
Stochastic Inverse Problem: stability, regularization and Wasserstein gradient flow
Qin Li, Maria Oprea, Li Wang +1
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unk…
Measure-Theoretic Time-Delay Embedding
Jonah Botvinick-Greenhouse, Maria Oprea, Romit Maulik +1
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical…