8 papers
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…
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…
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…
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 i…