6 papers
On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data
Jonah Botvinick-Greenhouse, Yunan Yang
We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynam…
AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition
Jonah Botvinick-Greenhouse, Wael H. Ali, Mouhacine Benosman +1
We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt…
Invariant Measures for Data-Driven Dynamical System Identification: Analysis and Application
Jonah Botvinick-Greenhouse
We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods…
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…
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…
An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems
Aaron Kirtland, Jonah Botvinick-Greenhouse, Marianne DeBrito +5
To address noise inherent in electronic data acquisition systems and real world sources, Araki et al. [Physica D: Nonlinear Phenomena, 417 (2021) 132819] demonstrated a grid based…