2024/07/15 by Victor Churchill, Churchill, Victor
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical and Computational Modeling
paper · pdf · doi:10.48550/arxiv.2407.10854
openalex publication_date 2024/07/15 · openalex created_date 2024/07/17 · openalex updated_date 2026/07/28
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional non-uniform grids. We address limitations of previous work on data-driven flow map learning in the sense that we focus on noisy and limited data to move toward data collection scenarios in real-world applications. Leveraging recent work on modeling PDEs in modal and nodal spaces, we present a neural network structure that is suitable for PDE modeling with noisy and limited data available only on a subset of the state variables or computational domain. In particular, spatial grid-point measurements are reduced using a learned linear transformation, after which the dynamics are learned in this reduced basis before being transformed back out to the nodal space. This approach yields a drastically reduced parameterization of the neural network compared with previous flow map models for nodal space learning. This allows for rapid high-resolution simulations, enabled by smaller training data sets and reduced training times.