Quadratic-manifold Neural Galerkin reduced models give locally unique, residual-minimizing trajectories and, for linear full models, online cost independent of the full dimension.
Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction
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abstract
This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in-situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.
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math.NA 1years
2024 1verdicts
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Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds
Quadratic-manifold Neural Galerkin reduced models give locally unique, residual-minimizing trajectories and, for linear full models, online cost independent of the full dimension.