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Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

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arxiv 2409.02703 v1 pith:BU4X3WO2 submitted 2024-09-04 math.NA cs.NA

Paul Schwerdtner , Prakash Mohan , Aleksandra Pachalieva , Julie Bessac , Daniel O'Malley , Benjamin Peherstorfer This is my paper · ORCID
classification math.NAcs.NA
keywords dataonlinequadraticgreedymanifoldsmethoddiskinput
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds

    math.NA 2024-12 conditional novelty 7.0 of 10

    Quadratic-manifold Neural Galerkin reduced models give locally unique, residual-minimizing trajectories and, for linear full models, online cost independent of the full dimension.

  2. Empirical sparse regression on quadratic manifolds

    math.NA 2024-12 conditional novelty 6.0 of 10

    QMSR trains a quadratic manifold with a greedy algorithm and reconstructs data from sparse samples via a linear encoder on the sampled components.

  3. A parallel implementation of reduced-order modeling of large-scale systems

    cs.DC 2025-04 conditional novelty 4.0 of 10

    A tutorial-style paper that details and demonstrates a fully distributed implementation of Operator Inference for building reduced-order models from datasets too large for a single computer.

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