mlsanityData to 7 Oct 2026

Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models

arXiv 2410.13376 ↗First posted 17 Oct 2024cs.LG cs.NA math.NAcited by 3

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Abstract (arXiv)

Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many methods fail in accurately generalizing in the entire time interval [0, T], when the training data is available only in a training time interval [0, T0], with T0<T. To improve the extrapolation capabilities of the surrogate models in the entire time domain, we propose a new deep learning framework, where kernel dynamic mode decomposition (KDMD) is employed to evolve the dynamics of the latent space generated by the encoder part of a convolutional autoencoder (CAE). After adding the KDMD-decoder-extrapolated data into the original data set, we train the CAE along with a feed-forward deep neural network using the augmented data. The trained network can predict future states outside the training time interval at any out-of-training parameter samples. The proposed method is tested on two numerical examples: a FitzHugh-Nagumo model and a model of incompressible flow past a cylinder. Numerical results show accurate and fast prediction performance in both the time and the parameter domain.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 12 of its 37 references that are in the map. First posted on arXiv 17 Oct 2024.

Builds on

12 of 37 references.

References · 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025Spatially-Enhanced Temporal Fusion Transformer: Interpretable Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputscited by 1
  2. 2025Drivetrain simulation using variational autoencoderscited by 0
  3. 2026Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applicationscited by 0