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A novel framework for generalization of deep hidden physics models

arXiv 2401.04648 ↗First posted 9 Jan 2024cs.LG cs.AI math.APcited by 0

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Abstract (arXiv)

Modelling of systems where the full system information is unknown is an oft encountered problem for various engineering and industrial applications, as it's either impossible to consider all the complex physics involved or simpler models are considered to keep within the limits of the available resources. Recent advances in greybox modelling like the deep hidden physics models address this space by combining data and physics. However, for most real-life applications, model generalizability is a key issue, as retraining a model for every small change in system inputs and parameters or modification in domain configuration can render the model economically unviable. In this work we present a novel enhancement to the idea of hidden physics models which can generalize for changes in system inputs, parameters and domains. We also show that this approach holds promise in system discovery as well and helps learn the hidden physics for the changed system inputs, parameters and domain configuration.

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References · 9

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  3. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
  4. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  5. 2020Physics-informed learning of governing equations from scarce datacited by 167
  6. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  7. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  8. 2023LNO: Laplace Neural Operator for Solving Differential Equationscited by 47
  9. 2022Physics guided neural networks for modelling of non-linear dynamicscited by 20

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