mlsanityData to 7 Oct 2026

PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs

arXiv 2405.08558 ↗First posted 14 May 2024math.NA cs.LG cs.NAcited by 4

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Abstract (arXiv)

The coupling of Proper Orthogonal Decomposition (POD) and deep learning-based ROMs (DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly accurate, surrogates for the real time solution of parametric nonlinear time-dependent PDEs. Inexpensive to evaluate, POD-DL-ROMs are also relatively fast to train, thanks to their limited complexity. However, POD-DL-ROMs account for the physical laws governing the problem at hand only through the training data, that are usually obtained through a full order model (FOM) relying on a high-fidelity discretization of the underlying equations. Moreover, the accuracy of POD-DL-ROMs strongly depends on the amount of available data. In this paper, we consider a major extension of POD-DL-ROMs by enforcing the fulfillment of the governing physical laws in the training process -- that is, by making them physics-informed -- to compensate for possible scarce and/or unavailable data and improve the overall reliability. To do that, we first complement POD-DL-ROMs with a trunk net architecture, endowing them with the ability to compute the problem's solution at every point in the spatial domain, and ultimately enabling a seamless computation of the physics-based loss by means of the strong continuous formulation. Then, we introduce an efficient training strategy that limits the notorious computational burden entailed by a physics-informed training phase. In particular, we take advantage of the few available data to develop a low-cost pre-training procedure; then, we fine-tune the architecture in order to further improve the prediction reliability. Accuracy and efficiency of the resulting pre-trained physics-informed DL-ROMs (PTPI-DL-ROMs) are then assessed on a set of test cases ranging from non-affinely parametrized advection-diffusion-reaction equations, to nonlinear problems like the Navier-Stokes equations for fluid flows.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 30 of its 71 references that are in the map. First posted on arXiv 14 May 2024.

Builds on

30 of 71 references.

References · 30

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18 more
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Cited by year

Citing papers per year: 2024: 1; 2025: 3.

4 papers.

  1. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  2. 2025Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEscited by 9
  3. 2025A discrete physics-informed training for projection-based reduced order models with neural networkscited by 1
  4. 2025Gaussian process surrogate with physical law-corrected prior for multi-coupled PDEs defined on irregular geometrycited by 1