mlsanityData to 7 Oct 2026

Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations

arXiv 2402.17853 ↗First posted 27 Feb 2024cs.LG cs.AI math.APcited by 5

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Abstract (arXiv)

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional discretized fields, we propose to learn the dynamics of the system in the latent space with much coarser discretizations. In our proposed framework - Latent Neural PDE Solver (LNS), a non-linear autoencoder is first trained to project the full-order representation of the system onto the mesh-reduced space, then a temporal model is trained to predict the future state in this mesh-reduced space. This reduction process simplifies the training of the temporal model by greatly reducing the computational cost accompanying a fine discretization. We study the capability of the proposed framework and several other popular neural PDE solvers on various types of systems including single-phase and multi-phase flows along with varying system parameters. We showcase that it has competitive accuracy and efficiency compared to the neural PDE solver that operates on full-order space.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 65 of its 89 references that are in the map. First posted on arXiv 27 Feb 2024.

Builds on

65 of 89 references.

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Cited by year

Citing papers per year: 2024: 4; 2025: 1.

5 papers.

  1. 2024Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularitycited by 33
  2. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
  3. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  4. 2024Pretraining a Neural Operator in Lower Dimensionscited by 5
  5. 2025Reframing Generative Models for Physical Systems using Stochastic Interpolantscited by 2