Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations
<|reference_start|>Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations: 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.<|reference_end|>
@article{li2024latent,
    title={Latent Neural PDE Solver: a reduced-order modelling framework for
  partial differential equations},
    author={Zijie Li, Saurabh Patil, Francis Ogoke, Dule Shu, Wilson Zhen, Michael
  Schneier, John R. Buchanan, Jr., Amir Barati Farimani},
    journal={arXiv preprint arXiv:2402.17853},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17853},
    primaryClass={cs.LG cs.AI math.AP}
}