Gong, Shiqi;
Hu, Peiyan;
Meng, Qi;
Zhu, Rongchan;
Chen, Bingguang;
Ma, Zhi-ming;
Ni, Hao;
(2023)
Deep Latent Regularity Network for Modeling Stochastic Partial Differential Equations.
In:
Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence.
AAAI
(In press).
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Abstract
Stochastic partial differential equations (SPDEs) are crucial for modelling dynamics with randomness in many areas including economics, physics, and atmospheric sciences. Recently, using deep learning approaches to learn the PDE solution for accelerating PDE simulation becomes increasingly popular. However, SPDEs have two unique properties that require new design on the models. First, the model to approximate the solution of SPDE should be generalizable over both initial conditions and the random sampled forcing term. Second, the random forcing terms usually have poor regularity whose statistics may diverge (e.g., the space-time white noise). To deal with the problems, in this work, we design a deep neural network called Deep Latent Regularity Net (DLR-Net). DLR-Net includes a regularity feature block as the main component, which maps the initial condition and the random forcing term to a set of regularity features. The processing of regularity features is inspired by regularity structure theory and the features provably compose a set of basis to represent the SPDE solution. The regularity features are then fed into a small backbone neural operator to get the output. We conduct experiments on various SPDEs including the dynamic Φ^{4}_{1} model and the stochastic 2D Navier-Stokes equation to predict their solutions, and the results demonstrate that the proposed DLR-Net can achieve SOTA accuracy compared with the baselines. Moreover, the inference time is over 20 times faster than the traditional numerical solver and is comparable with the baseline deep learning models.
| Type: | Proceedings paper |
|---|---|
| Title: | Deep Latent Regularity Network for Modeling Stochastic Partial Differential Equations |
| Event: | Thirty-Seventh AAAI Conference on Artificial Intelligence |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://aaai.org/Conferences/AAAI-23/ |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10163280 |
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