Deep Latent Regularity Network for Modeling Stochastic Partial Differential Equations
نویسندگان
چکیده
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 accelerating simulation becomes increasingly popular. However, SPDEs have two unique properties that require new design on models. First, model approximate of SPDE should be generalizable over both initial conditions random sampled forcing term. Second, terms usually poor regularity whose statistics may diverge (e.g., space-time white noise). To deal problems, this work, we a neural network called \emph{Deep Latent Regularity Net} (DLR-Net). DLR-Net includes feature block as main component, which maps condition term set features. The processing features is inspired by structure theory provably compose basis represent solution. then fed into small backbone operator get output. We conduct experiments various dynamic $\Phi^4_1$ stochastic 2D Navier-Stokes equation predict their solutions, results demonstrate proposed can achieve SOTA accuracy compared baselines. Moreover, inference time 20 times faster than traditional numerical solver comparable baseline
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ژورنال
عنوان ژورنال: Proceedings of the ... AAAI Conference on Artificial Intelligence
سال: 2023
ISSN: ['2159-5399', '2374-3468']
DOI: https://doi.org/10.1609/aaai.v37i6.25938