{"id":5735,"date":"2025-07-31T07:03:14","date_gmt":"2025-07-31T07:03:14","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/07\/31\/2507-22493\/"},"modified":"2025-07-31T07:03:14","modified_gmt":"2025-07-31T07:03:14","slug":"2507-22493","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/07\/31\/2507-22493\/","title":{"rendered":"LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process"},"content":{"rendered":"

LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process
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arXiv:2507.22493v1 Announce Type: new
\nAbstract: We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the input to a high-dimensional latent representation, enabling uncertainty-aware prediction of the solution. Specifically, the architecture consists of a confidence-aware encoder and a probabilistic decoder. The encoder implements a high-dimensional latent variable model based on a Gaussian process (LVM-GP), where the latent representation is constructed by interpolating between a learnable deterministic feature and a Gaussian process prior, with the interpolation strength adaptively controlled by a confidence function learned from data. The decoder defines a conditional Gaussian distribution over the solution field, where the mean is predicted by a neural operator applied to the latent representation, allowing the model to learn flexible function-to-function mapping. Moreover, physical laws are enforced as soft constraints in the loss function to ensure consistency with the underlying PDE structure. Compared to existing approaches such as Bayesian physics-informed neural networks (B-PINNs) and deep ensembles, the proposed framework can efficiently capture functional dependencies via merging a latent Gaussian process and neural operator, resulting in competitive predictive accuracy and robust uncertainty quantification. Numerical experiments demonstrate the effectiveness and reliability of the method.<\/div>\n

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\n Xiaodong Feng, Ling Guo, Xiaoliang Wan, Hao Wu, Tao Zhou, Wenwen Zhou
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LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process arXiv:2507.22493v1 Announce Type: new Abstract: We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the input to a high-dimensional […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,187,113,112],"tags":[338,1338,384],"class_list":["post-5735","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-ai","category-cs-lg","category-stat-ml","tag-gaussian","tag-latent","tag-uncertainty"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5735"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=5735"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5735\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}