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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2404.15731 |
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| _version_ | 1866913830135660544 |
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| author | Thakur, Akshay Chakraborty, Souvik |
| author_facet | Thakur, Akshay Chakraborty, Souvik |
| contents | We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the pointwise operator learning neural architecture nonlinear manifold decoder (NOMAD) with mixture density-based methods to estimate conditional probability distributions for stochastic output functions. MD-NOMAD harnesses the ability of probabilistic mixture models to estimate complex probability and the high-dimensional scalability of pointwise neural operator NOMAD. We conduct empirical assessments on a wide array of stochastic ordinary and partial differential equations and present the corresponding results, which highlight the performance of the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation Thakur, Akshay Chakraborty, Souvik Machine Learning We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the pointwise operator learning neural architecture nonlinear manifold decoder (NOMAD) with mixture density-based methods to estimate conditional probability distributions for stochastic output functions. MD-NOMAD harnesses the ability of probabilistic mixture models to estimate complex probability and the high-dimensional scalability of pointwise neural operator NOMAD. We conduct empirical assessments on a wide array of stochastic ordinary and partial differential equations and present the corresponding results, which highlight the performance of the proposed framework. |
| title | MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2404.15731 |