Physics-informed neural networks for operator equations with stochastic data
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910434204844032 |
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| author | Escapil-Inchauspé, Paul Ruz, Gonzalo A. |
| author_facet | Escapil-Inchauspé, Paul Ruz, Gonzalo A. |
| contents | We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of existing PINNs code, and enabling handling of non-linear and time-dependent operators. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations. Exhaustive numerical experiments are performed; demonstrating applicability and performance; raising a variety of new promising research avenues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10344 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Physics-informed neural networks for operator equations with stochastic data Escapil-Inchauspé, Paul Ruz, Gonzalo A. Machine Learning Numerical Analysis We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of existing PINNs code, and enabling handling of non-linear and time-dependent operators. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations. Exhaustive numerical experiments are performed; demonstrating applicability and performance; raising a variety of new promising research avenues. |
| title | Physics-informed neural networks for operator equations with stochastic data |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2211.10344 |