Neural Measures for learning distributions of Random PDEs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917172769456128 |
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| author | Arampatzis, Georgios Katsarakis, Stylianos Makridakis, Charalambos |
| author_facet | Arampatzis, Georgios Katsarakis, Stylianos Makridakis, Charalambos |
| contents | The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems. Our approach enhances the representation of uncertainty in forward problems by combining generative modeling techniques with PINNs. This integration enables in a systematic fashion uncertainty control while maintaining the predictive accuracy of the model. We demonstrate the utility of this method through applications to random differential equations and random partial differential equations (PDEs). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural Measures for learning distributions of Random PDEs Arampatzis, Georgios Katsarakis, Stylianos Makridakis, Charalambos Machine Learning Numerical Analysis The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems. Our approach enhances the representation of uncertainty in forward problems by combining generative modeling techniques with PINNs. This integration enables in a systematic fashion uncertainty control while maintaining the predictive accuracy of the model. We demonstrate the utility of this method through applications to random differential equations and random partial differential equations (PDEs). |
| title | Neural Measures for learning distributions of Random PDEs |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2507.01687 |