Neural Measures for learning distributions of Random PDEs
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Abstract (arXiv)
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).
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 30 of its 54 references that are in the map. First posted on arXiv 2 Jul 2025.
Builds on
30 of 54 references.
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18 more
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