A generative modeling / Physics-Informed Neural Network approach to random differential equations
This work addresses uncertainty control in scientific machine learning for computational science, representing an incremental advancement in Physics-Informed Neural Networks.
The paper tackles uncertainty quantification in complex systems by integrating generative modeling with Physics-Informed Neural Networks, resulting in enhanced uncertainty representation and maintained predictive accuracy for random differential equations.
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).