Stacked networks improve physics-informed training: applications to neural networks and deep operator networks
Physics-informed neural networks and operator networks have shown promise for effectively
solving equations modeling physical systems. However, these networks can be difficult or …
solving equations modeling physical systems. However, these networks can be difficult or …
[PDF][PDF] Multifidelity domain decomposition-based physics-informed neural networks for time-dependent problems
Multiscale problems are challenging for neural network-based discretizations of differential
equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed …
equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed …
Faithful and efficient explanations for neural networks via neural tangent kernel surrogate models
A recent trend in explainable AI research has focused on surrogate modeling, where neural
networks are approximated as simpler ML algorithms such as kernel machines. A second …
networks are approximated as simpler ML algorithms such as kernel machines. A second …
A multifidelity approach to continual learning for physical systems
We introduce a novel continual learning method based on multifidelity deep neural
networks. This method learns the correlation between the output of previously trained …
networks. This method learns the correlation between the output of previously trained …
The conjugate kernel for efficient training of physics-informed deep operator networks
Recent work has shown that the empirical Neural Tangent Kernel (NTK) can significantly
improve the training of physics-informed Deep Operator Networks (DeepONets). The NTK …
improve the training of physics-informed Deep Operator Networks (DeepONets). The NTK …