| Abstract Scope |
As an emerging paradigm in scientific machine learning, deep neural operators pioneered by us can learn nonlinear operators of complex dynamic systems via neural networks. I will present the deep operator network to learn various operators. I will also present several extensions of DeepONet, such as diffeomorphic mapping operator learning. I will demonstrate the effectiveness of DeepONet to diverse multiphysics and multiscale 3D problems. Deep learning models are usually limited to interpolation scenarios, and I will quantify the extrapolation complexity and develop a complete workflow to address the challenge of extrapolation for deep neural operators. Moreover, I will present the first operator learning method that only requires one PDE solution, i.e., one-shot learning, by introducing a new concept of local solution operator based on the principle of locality. I will also present the first systematic study of federated scientific machine learning for approximating functions and solving PDEs with data heterogeneity. |