ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance
This addresses a key challenge in scientific computing for researchers and engineers by providing a more robust and efficient operator learning algorithm, though it builds on existing methods like Reduced Basis Method and Generative Pre-Trained Physics-Informed Neural Networks.
The paper tackles the problem of generalization gaps and discretization dependence in operator learning for PDEs by proposing ReBaNO, which significantly outperforms state-of-the-art methods in reducing generalization errors and achieving strict discretization invariance.
We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative Pre-Trained Physics-Informed Neural Networks, ReBaNO relies on a mathematically rigorous greedy algorithm to build its network structure offline adaptively from the ground up. Knowledge distillation via task-specific activation function allows ReBaNO to have a compact architecture requiring minimal computational cost online while embedding physics. In comparison to state-of-the-art operator learning algorithms such as PCA-Net, DeepONet, FNO, and CNO, numerical results demonstrate that ReBaNO significantly outperforms them in terms of eliminating/shrinking the generalization gap for both in- and out-of-distribution tests and being the only operator learning algorithm achieving strict discretization invariance.