Implement POD-DeepONet

Summary

Implement POD-DeepONet, which replaces the trainable trunk network with pre-computed Proper Orthogonal Decomposition (POD) basis functions.

Reference

• Lu et al., "A comprehensive and fair comparison of two neural operators (FNO vs DeepONet) based on FAIR data," Computer Methods in Applied Mechanics and Engineering, 2022. DOI: 10.1016/j.cma.2022.114778

Description

POD-DeepONet uses fixed POD basis functions (computed from training data via SVD) as the trunk net, while keeping the branch net trainable. This reduces the number of trainable parameters, often improves accuracy, and provides a principled basis informed by the data distribution.

Implementation could extend the existing DeepONet by accepting pre-computed basis functions in place of the trunk network, or as a new constructor that takes training snapshots and computes the POD basis internally.

Start by reading the existing DeepONet implementation and the Lu et al. reference to understand the intended POD-DeepONet design. Determine whether the API should accept pre-computed POD basis functions or training snapshots for SVD, then consider the work complete when the fixed POD trunk and trainable branch are supported with reduced trainable parameters.