Convolutional-neural-operator-based transfer learning for solving PDEs (arxiv.org)

A recent study introduces an advanced convolutional neural operator (CNO) that enhances transfer learning techniques for solving partial differential equations (PDEs). This CNN-based model has demonstrated superior performance compared to previous methodologies like DeepONet and Fourier neural operators, particularly in achieving accurate surrogate solutions for complex PDEs. Notably, the researchers have extended CNO's capabilities to few-shot learning, enabling effective model adaptation with minimal data from target datasets. Three strategies were evaluated for fine-tuning the pre-trained CNO: fine-tuning, low-rank adaptation, and neuron linear transformation. Among these, neuron linear transformation yielded the highest accuracy in resolving various PDEs, including the Kuramoto-Sivashinsky equation and the Navier-Stokes equations. This advancement is significant for the AI/ML community as it opens new avenues for applying deep learning in mathematical modeling, reducing the data requirements for training models in complex scientific computations, and thereby accelerating research and practical applications in areas such as physics and engineering.