Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
Authors: Wuzhe Xu, Yulong Lu, Li Wang
AAAI 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through systematic experiments, we show that the proposed method not only improves the long-time accuracy of Deep ONet while maintaining similar computational cost but also substantially reduces the sample size of the training set. In this section, we demonstrate the effectiveness of transfer learning enhanced Deep ONet and show its advantages over the vanilla Deep ONet through several evolutionay PDEs, including reaction diffusion equation, Allen-Cahn and Cahn Hilliard equations, Navier-Stokes equation and multiscale linear radiative transfer equation. |
| Researcher Affiliation | Academia | Wuzhe Xu1* , Yulong Lu2, Li Wang1 1 School of Mathematics, University of Minnesota 2 Department of Mathematics and Statistics, University of Massachusetts Amherst |
| Pseudocode | No | The paper does not contain any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access to source code, such as a repository link or an explicit statement about code release. |
| Open Datasets | No | The paper describes how training data was generated for various PDEs (e.g., 'randomly sampled functions', 'reference solutions... using conventional high-fidelity numerical solvers') and does not provide concrete access information (link, DOI, formal citation) for a publicly available or open dataset. |
| Dataset Splits | No | The paper mentions 'M training initial data' and 'test initial conditions' but does not specify training/validation/test dataset splits, percentages, or sample counts for validation. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library or solver names with version numbers, needed to replicate the experiment. |
| Experiment Setup | No | While the paper describes the architecture, loss functions, and parameter update strategy (e.g., 'update w by re-training the loss (4)'), it does not provide specific hyperparameter values such as learning rate, batch size, number of epochs, or the type of optimizer used for training. |