Convolutional-neural-operator-based transfer learning for solving PDEs
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Abstract (arXiv)
Convolutional neural operator is a CNN-based architecture recently proposed to enforce structure-preserving continuous-discrete equivalence and enable the genuine, alias-free learning of solution operators of PDEs. This neural operator was demonstrated to outperform for certain cases some baseline models such as DeepONet, Fourier neural operator, and Galerkin transformer in terms of surrogate accuracy. The convolutional neural operator, however, seems not to be validated for few-shot learning. We extend the model to few-shot learning scenarios by first pre-training a convolutional neural operator using a source dataset and then adjusting the parameters of the trained neural operator using only a small target dataset. We investigate three strategies for adjusting the parameters of a trained neural operator, including fine-tuning, low-rank adaption, and neuron linear transformation, and find that the neuron linear transformation strategy enjoys the highest surrogate accuracy in solving PDEs such as Kuramoto-Sivashinsky equation, Brusselator diffusion-reaction system, and Navier-Stokes equations.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 25 of its 47 references that are in the map. First posted on arXiv 19 Dec 2025.
Builds on
25 of 47 references.
References · 25
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13 more
- 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
- 2024APEBench: A Benchmark for Autoregressive Neural Emulators of PDEscited by 60
- 2023Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learningcited by 57
- 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 46
- 2024Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solverscited by 35
- 2024PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamicscited by 34
- 2020Neuron Linear Transformation: Modeling the Domain Shift for Crowd Countingcited by 19
- 2025Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptationcited by 15
- 2024Strategies for Pretraining Neural Operatorscited by 14
- 2025Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flowscited by 13
- 2025Operator Learning at Machine Precisioncited by 7
- 2024Uncertainty quantification for deeponets with ensemble kalman inversioncited by 4
- 2025Low-Rank Evolutionary Deep Neural Networks via Adaptive Tangent-Space Reductioncited by 1
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Citing papers per year: 2026: 2.
2 papers.