C2BNet可快速适配不同网格，高效求解反问题。
Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guarantees
- 通过系数到基的映射，微调即可适应新离散化。
- 理论证明其误差可控，且无需显式编码低维结构。
- 适合需频繁切换网格的科学计算与工程场景。
我们提出一种系数到基网络（C2BNet），用于在算子学习范式下求解反问题。该框架通过微调实现对不同离散化的高效适配，利用预训练模型显著降低计算成本，同时保持高精度。不同于传统方法需针对新离散化从头训练，本方法可无缝迁移且不损失预测性能。我们通过挖掘底层数据集的低维结构，建立了C2BNet的近似与泛化误差理论界。分析表明，该模型能在不依赖显式编码机制的前提下自适应低维结构，体现其鲁棒性与高效性。大量数值实验验证了理论结果，结果显示C2BNet在多个反问题上表现优异，有效平衡了计算效率与精度，是科学计算与工程应用中求解反问题的有力工具。
原文摘要 · Abstract (English)
We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。