用无反向传播的ELM加速DeepONet训练，提升效率与精度。
ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines
- 将DeepONet训练转为无反向传播的最小二乘问题求解。
- 在非线性常微分方程和偏微分方程上实现更高精度与更低计算成本。
- 适合需要高效训练的科学计算场景，尤其关注可扩展性。
Deep Operator Networks（DeepONets）是算子学习中最具代表性的框架之一，基于算子的通用逼近定理。然而，训练DeepONets通常需要大量计算资源。为解决这一限制，我们提出ELM-DeepONets，一种基于极限学习机（ELM）的DeepONet框架，利用ELM无需反向传播的特性。通过将DeepONet训练重新表述为新引入参数的最小二乘问题，该方法显著降低训练复杂度。在典型基准问题（包括非线性常微分方程与偏微分方程）上的验证表明，所提方法不仅实现更优精度，且大幅降低计算成本。本工作为科学计算中的算子学习提供了一种可扩展、高效的替代方案。
原文摘要 · Abstract (English)
Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational resources. To address this limitation, we propose ELM-DeepONets, an Extreme Learning Machine (ELM) framework for DeepONets that leverages the backpropagation-free nature of ELM. By reformulating DeepONet training as a least-squares problem for newly introduced parameters, the ELM-DeepONet approach significantly reduces training complexity. Validation on benchmark problems, including nonlinear ODEs and PDEs, demonstrates that the proposed method not only achieves superior accuracy but also drastically reduces computational costs. This work offers a scalable and efficient alternative for operator learning in scientific computing.
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