用快速神经网络解决金融期权定价方程，速度比传统方法快30倍。
Towards Fast Option Pricing PDE Solvers Powered by PIELM
- 用单次最小二乘法替代迭代优化，实现快速训练。
- 在黑斯科尔斯和赫斯顿-赫尔-怀特模型上精度接近PINN，速度提升30倍。
- 适合需要实时计算的金融建模场景，如高频交易或风险评估。
偏微分方程（PDE）求解器是现代量化金融的核心，用于期权定价与风险评估。物理信息神经网络（PINNs）利用深度学习求解PDE的正问题与逆问题，但因其基于梯度下降的迭代优化，计算成本高且难以扩展。本文提出物理信息极限学习机（PIELM），作为PINNs在金融PDE求解中的快速替代方案。PIELM以单次最小二乘求解取代迭代优化，实现确定性高效训练。我们在黑斯科尔斯（Black-Scholes）与赫斯顿-赫尔-怀特（Heston-Hull-White）模型上对前向定价进行基准测试，并验证其在含噪数据下反演波动率与利率参数的能力。实验表明，PIELM在精度上与PINN相当，速度最高提升30倍，展现出实现实时金融建模的巨大潜力。
原文摘要 · Abstract (English)
Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and inverse problems of partial differential equations (PDEs) using deep learning. However they remain computationally expensive due to their iterative gradient descent based optimization and scale poorly with increasing model size. This paper introduces Physics-Informed Extreme Learning Machines (PIELMs) as fast alternative to PINNs for solving both forward and inverse problems in financial PDEs. PIELMs replace iterative optimization with a single least-squares solve, enabling deterministic and efficient training. We benchmark PIELM on the Black-Scholes and Heston-Hull-White models for forward pricing and demonstrate its capability in inverse model calibration to recover volatility and interest rate parameters from noisy data. From experiments we observe that PIELM achieve accuracy comparable to PINNs while being up to $30\times$ faster, highlighting their potential for real-time financial modeling.
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