# Towards Fast Option Pricing PDE Solvers Powered by PIELM

arXiv: https://arxiv.org/abs/2510.04322 · HTML: https://mlsanity.com/paper/2510.04322/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 3 of 3)

- [Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations](https://mlsanity.com/paper/1907.03507/) (2019)
- [Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2205.06948/) (2022)
- [Curriculum Learning-Driven PIELMs for Fluid Flow Simulations](https://mlsanity.com/paper/2503.06347/) (2025)

## Built on by (most cited first, 1 of 1)

- [DeepSVM: Learning Stochastic Volatility Models with Physics-Informed Deep Operator Networks](https://mlsanity.com/paper/2512.07162/) (2025)

## Abstract (arXiv)

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× faster, highlighting their potential for real-time financial modeling.