# Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models

arXiv: https://arxiv.org/abs/2504.03244 · HTML: https://mlsanity.com/paper/2504.03244/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2025.

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

- [MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems](https://mlsanity.com/paper/2603.10987/) (2026)

## Abstract (arXiv)

In this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where solutions often exhibit significant curvature or shock waves over time. The AM-PIRN architecture is designed to concurrently minimize PDE residuals and achieve high-fidelity option price approximations by dynamically redistributing training points based on evolving PDE residuals, while maintaining a fixed total number of points. To enhance stability and training efficiency, we integrate a ResNet backbone, replacing conventional fully connected neural networks used in Physics-Informed Neural Networks (PINNs). Numerical experiments across nonlinear option pricing models demonstrate that AM-PIRN outperforms PINN, RAM-PINN, and WAM-PINN in both resolving PDE constraints and accurately estimating option prices. The method's advantages are particularly pronounced in complex or multi-dimensional models, where its adaptive sampling and robust architecture effectively mitigate challenges posed by sharp gradients and high nonlinearity.