Improved constrained physics-informed neural networks (ICPINNs) to solve PDE and its application to option pricing

Jianguo Tan and Xingyu Zhang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PA, 908-924

Abstract: Previous deep learning methods, whether using hard or soft constraints, have often exhibited slow convergence when dealing with more than two types of boundary conditions (BCs). In general, option pricing partial differential equations (PDEs) encompass a mix of Dirichlet and non-Dirichlet BCs [1]. Hence, we propose a new method, the ICPINN method, which combines the soft-constraint and hard-constraint BCs to impose constraints based on different types of BCs for PDE. The ICPINN method is highly accurate for solving PDEs with Dirichlet and non-Dirichlet BCs. To verify the capacity of the ICPINN method, we apply it to the Black-Scholes (BS) model, the Heston option pricing PDE, and the three-asset BS model. The results show that the numerical solutions obtained by the ICPINN method can accurately converge to the exact solutions of the three financial option pricing PDEs. At the same time, the ICPINN method is more accurate. It converges faster than Physics-Informed Neural Networks (PINNs), PINNs with hard constraints (hPINNs), and boundary-safe PINNs.

Keywords: Deep learning; Hard-constraint and soft-constraint boundary conditions; Neural network; Option pricing (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pa:p:908-924

DOI: 10.1016/j.matcom.2025.10.005

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