4 papers
Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations
Heng Wu, Junjie Wang, Benzhuo Lu
Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical appl…
From Volatility to Variance: A Skew-Enhanced SABR Model and Its Empirical Study in the Chinese Financial Options Market
Wenxuan Zhang, Zhouchi Lin, Benzhuo Lu
Accurately characterizing the implied volatility curves is a central challenge in option pricing and risk management. The classical SABR model by Hagan et al. has been widely adopt…
Operator learning on domain boundary through combining fundamental solution-based artificial data and boundary integral techniques
Haochen Wu, Heng Wu, Benzhuo Lu
For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data…
Mathematical artificial data for operator learning
Heng Wu, Benzhuo Lu
Machine learning has emerged as a transformative tool for solving differential equations (DEs), yet prevailing methodologies remain constrained by dual limitations: data-driven met…