arXiv:2601. 12704v2 Announce Type: replace Abstract: The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets.
arXiv:2608. 02778v1 Announce Type: new Abstract: We present a novel application of Neural Networks with Local Converging Inputs (NNLCI) to improve the efficiency of existing numerical methods for pricing multi-asset options.
arXiv:2608. 14619v1 Announce Type: new Abstract: This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture.
arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.
Physics-Informed Error Field Learning (PIEFL) is a post‑training optimization framework for Physics‑Informed Neural Networks (PINNs). After a primary network reaches satisfactory accuracy, PIEFL introduces an auxiliary error network that learns the discrepancy between the current approximation and the exact solution by deriving error control equations under physical constraints. The learned error correction is then combined with the primary prediction, improving solution accuracy without modifying the primary network architecture and focusing computational resources on correcting existing prediction errors.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
The paper introduces asymptotically-informed neural‑network architectures for computing Black‑Scholes implied volatility. By learning a trainable partition of the price‑log‑moneyness domain and combining specialised local approximations, the models outperform standard feed‑forward networks across a wide range of parameters. The neural‑network outputs also serve as highly accurate initial guesses for a third‑order Householder scheme, enabling near machine‑precision results after only two refinement iterations.
arXiv:2606. 16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters.
arXiv:2605. 31027v2 Announce Type: replace Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs).
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2609.27764v1 Announce Type: new Abstract: We treat options pricing as a representation problem: can machine learning detect systematic deviations from Black-Scholes using 2.6M real option contr...
The paper proposes a method to amortize physics-informed neural networks (PINNs) across related partial differential equations (PDEs) by explicitly modeling equation relationships in an operator graph. Coefficient vectors encode numerical parameters, while the graph hypernetwork generates diagonal codes that initialize a meta‑trained factorized PINN for each target equation. Experiments on scalar convection‑diffusion‑reaction, two‑field Fisher‑KPP, and a capacitively coupled plasma model show that term‑based descriptors and graph conditioning improve solution accuracy compared to coefficient‑vector conditioning alone.
arXiv:2602.01176v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physica...