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.
By Samira Amiriyan, Youness Boutaib
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.
By Yan Ma, Yumeng Ren, Elisabeth Larsson
arXiv:2609.31570v1 Announce Type: new
Abstract: Deep learning has substantially accelerated the calibration of complex stochastic-volatility models, but neural point calibration alone does not captur...
By Damiano Brigo, Rapha\"el Huser, Dan Leonte
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...
By Juli Huang, Jake Cheng, Rupert Lu
arXiv:2609.38916v1 Announce Type: new
Abstract: Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and...
By Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith, Soledad Villar
arXiv:2607. 01185v1 Announce Type: new Abstract: Combinatorial optimization (CO) problems are difficult because certifiable discrete structure induces exponential search.
By Jingyi Chen, Xinyuan Zhang, Xinwu Qian
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou
arXiv:2607. 23068v1 Announce Type: cross Abstract: This paper introduces a compact reformulation of a modular end-to-end neural network for global minimum-variance portfolio optimization that decouples model complexity from both look-back window length and universe size.
By Christian Bongiorno, Efstratios Manolakis, Rosario Nunzio Mantegna
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
By Yushun Zhang
arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.
By Marc Haltmayer, Jaemin Seo, Yuseung Lee, Sungyeop Lee, Jaehoon Jeong, Jae Yong Lee
arXiv:2606. 28519v1 Announce Type: new Abstract: Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints, and limited training data.
By Christian Munoz, Alexandre Tartakovsky
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
By Joseph Webb, Sadok Jerad, Coralia Cartis