Results 101 to 110 of about 2,183,872 (273)

Rough PDEs for Local Stochastic Volatility Models

Mathematical Finance, EarlyView.
ABSTRACT In this work, we introduce a novel pricing methodology in general, possibly non‐Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time‐inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely
Peter Bank, Christian Bayer, Peter K. Friz, Luca Pelizzari   +3 more
wiley   +1 more source

Systemic Robustness: A Mean‐Field Particle System Approach

Mathematical Finance, EarlyView.
ABSTRACT This paper is concerned with the problem of capital provision in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a financial network. Motivated by Tang and Tsai, we focus on the number or proportion of surviving entities that never default to ...
Erhan Bayraktar, Gaoyue Guo, Wenpin Tang, Yuming Paul Zhang   +3 more
wiley   +1 more source

Geometry physics neural operator solver for solid mechanics

Computer-Aided Civil and Infrastructure Engineering, EarlyView.
Abstract This study developed Geometry Physics neural Operator (GPO), a novel solver framework to approximate the partial differential equation (PDE) solutions for solid mechanics problems with irregular geometry and achieved a significant speedup in simulation time compared to numerical solvers. GPO leverages a weak form of PDEs based on the principle
Chawit Kaewnuratchadasorn, Jiaji Wang, Chul‐Woo Kim, Xiaowei Deng   +3 more
wiley   +1 more source

Hybrid physics‐informed neural network with parametric identification for modeling bridge temperature distribution

Computer-Aided Civil and Infrastructure Engineering, EarlyView.
Abstract This paper introduces a novel hybrid multi‐model thermo‐temporal physics‐informed neural network (TT‐PINN) framework for thermal loading prediction in composite bridge decks. Unlike the existing PINN applications in heat transfer that focus on simple geometries, this framework uniquely addresses multi‐material domains and realistic boundary ...
Yanjia Wang, Dong Yang, Ye Yuan, Jing Zhang, Francis T. K. Au   +4 more
wiley   +1 more source

PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs [PDF]

arXiv
While recent AI-for-math has made strides in pure mathematics, areas of applied mathematics, particularly PDEs, remain underexplored despite their significant real-world applications. We present PDE-Controller, a framework that enables large language models (LLMs) to control systems governed by partial differential equations (PDEs).
arxiv  

Intrinsic Hopf–Lax formula and Hamilton–Jacobi equation

Bulletin of the London Mathematical Society, EarlyView.
Abstract The purpose of this article is to analyze the notion of intrinsic Hopf–Lax formula and its connection with the Hamilton–Jacobi‐type equation.
Daniela Di Donato
wiley   +1 more source

On the deep‐water and shallow‐water limits of the intermediate long wave equation from a statistical viewpoint

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley   +1 more source

Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge

Quantitative Biology, Volume 13, Issue 3, September 2025.
Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Peng Zhang, Ting Gao, Jin Guo, Jinqiao Duan   +3 more
wiley   +1 more source

On the isoperimetric Riemannian Penrose inequality

Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 1042-1085, May 2025.
Abstract We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM$\operatorname{ADM}$ mass being a well‐defined geometric invariant.
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri   +2 more
wiley   +1 more source

Weak gauge PDEs [PDF]

arXiv
Gauge PDEs generalise the AKSZ construction when dealing with generic local gauge theories. Despite being very flexible and invariant, these geometrical objects are usually infinite-dimensional and are difficult to define explicitly, just like standard infinitely-prolonged PDEs.
arxiv