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Schrödingerisation based computationally stable algorithms for ill-posed problems in partial differential equations

组织者

李震 , 梁鑫 , 马志婷 , 哈米德·莫菲迪 , 王丽 , 熊繁升 , 杨朔 , 杨武岳

演讲者

马楚雯

时间

2025年05月08日 15:00 至 16:00

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

We introduce a simple and stable computational method for ill-posed partial differential equation (PDE) problems. The method is based on Schrödingerisation, introduced in [S. Jin, N. Liu and Y. Yu, arXiv:2212.13969], which maps all linear PDEs into Schrödinger-type equations in one higher dimension, for quantum simulations of these PDEs. Although the original problem is ill-posed, the Schrödingerised equations are Hamiltonian systems and time-reversible, allowing stable computation both forward and backward in time. The original variable can be recovered by data from suitably chosen domain in the extended dimension. We will use the (constant and variable coefficient) backward heat equation and the linear convection equation with imaginary wave speed as examples. Error analysis of these algorithms are conducted and verified numerically. The methods are applicable to both classical and quantum computers, and we also lay out quantum algorithms for these methods.