What question did this study set out to answer?

This research aims to solve the inverse problem related to high-dimensional sideways parabolic equations and to establish the uniqueness and stability of solutions.

June 28, 2026Applicable Analysis

Numerical optimization method for solving high-dimensional sideways parabolic problems

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Authors

ZQZhonglong QiuShanghai University of Finance and Economics DXDinghua XuZhejiang Sci-Tech University

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Implication

Randomized trial explores solutions for high-dimensional parabolic equations, suggesting stability and uniqueness.

Key Points

This research aims to solve the inverse problem related to high-dimensional sideways parabolic equations and to establish the uniqueness and stability of solutions.
Reformulated the inverse problem as an optimal control problem using Kohn-Vogelius regularization.
Analyzed the ill-posedness of the problem and established the uniqueness of its solutions.
Applied a physics-informed neural network framework for numerical examples.
Demonstrated existence of stable solutions for the optimal control problem.
Supported the uniqueness of solutions through theoretical analysis.
Showcased the effectiveness of the physics-informed neural network framework in numerical examples.

Cite This Study

Qiu et al. (2026) studied this question.

synapsesocial.com/papers/6a40b92b61bb0a67205c5886 https://doi.org/10.1080/00036811.2026.2689704

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Numerical optimization method for solving high-dimensional sideways parabolic problems

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Implication

Key Points

Cite This Study

Numerical optimization method for solving high-dimensional sideways parabolic problems

Discussion

Member takes

Implication

Key Points

Cite This Study

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