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LieSolver: A PDE-constrained solver for IBVPs using Lie symmetries

arXiv — cs.LG•Thursday, October 30, 2025 at 4:00:00 AM
PositiveArtificial Intelligence
A new method called LieSolver has been introduced for solving initial-boundary value problems (IBVPs) using Lie symmetries. This innovative approach ensures that the associated partial differential equations (PDEs) are accurately enforced by construction, which means the model can effectively incorporate physical laws and learn from initial and boundary data. This leads to a more accurate measurement of the model's performance and improved convergence rates. The development of such a solver is significant as it enhances the efficiency and reliability of solving complex mathematical problems, which can have wide-ranging applications in science and engineering.
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