Meshless solutions of PDE inverse problems on irregular geometries

arXiv — cs.LGThursday, October 30, 2025 at 4:00:00 AM
A new method for solving inverse and optimization problems related to nonlinear partial differential equations (PDEs) on complex geometries has been introduced. This approach uses spectral bases defined on hyperrectangles to parameterize solutions, making it easier to tackle long-standing challenges in the field. This advancement is significant as it opens up new possibilities for researchers dealing with irregular spatial domains, potentially leading to more efficient and accurate solutions in various applications.
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