This volume contains the proceedings of the Verification of Scientific Software (VSS 2025) workshop, held on 4 May 2025 at McMaster University, Canada, as part of ETAPS 2025. VSS brings together researchers in software verification and scientific computing to address challenges in ensuring the correctness and reliability of large-scale scientific codes. The program featured five peer-reviewed papers, three invited contributions, and a set of challenge problems, covering themes such as deductive verification, floating-point error analysis, specification of coupled models, and domain-aware testing. VSS builds on the Correctness Workshop series at Supercomputing and the 2023 NSF/DOE report on scientific software correctness. It serves as yet another snapshot of this important area, showcasing a wide range of perspectives, problems and their solutions in progress, with the challenge problems having the potential to bring together separate verification tools into concerted action.
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