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Explore a 14-minute conference presentation from OOPSLA 2025 that introduces Phocus, the first abstract interpretation framework specifically designed for hyperbolic partial differential equation (PDE) solvers. Learn how researchers from Georgia Institute of Technology, Lawrence Livermore National Laboratory, and Argonne National Laboratory developed this groundbreaking tool to address critical challenges in scientific computing and engineering applications. Discover how Phocus certifies precise bounds on nonlinear PDE solutions and verifies essential numerical invariants including the CFL condition and total variation bounds, enabling verification of shock formation absence, solver stability, and spurious numerical effects control. Understand the novel optimization-based procedure used to synthesize precise abstract transformers for multiple finite difference schemes, which enables effective abstract interpretation of hyperbolic PDE solvers. Examine the comprehensive experimental evaluation demonstrating Phocus's significant precision benefits and scalability to several thousand mesh points using a newly developed set of PDE benchmark programs. Gain insights into how this research addresses the fundamental problems of program execution crashes due to overflow and unacceptable inaccuracy levels from spurious oscillations or dissipation that plague numerical PDE solvers, particularly for nonlinear hyperbolic equations where shock wave formation and numerical approximations create complex computational challenges.
