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Explore advanced techniques for solving stiff ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) through innovative symbolic-numeric compiler approaches in this 30-minute conference talk. Learn how breaking conventional numerical-only solver assumptions can dramatically improve performance and robustness by integrating specialized computation and symbolic-numeric techniques directly into ODE solvers. Discover how BDF methods and SDIRK methods can be enhanced through automatic splitting of nonlinear systems into strongly connected components, specialized tearing passes, symbolic nonlinear solvers, and homotopy routines using ModelingToolkit's code generation capabilities. Understand the revolutionary approach that achieves orders of magnitude performance improvements over traditional open source solvers by fundamentally changing the computational paradigm from purely numerical to hybrid symbolic-numeric methods, and gain insights into the algorithmic possibilities that emerge when symbolic techniques are seamlessly integrated into numerical computations.
