Differentiating Singular Computations

Researchers from the Massachusetts Institute of Technology, POSTECH, and KAIST have created SingularFlow, the first programming language with well-defined semantics for integrating and differentiating singular functions—mathematical functions that become undefined at certain points. The system addresses a fundamental challenge in scientific computing where traditional programming languages struggle with singularities that arise in physics, aerodynamics, mechanical engineering, and computer graphics. SingularFlow enables the evaluation and differentiation of singular integrals, opening new possibilities for neural approximations of complex physical simulations and mathematical problems. The work demonstrates practical applications in areas such as aerodynamics modeling and electrical engineering. The research was recently accepted for publication at the Conference on Programming Language Design and Implementation (PLDI) 2025