From PDE to Pipeline: When LLMs Become Numerical Architects
Simulation has an awkward little secret: the hard part is often not writing code. It is choosing the right numerical method before the code exists. Anyone can ask an LLM to produce a solver for an advection equation, a heat equation, or a Navier–Stokes toy problem. The result may even run. That is not the same as being numerically sane. A PDE solver can be syntactically valid, computationally impressive, and mathematically ridiculous at the same time. In scientific computing, this is not a charming personality flaw. It is how bad answers acquire nice plots. ...