Numerical Methods for Partial Differential Equations Seminar

PDE-constrained optimization (PDE-CO) is central to scientific and engineering design but remains limited by computationally expensive solvers and the lack of reusable structure across tasks. Solver-informed learning offers a promising alternative: training AI models in the input space of PDE solvers to preserve physics fidelity, yield interpretable parameterizations, and support generalization while reducing overall design cost. This presentation outlines how input-space representations can bridge physics, optimization, and machine learning—encoding mathematical structure, enabling effective use of low-fidelity solvers, and revealing latent spaces suitable for optimization.

TBD