Unlocking the Performance of Neural Surrogates in Real-World Applications

Partial Differential Equations (PDEs) are foundational to modeling complex phenomena across the natural sciences and engineering, from fluid dynamics and quantum systems to climate modeling and materials science. Despite their ubiquity, solving PDEs remains computationally intensive, especially in high-dimensional, multi-physics, and uncertain regimes. Recent advances in machine learning—such as neural operators, physics-informed networks, and foundation models—offer transformative potential to accelerate and generalize PDE solutions. However, realizing this promise requires addressing critical challenges in representation, stability, generalization, and benchmarking.

In this Keynotes we present advances on AI for PDEs at IBM Research in collaboration with three prestigious collaboartors: Dallara, LNCC, and NASA.