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ABSTRACT: This colloquium surveys a programme that fuses modern machine learning with classical scientific computing. I will begin with operator networks that learn the solution map of partial differential equations and show that full 3D Navier–Stokes simulations can match high-fidelity CFD accuracy while cutting computational cost by orders of magnitude. I will then introduce an AI-guided metamaterial pipeline in which deep generative models, constrained by physics, traverse vast design spaces to uncover novel acoustic and electromagnetic structures beyond conventional optimisation. Finally, I will present physics-aware weather models that embed physics laws into transformer-based spatiotemporal networks, yielding kilometre-scale forecasts that outperform other recent approaches. Time permitting, I will outline current work on a cross-domain “foundation” model unifying these ideas.