The Data Bottleneck in Neural Operators for Engineering Systems: Challenges and Paths Forward

Abstract: Neural operators such as DeepONet and Fourier Neural Operators have shown remarkable promise in learning solution mappings for parametric partial differential equations, offering orders-of-magnitude speedups over traditional solvers. However, their deployment in real engineering systems faces a fundamental chicken-and-egg problem: training these data-hungry models demands large, high-fidelity datasets that are precisely what engineering applications struggle to provide. In practice, experimental measurements are expensive, sparse, and often limited to a handful of observable quantities — for instance, only a few discrete temperature readings may be available in a low-pressure turbine environment, while velocity and pressure fields remain entirely unobservable. High-fidelity simulations can in principle fill these gaps, but they carry their own burdens: long turnaround times, high computational cost, and persistent difficulties in calibration against complex real-world geometries. This talk examines the tension between the data requirements of modern operator learning and the realities of engineering data acquisition, and discusses emerging strategies — including physics-informed training, multi-fidelity fusion, transfer learning, and hybrid simulation-measurement frameworks — for charting a viable path forward.