  Solving partial differential equations (PDEs) by learning the solution
operators has emerged as an attractive alternative to traditional numerical
methods. However, implementing such architectures presents two main challenges:
flexibility in handling irregular and arbitrary input and output formats and
scalability to large discretizations. Most existing architectures are limited
by their desired structure or infeasible to scale large inputs and outputs. To
address these issues, we introduce an attention-based model called an
inducing-point operator transformer (IPOT). Inspired by inducing points
methods, IPOT is designed to handle any input function and output query while
capturing global interactions in a computationally efficient way. By detaching
the inputs/outputs discretizations from the processor with a smaller latent
bottleneck, IPOT offers flexibility in processing arbitrary discretizations and
scales linearly with the size of inputs/outputs. Our experimental results
demonstrate that IPOT achieves strong performances with manageable
computational complexity on an extensive range of PDE benchmarks and real-world
weather forecasting scenarios, compared to state-of-the-art methods.
