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Solving partial differential equations (PDEs) by learning the solutionoperators has emerged as an attractive alternative to traditional numericalmethods. However, implementing such architectures presents two main challenges:flexibility in handling irregular and arbitrary input and output formats andscalability to large discretizations. Most existing architectures are limitedby their desired structure or infeasible to scale large inputs and outputs. Toaddress these issues, we introduce an attention-based model called aninducing-point operator transformer (IPOT). Inspired by inducing pointsmethods, IPOT is designed to handle any input function and output query whilecapturing global interactions in a computationally efficient way. By detachingthe inputs/outputs discretizations from the processor with a smaller latentbottleneck, IPOT offers flexibility in processing arbitrary discretizations andscales linearly with the size of inputs/outputs. Our experimental resultsdemonstrate that IPOT achieves strong performances with manageablecomputational complexity on an extensive range of PDE benchmarks and real-worldweather forecasting scenarios, compared to state-of-the-art methods.

Inducing Point Operator Transformer: A Flexible and Scalable Architecture for Solving PDEs