Size Lowerbounds for Deep Operator Networks

Anirbit Mukherjee, Amartya Roy

Research output: Contribution to journalArticlepeer-review


Deep Operator Networks are an increasingly popular paradigm for solving regression in infinite dimensions and hence solve families of PDEs in one shot. In this work, we aim to establish a first-of-its-kind data-dependent lowerbound on the size of DeepONets required for them to be able to reduce empirical error on noisy data. In particular, we show that for low training errors to be obtained on n data points it is necessary that the common output dimension of the branch and the trunk net be scaling as Ω (n¼). This inspires our experiments with DeepONets solving the advection-diffusion-reaction PDE, where we demonstrate the possibility that at a fixed model size, to leverage an increase in this common output dimension and get a monotonic lowering of training error, the size of the training data might necessarily need to scale at least quadratically with it.
Original languageEnglish
Number of pages25
JournalTransactions on Machine Learning Research
Publication statusPublished - 1 Feb 2024


  • Partial differential equations (PDEs)
  • Operators
  • Deep Learning

Research Beacons, Institutes and Platforms

  • Institute for Data Science and AI


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