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<p>Deep operator network (DeepONet) has shown great success in learning nonlinear operators, but their reliance on uniformly sampled inputs limits their applicability to real-world scenarios where data are often collected at irregular spatial locations. To address this issue, we propose an enhanced DeepONet architecture capable of handling irregular input grids. Specifically, we replace the conventional fast Fourier transform (FFT) in the Fourier neural operator (FNO) with a nonuniform discrete Fourier transform (NDFT), enabling direct processing of nonuniformly sampled inputs. We refer to this modified network as the nonuniform Fourier neural operator (NFNO). By integrating the NFNO into the branch network of the standard DeepONet architecture, the resulting framework, referred to as NFNO-DeepONet, enables the network to learn operator mappings directly from nonuniformly sampled data. A series of numerical experiments demonstrates the effectiveness of the proposed NFNO-DeepONet framework. Moreover, the framework exhibits strong flexibility in handling different sampling strategies, enabling better capture of localised features.</p>

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Deeponet with a modified FNO branch network based on nonuniform Fourier transform for irregular input grids

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Andong Cong,
  • Yuhong Jin,
  • Haiming Yi,
  • Yifan Jiang,
  • Jun Li,
  • Shijun Wang,
  • Lei Hou

摘要

Deep operator network (DeepONet) has shown great success in learning nonlinear operators, but their reliance on uniformly sampled inputs limits their applicability to real-world scenarios where data are often collected at irregular spatial locations. To address this issue, we propose an enhanced DeepONet architecture capable of handling irregular input grids. Specifically, we replace the conventional fast Fourier transform (FFT) in the Fourier neural operator (FNO) with a nonuniform discrete Fourier transform (NDFT), enabling direct processing of nonuniformly sampled inputs. We refer to this modified network as the nonuniform Fourier neural operator (NFNO). By integrating the NFNO into the branch network of the standard DeepONet architecture, the resulting framework, referred to as NFNO-DeepONet, enables the network to learn operator mappings directly from nonuniformly sampled data. A series of numerical experiments demonstrates the effectiveness of the proposed NFNO-DeepONet framework. Moreover, the framework exhibits strong flexibility in handling different sampling strategies, enabling better capture of localised features.