mlsanityData to 14 Oct 2026

Spectral-Embedded Operator Learning for Three-Phase Interfacial Flow: A Ternary Cahn-Hilliard-Navier-Stokes Benchmark

arXiv 2608.29069 ↗First posted 29 Aug 2026physics.flu-dyn cs.LGcited by 0

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Abstract (arXiv)

Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices validated in those settings transfer to constrained, multiphase flows. We introduce a three-phase interfacial-flow benchmark to examine whether the trunk coordinate representation matters for a multi-channel, interface-dominated target. The configuration consists of an air bubble rising through water, piercing a water-oil interface, and entraining a water plume into the oil within a bounded, wall-confined domain. Reference data are generated using a structure-preserving ternary Cahn-Hilliard-Navier-Stokes solver that algebraically preserves the simplex constraint. From 1,024 Sobol-sampled simulations spanning a nine-dimensional parameter space, we learn the mapping from physical parameters to five-channel space-time fields. We compare three parameter-matched DeepONet variants differing only in trunk representation: raw coordinates (DeepONet), random Fourier features (FEDONet), and a fixed tensor-product Chebyshev dictionary (SEDONet). SEDONet reduces the test relative L2 error by 16.8% compared with FEDONet and by 24.0% compared with DeepONet, while improving all five output channels. Spatial and temporal error analyses localize the principal gains near the diffuse interfaces and after bubble breakthrough. The results indicate that the Chebyshev representation is particularly effective for the strongly non-periodic wall-normal and temporal structure of this three-phase flow.

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References · 25

  1. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
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  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
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  12. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
13 more
  1. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  2. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  3. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 284
  4. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214
  5. 2024Poseidon: Efficient Foundation Models for PDEscited by 200
  6. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 138
  7. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  8. 2022Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operatorscited by 47
  9. 2022Mitigating spectral bias for the multiscale operator learningcited by 44
  10. 2025Neural Chaos: A Spectral Stochastic Neural Operatorcited by 21
  11. 2025FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learningcited by 8
  12. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 6
  13. 2024Chebyshev Feature Neural Network for Accurate Function Approximationcited by 4

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