mlsanityData to 7 Oct 2026

Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks

arXiv 2512.04434 ↗First posted 4 Dec 2025physics.flu-dyn cs.LGcited by 0

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Abstract (arXiv)

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains ~ 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 19 of its 44 references that are in the map. First posted on arXiv 4 Dec 2025.

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19 of 44 references.

References · 19

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  3. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  6. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  7. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
  8. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  9. 2023Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loadscited by 47
  10. 2024Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometriescited by 47
  11. 2023Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionalscited by 26
  12. 2023Improved generalization with deep neural operators for engineering systems: Path towards digital twincited by 19
7 more
  1. 2024FlowBench: A Large Scale Benchmark for Flow Simulation over Complex Geometriescited by 18
  2. 2023A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel constructioncited by 12
  3. 2024Advanced Deep Operator Networks to Predict Multiphysics Solution Fields in Materials Processing and Additive Manufacturingcited by 12
  4. 2019SkelNetOn 2019: Dataset and Challenge on Deep Learning for Geometric Shape Understandingcited by 10
  5. 2022Neural PDE Solvers for Irregular Domainscited by 6
  6. 2025Direct Flow Simulations with Implicit Neural Representation of Complex Geometrycited by 2
  7. 20253D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraintscited by 2

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