No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

arXiv:2607.23667 · math.NA, cs.LG, cs.NA, physics.flu-dyn · Submitted 2026-07-26 · Read on arXiv

math.NA, cs.LG, cs.NA, physics.flu-dyn

Submitted: 2026-07-26

Updated: 2026-09-24

Comments: 23 pages, 12 figures. v2: revised version, under review at Journal of Computational Science

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• DeepONet — 29× in this paper · explained in 2 episodes
• Accuracy — 13× in this paper · explained in 1 episode
• Hallucination — 10× in this paper · explained in 3 episodes
• Benchmark — 8× in this paper · explained in 2 episodes
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• International Conference on Learning Representations — 3× in this paper
• Latent Representation — 3× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Active Learning — 2× in this paper · explained in 6 episodes
• Decode — 2× in this paper · explained in 2 episodes
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• Inverse Problem — 2× in this paper · explained in 2 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Dynamic Time Warping (DTW) — 1× in this paper · explained in 2 episodes
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• International Conference on Machine Learning — 1× in this paper
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• Time Series Forecasting — 1× in this paper · explained in 3 episodes
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Sources

• AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields
• Fourier Neural Operator for Parametric Partial Differential Equations
• Variational Autoencoding Neural Operators
• Choose a Transformer: Fourier or Galerkin
• GNOT: A General Neural Operator Transformer for Operator Learning
• U-NO: U-shaped Neural Operators
• On the Benefits of Memory for Modeling Time-Dependent PDEs
• What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning
• Neural Emulator Superiority: When Machine Learning for PDEs Surpasses its Training Data
• Recurrent Neural Operators: Stable Long-Term PDE Prediction
• Message Passing Neural PDE Solvers
• PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
• Performance of Neural and Polynomial Operator Surrogates
• On instabilities in neural network-based physics simulators
• Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
• Efficiently Modeling Long Sequences with Structured State Spaces
• On the Parameterization and Initialization of Diagonal State Space Models
• Mamba: Linear-Time Sequence Modeling with Selective State Spaces
• Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems
• Geometry-Informed Neural Operator for Large-Scale 3D PDEs

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