A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows

Harish Ramachandran¹ Björn Kimpel¹ Thomas Paula¹ Josef Winter¹ Steffen Schmidt¹ Nikolaus Adams^1,2

¹ Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Germany
² Munich Institute of Integrated Materials, Energy and Process Engineering, Technical University of Munich, Germany

Read Paper arXiv GitHub Code Hugging Face

Datasets

Trajectories

Baselines

Evaluation Metrics

TL;DR

~3 TB high-fidelity benchmark dataset for shock-driven compressible multiphase flows, covering bubble collapse and droplet breakup in 2D and 3D.
systematic benchmark of diverse surrogate models, including convolutional, operatorbased, transformer-based, and pre-trained PDE foundation models.
investigation of physics- and structure-aware composite losses, combining MSE with derivative-, interface-, and structure-focused terms and adaptive loss balancing.
reliability-focused evaluation framework extending beyond pointwise errors to spectral, structural, flow feature-focused, structure-aware and physics-informed metrics.

Abstract

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 3 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna , including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, featurefocused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

Datasets & Benchmark Results

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Model Performance Comparison

Raw metric values are min-max normalized across all baseline models and training-loss strategies for each dataset, then inverted (1 - normalized value) so lower errors correspond to higher radar-chart scores. The models were trained with a resolution of 256x256 in 2D and 128x128x128 in 3D, but we provide other resolutions in the HuggingFace repository.

Training Strategies

Toggle multiple strategies to overlay:

Standard ―

Training Metric: Fixed weight
MSE: 1.0

SoftAdapt --

Training Metric: Initial weight
MSE: 1.0, IRMSE: 1.0, SSIM: 0.5, H1: 2.0

GradNorm ···

Training Metric: Initial weight
MSE: 1.0, IRMSE: 1.0, SSIM: 0.5, H1: 2.0

Models:

Info: 4, 1, 10 → 4 input snapshots, 1 predicted snapshot, with a stride of 10 frames between two consecutive snapshots.

Citation

If you use Neptuna or its benchmark datasets in your research, please cite our work:

@article{ramachandran2026neptunacomprehensivemachinelearning,
      title={Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows}, 
      author={Harish Ramachandran and Björn Kimpel and Thomas Paula and Josef Winter and Steffen Schmidt and Nikolaus Adams},
      year={2026},
      eprint={2607.22280},
      archivePrefix={arXiv},
      primaryClass={physics.flu-dyn},
      url={https://arxiv.org/abs/2607.22280}, 
}