# Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows

arXiv: https://arxiv.org/abs/2607.22280 · HTML: https://mlsanity.com/paper/2607.22280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Understanding SSIM](https://mlsanity.com/paper/2006.13846/) (2020)
- [SoftAdapt: Techniques for Adaptive Loss Weighting of Neural Networks with Multi-Part Loss Functions](https://mlsanity.com/paper/1912.12355/) (2019)
- [BubbleML: A Multi-Physics Dataset and Benchmarks for Machine Learning](https://mlsanity.com/paper/2307.14623/) (2023)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [Sobolev Training for Operator Learning](https://mlsanity.com/paper/2402.09084/) (2024)
- [Benchmarking neural surrogates on realistic spatiotemporal multiphysics flows](https://mlsanity.com/paper/2512.18595/) (2025)
- [A generalised novel loss function for computational fluid dynamics](https://mlsanity.com/paper/2411.17059/) (2024)
- [Wavelet-based Loss for High-frequency Interface Dynamics](https://mlsanity.com/paper/2209.02316/) (2022)

## Abstract (arXiv)

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 2.4 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 {https://github.com/tumaer/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, feature-focused, 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.