MPFBench: A Large Scale Dataset for SciML of Multi-Phase-Flows: Droplet and Bubble Dynamics

Mehdi Shadkhah, Ronak Tali, Ali Rabeh, Cheng-Hau Yang, Ethan Herron, Abhisek Upadhyaya, Adarsh Krishnamurthy, Chinmay Hegde, Aditya Balu, Baskar Ganapathysubramanian

Abstract: Multiphase fluid dynamics, such as falling droplets and rising bubbles, is critical for many industrial applications. However, simulating these phenomena efficiently is challenging due to the complexity of instabilities, wave patterns, and bubble breakup. This paper investigates the potential of scientific machine learning (SciML) to model these dynamics using neural operators and foundation models. We apply sequence-to-sequence learning techniques to a comprehensive dataset of 11,000 simulations, which includes over 1 million time snapshots, generated using a well-validated, CUDA-accelerated Lattice Boltzmann Method (LBM) framework. The results demonstrate the ability of machine learning models to capture transient dynamics and intricate fluid interactions, paving the way for more accurate and computationally efficient SciML-based solvers for multiphase applications.

Keywords: Scientific Machine Learning, Multiphase Flow Simulation, Neural Operators, vision transformers (ViT), Bubble and Droplet Dynamics, Benchmark Dataset

Changes Since Last Submission:

- **Abstract**: Clarified dataset description — standardized number formatting (e.g., `11000` → `11,000`), added “CUDA-accelerated” before Lattice Boltzmann Method, and expanded abbreviation (LBM) on first use. Replaced “produced with” with “generated using” for precision.

- **Introduction**: Revised SciML definition to explicitly connect it to solving multiphase flow problems.

- **Related Work**: Expanded definition of “sample” to include a concrete example (e.g., bubble-rising experiment) and clarified the difference between “sample” and “snapshot”.

- **Section 3.1 – Boundary Conditions**: Added explicit coordinate notation `(x, y) = (64, 64)` for clarity and consistency with later sections.

- **Section 3.1 – Parameter Ranges**: Rephrased “selected random, dimensionless numbers uniformly…” to “uniformly sampled the dimensionless numbers…” for conciseness.

- **Metadata – Input Fields**: Changed “have provisioned” to “use” for simplicity and added reference to Section 3.1 for traceability.

- **Difficulty Classification**: Expanded explanation of how “High”, “Low”, and transitional difficulty levels are determined using a quantile-based method (upper 40%, lower 40%, middle 20%).

- **General Formatting**: Standardized number formatting (e.g., `11000` → `11,000`), ensured consistent capitalization and abbreviation expansion for technical terms (e.g., LBM, neural operator), and improved grammar for conciseness and clarity.

Assigned Action Editor: ~Yi_Liu12

Submission Number: 108