SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Sheikh Md Shakeel Hassan $^{1*†}$  Arthur Feeney $^{1*†}$  Akash Dhruv $^{2}$  Jihoon Kim $^{3}$  Youngjoon Suh $^{1}$  Jaiyoung Ryu $^{3}$  Yoonjin Won $^{1}$  Aparna Chandramowlishwaran $^{1†}$ $^{1}$ University of California, Irvine  $^{2}$ Argonne National Laboratory  $^{3}$ Korea University
In the field of phase change phenomena, the lack of accessible and diverse datasets suitable for machine learning (ML) training poses a significant challenge. Existing experimental datasets are often restricted, with limited availability and sparse ground truth, impeding our understanding of this complex multiphysics phenomena. To bridge this gap, we present the BubbleML dataset which leverages physics-driven simulations to provide accurate ground truth information for various boiling scenarios, encompassing nucleate pool boiling, flow boiling, and sub-cooled boiling. This extensive dataset covers a wide range of parameters, including varying gravity conditions, flow rates, sub-cooling levels, and wall superheat, comprising 79 simulations. BubbleML is validated against experimental observations and trends, establishing it as an invaluable resource for ML research. Furthermore, we showcase its potential to facilitate the exploration of diverse downstream tasks by introducing two benchmarks: (a) optical flow analysis to capture bubble dynamics, and (b) neural PDE solvers for learning temperature and flow dynamics. The BubbleML dataset and its benchmarks aim to catalyze progress in ML-driven research on multiphysics phase change phenomena, providing robust baselines for the development and comparison of state-of-the-art techniques and models.
Phase-change phenomena, such as boiling, involve complex multiphysics processes and dynamics that are not fully understood. The interplay between bubble dynamics and heat transfer performance during boiling presents significant challenges in accurately predicting and modeling these heat and mass transfer processes. Machine learning (ML) has the potential to revolutionize this field, enabling data-driven discovery to unravel new physical insights [1], develop accurate surrogate and predictive models [2, 3], optimize the design of heat transfer systems, and facilitate adaptive real-time monitoring and control [4].
The applications of ML in this domain are diverse and impactful. Consider the context of high-performance computing in data centers, where efficient cooling is critical. Boiling-based cooling techniques, such as two-phase liquid cooling, offer enhanced heat dissipation capabilities, ensuring reliable and optimal operation of power-intensive electronic components such as GPUs [5, 6]. Boiling also plays a central role in optimizing heat transfer in nuclear reactors, where precise modeling and prediction of boiling dynamics contribute to advancing the safety and efficiency of nuclear power systems [7]. Furthermore, boiling processes play a vital role in thermal desalination methods that provide clean drinking water in water-scarce regions [8]. These advancements in pivotal areas such
*Equal contributions
†Corresponding authors: {sheikhh1,afeeney,amowli}@uci.edu
<sup>3</sup>https://github.com/HPCForge/BubbleML
Figure 1: BubbleML Dataset. Diverse two-phase boiling phenomena with ground truth for key physical variables—velocity, temperature, and pressure. (a) Single bubble rising from a nucleation site on the heater surface. (b) Chaotic multi-bubble dynamics—merging and splitting. (c) Flow boiling transitions from bubbly to slug regime with increasing inlet velocity. Velocity and temperature fields are obtained by solving equations 1a and 1b, pressure field is obtained by solving the Poisson equation which ensures that continuity is satisfied. The physical quantities are in non-dimensional units.
as thermal management, energy efficiency, and heat transfer applications, driven by ML techniques have far-reaching implications, empowering us to design more sustainable energy systems, enhance environmental preservation efforts, and advance engineering capabilities across various domains.
To train data-driven ML algorithms effectively, we need large, diverse, and accurately labeled datasets. However, obtaining high-fidelity datasets that encompass a wide range of phase-change phenomena and operating conditions is a significant challenge. Boiling processes are highly sensitive to factors like surface properties, pressure, orientation, and working fluid composition [9]. Additionally, the chaotic nature of vapor interactions and occlusions makes quantifying boiling processes inherently difficult. Specialized experimental setups, involving instrumentation, sensors, and high-speed visualization techniques, come with substantial costs, further limiting the availability of extensive and accurate large-scale experimental data [3]. As a result, only a few well-funded research laboratories have access to precise ground truth data, and even then, this data often lacks fidelity and fails to capture detailed microscale dynamics, such as local bubble-induced turbulence and its impact on overall heat transfer. This scarcity of high-fidelity datasets poses challenges in designing accurate ML models for multiphase and phase change processes. While scientific ML (SciML) approaches can incorporate physical knowledge and constraints into the training process to reduce some of this data burden [10], the validation and quantification of uncertainty still rely on the availability of ground truth data. Therefore, there is an urgent need for open, diverse, and large-scale datasets to develop robust models and advance research in multiphysics problems such as phase change phenomena.
Simulations have played a key role as the third pillar of science in overcoming the inherent challenges faced by experimental studies in various scientific domains. High-fidelity multiscale data from simulations complement and enhance experimental measurements. In the field of phase change, simulations
have successfully modeled transport equations for momentum, energy, and phase transition, enabling accurate measurements of velocity, pressure, and temperature fields around bubbles [11, 12]. As a result, simulations serve as powerful tools for understanding and quantifying boiling. However, SciML researchers often set up their own simulations to generate ground truth solutions for training and testing their models rather than relying on open-source benchmark datasets. This practice is common even among impactful papers [10, 13, 14, 15]. While this approach is reasonable for studying specific, simple partial differential equations (PDEs), real-world applications of PDE solvers and simulations often involve large-scale systems with complex multiphase physics and a combination of Dirichlet and Neumann boundary conditions [16]. These real-world problems require significant domain expertise, engineering time, and computational resources. Independently performing such simulations is impractical and even infeasible for many ML researchers. This difficulty in dataset generation has led to a drought of SciML research to study real-world physics problems. Prior efforts to build benchmark datasets have primarily focused on single- and multiphysics problems with single-phase dynamics [17, 18, 19, 20].
As a response to the above challenges, we introduce the BubbleML Dataset  $^{4}$ , an extensive and innovative collection of data generated through Flash-X simulations [21]. This dataset encompasses a wide range of boiling phenomena, including nucleate boiling of single bubbles, merging bubbles, flow boiling in different configurations, and subcooled boiling. Figure 1 is a visual glimpse into the diverse range of physical phenomena and variables in the dataset. To further enhance its applicability, the dataset covers various gravity conditions ranging from earth gravity to gravity at the International Space Station, different heater temperatures, and different inlet velocities. In total, we present around 80 simulations, each capturing a specific combination of parameters and conditions. In summary, the key contributions are as follows:
Multiphase and Multiphysics Dataset. A comprehensive dataset encompassing a range of two-phase (liquid-vapor) phase change phenomena in boiling, with a focus on bubble and flow dynamics.
Real-world Validation. Validation against experimental data to ensure the dataset's accuracy and reliability. This validation process enhances the dataset's fidelity and establishes a strong connection between simulation and real-world phenomena.
Diverse Downstream Tasks. BubbleML is designed to facilitate diverse downstream applications. To demonstrate its potential, we present two benchmark tasks: optical flow for learning bubble dynamics and neural PDE solvers for modeling temperature and flow dynamics.
Scientific Machine Learning Datasets. There have been several efforts to develop benchmark datasets for scientific machine learning tasks [17, 18, 19, 20, 22, 23]. Notably, the ERA5 atmospheric reanalysis dataset [23], curated by the European Center for Medium-Range Weather Forecasting (ECMWF) provides hourly estimates of a large number of atmospheric, land, and oceanic climate variables since 1940. It is the most popular publicly available source for weather forecasting, facilitating the training of neural weather models such as FourCastNet [24], GraphCast [25], and ClimaX [26]. PDEBench [17] provides an impressive collection of datasets for 11 PDEs commonly encountered in computational fluid dynamics. Boundary conditions in scientific simulations play a crucial role in capturing the dynamics of the underlying physical systems. The majority of datasets in PDEBench utilize periodic boundary conditions. Although some datasets encompass Neumann or Dirichlet boundary conditions, none consider a combination of both which presents a noteworthy gap in accurately modeling real-world scenarios. Another challenging problem is the modeling of turbulent Kolmogorov flows and the dataset generated using JAX-CFD [27] is gaining popularity in benchmarking neural flow models [28, 29]. BlastNet [19] generated using DNS solver, S3D [30] focuses on simulating the behavior of a single fluid phase solving for compressible fluid dynamics, combustion, and heat transfer. AirfRANS [20] is a dataset for studying the 2D incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils. Current datasets have made commendable strides in addressing single- and multiphysics scenarios, and provide a valuable foundation for developing and evaluating SciML algorithms. Nonetheless, their scope falls short of capturing the range of behaviors and phenomena encountered in phase change physics.
4Through Zenodo, a permanent DOI for the dataset 10.5281/zenodo.8039786
In contrast, BubbleML focuses on capturing the complex dynamics and physics associated with multiphase phenomena, particularly in the context of phase change simulations. Unlike many existing datasets that predominantly utilize a single type of boundary condition, BubbleML incorporates a combination of Dirichlet and Neumann boundary conditions [16]. This inclusion enables researchers to explore and model scenarios where multiple boundary conditions coexist, enhancing the realism and applicability of the dataset. Moreover, the presence of "jump" conditions along the liquid-vapor interface adds an additional layer of complexity. These conditions arise due to surface tension effects and require careful modeling to accurately capture the interface behavior [31, 32]. By incorporating such challenges, BubbleML provides a realistic and demanding testbed for ML models.
Optical Flow Datasets. Optical flow estimation, a classical ill-posed problem [33] in image processing, has witnessed a shift from traditional methods to data-driven deep learning approaches. Middlebury [34] is a dataset with dense ground truth for small displacements, while KITTI2015 [35] provides sparse ground truth for large displacements in real-world scenes. MPI-Sintel [36] offers synthetic data with very large displacements, up to 400 pixels per frame. However, these datasets are relatively small for training deep neural networks. FlyingChairs [37], a large synthetic dataset, contains around 22,000 image pairs generated by applying affine transformations to rendered chairs on random backgrounds. FlyingThings3D [38] is another large synthetic dataset with approximately 25,000 stereo frames of 3D objects on different backgrounds.
While these datasets have been instrumental in advancing data-driven optical flow methods, they primarily focus on rigid object motion in visual scenes and do not address the specific challenges posed by multiphase simulations. Efforts have been made to capture non-rigid motion in nature, such as piece-wise rigid motions seen in animals [39]. In boiling, the non-rigid dynamics of bubbles and the motion of liquid-vapor interfaces play a crucial role in the distribution and transfer of thermal energy. The BubbleML dataset provides a unique opportunity to explore and develop optical flow algorithms tailored to phase change dynamics. Unlike existing datasets, it offers a diverse range of bubble behaviors, including merging, growing, splitting, and complex interactions (see Figure 1). The ability to accurately predict and forecast bubble dynamics has practical implications in various fields.
3 BubbleML: A Multiphase Multiphysics Dataset for ML
We first introduce the preliminary concepts underlying the SciML learning problem and give insights into the simulation and PDEs in this domain. Then, we present an overview of the dataset pipeline.
A common application for SciML is approximating the solution of boundary value problems (BVPs). BVPs are widely used to model various physical phenomena, including fluid dynamics, heat transfer, electromagnetics, and quantum mechanics [16, 40, 41, 42]. BVPs take the form:  $L[u(x)] = f(x)$ ,  $x \in \Omega$  and  $B[u(x)] = g(x)$ ,  $x \in \partial \Omega$ . The goal is to determine the vector-valued solution function,  $u$ ,  $x$  is a point in the domain  $\Omega$  and may include a temporal component. The boundary of the domain is denoted as  $\partial \Omega$ . The governing equation is described by the PDE operator  $L$ , and the forcing function is denoted as  $f$ . The boundary condition (BC) is given by the boundary operator  $B$  and the boundary function  $g$ .  $B[u] = g$  ensures the existence and uniqueness of the solution.
There are three common types of BCs: periodic, Dirichlet, and Neumann. Periodic BCs enforce the equality of the solution at distinct points in the domain:  $u(x_{1}) = u(x_{2})$ . Dirichlet BCs specify the values of the solution on the boundary:  $u(x) = g(x)$ . Neumann BCs enforce constraints on the derivatives of the solution:  $\partial_{n}u(x) = g(x)$  [16]. As seen in Figure 1, BubbleML combines both Dirichlet (no-slip walls, heater, inflow) and Neumann (outflow) boundaries, which impose constraints on flow and temperature dynamics. Additionally, the "jump conditions" that govern the transitions between the liquid and vapor phases use Dirichlet and Neumann boundaries [31].
3.2 Overview of PDEs and Flash-X Simulation
A comprehensive description of the simulations is well beyond the scope of this paper and can be found in [31, 32]. We provide a concise description here as knowledge of the PDEs is important when training physics-informed models.
The liquid  $(l)$  and vapor  $(v)$  phases of a boiling simulation are characterized by differences in fluid and thermal properties: density,  $\rho$ ; viscosity,  $\mu$ ; thermal diffusivity,  $\alpha$ ; and thermal conductivity  $k$ . The phases are tracked using a level-set function,  $\phi$ , which is positive inside the vapor and negative in the liquid.  $\phi = 0$  provides implicit representation of the liquid-vapor interface,  $\Gamma$  (see Figure 1). The transport equations are non-dimensionalized and scaled using the values in liquid and are given as,
$$
\frac {\partial \vec {u}}{\partial t} + \vec {u} \cdot \nabla \vec {u} = - \frac {1}{\rho^ {\prime}} \nabla P + \nabla \cdot \left[ \frac {\mu^ {\prime}}{\rho^ {\prime}} \frac {1}{\mathrm {R e}} \nabla \vec {u} \right] + \frac {\vec {g}}{\mathrm {F r} ^ {2}} + \vec {S} _ {u} ^ {\mathrm {T}} + S _ {P} ^ {\mathrm {T}} \tag {1a}
$$
$$
\frac {\partial T}{\partial t} + \vec {u} \cdot \nabla T = \nabla \cdot \left[ \frac {\alpha^ {\prime}}{\operatorname {R e} \Pr} \nabla T \right] + S _ {T} ^ {\Gamma} \tag {1b}
$$
where,  $\vec{u}$ , is the velocity,  $P$  is the pressure, and  $T$  is the temperature everywhere in the domain. The Reynolds number (Re), Froude number (Fr), and Prandtl Number (Pr) are constants set for each simulation. Scaled fluid properties like  $\rho'$  represent the local value of the phase scaled by the corresponding value in liquid. Therefore,  $\rho'$  is 1 in liquid phase, and  $\rho_v / \rho_l$  for vapor phase. The effect of surface tension is modeled using Weber number (We) and incorporated by a sharp pressure jump,  $S_P^\Gamma$ , at the liquid-vapor interface,  $\Gamma$ . The effects of evaporation and saturation conditions on velocity and temperature,  $\vec{S}_u^\Gamma$ , and  $S_T^\Gamma$ , are modeled using a ghost fluid method [31]. For a more detailed discussion of non-dimensional parameters and values, we refer the reader to Appendix D.
The continuity equation is given by,  $\nabla \cdot \vec{u} = -\dot{m}\nabla (\rho^{\prime})^{-1}\cdot \vec{n}$ , where the mass transfer  $\dot{m}$  is computed using local temperature gradients in liquid and vapor phase,  $\dot{m} = \mathrm{St}(\mathrm{RePr})^{-1}\left[\nabla T_{l}\cdot \vec{n}^{\Gamma} - k^{\prime}\nabla T_{v}\cdot \vec{n}^{\Gamma}\right]$  where,  $\vec{n}^{\Gamma}$  is the surface normal vector to the liquid-vapor interface. The Stefan number St, is another constant defined for the simulation and depends on the temperature scaling given by  $\Delta T = T_{wall} - T_{bulk}$ , and latent heat of evaporation,  $h_{lv}$ . Simulation data is scaled to dimensional values using the characteristic length  $l_0$ , velocity  $u_0$ , and temperature  $(T - T_{bulk}) / \Delta T$  scale. Temporal integration is implemented using a fractional step predictor-corrector formulation to enforce incompressible flow constraints. The solver has been extensively validated and demonstrates an overall second-order accuracy in space [31, 32].
In thermal science, heat flux measured as the integral of the temperature gradient across the heater surface  $(\overline{q} = \partial T / \partial y)$  serves as a vital indicator of boiling efficiency. It reflects the contribution of multiple sub-processes, such as conduction, convection, microlayer evaporation, and bubble-induced turbulence. Identifying and managing the impact of each sub-process to enhance  $\overline{q}$  is an open challenge [4, 43]. Critical heat flux (CHF) signifies peak heat flux before a sharp drop in efficiency occurs due to the formation of a vapor barrier (see Figure 5b). It is arguably the most important design and safety parameter for any heat flux controlled boiling application [44]. Accurate heat flux modeling and prediction of boiling crisis are paramount for the reliability of heat transfer systems [45, 46, 47].
The simulations in this study are implemented within the Flash-X framework [21, 31], and a dedicated environment is provided for running new simulations  $^{5}$ . The repository contains example configuration files for various multiphase simulations, including those used in this dataset. To ensure reproducibility, a lab notebook and Flash-X source code are open-source to allow for community development and contribution, enabling the creation of new datasets beyond the scope of this paper. The simulation archives store HDF5 output files and bash scripts that document software environment and repository tags for reproducibility. The lab notebook also provides an option to package Flash-X simulations as standalone Docker/Singularity containers, which can be deployed on cloud and supercomputing platforms without the need for installing third-party software dependencies. The latter is ongoing work towards software sustainability [48].
3.3 Dataset Overview
The study encompasses two types of boiling - pool boiling and flow boiling. Pool boiling represents fluid confined in a tank above a heater, resembling scenarios like cooling nuclear waste. The BCs for pool boiling include walls on the left and right, an outlet at the top, and a heater at the bottom. In contrast, flow boiling models water flowing through a channel with a heater, simulating liquid
$^{5}$  https://github.com/Lab-Notebooks/Outflow-Forcing-BubbleML
cooling of data center GPUs. There is an inlet BC modeling flow into the system and an outlet. The fluid used for the simulations is FC-72 (perfluorohexane), an electrically insulating and stable fluorocarbon-based fluid commonly used for cooling applications in electronics operating at low temperatures (ranging from  $50^{\circ}\mathrm{C}$  to  $100^{\circ}\mathrm{C}$ ). To explore various phenomena, different parameters such as heater temperature, liquid temperature, inlet velocity, and gravity scale are adjusted in each simulation. Table 1 presents a summary of the dataset. Appendix E provides detailed illustrations of the boundary conditions and descriptions of each simulation for reference.
Table 1: Summary of BubbleML datasets and their parameters.  $\Delta t$  is the temporal resolution in non-dimensional time ( $\Delta t = 1 = 0.008$  seconds). For rationale behind the parameter choices, refer to appendix A.3. PB: pool boiling. FB: flow boiling.
Dim	Type - Physics	Sims	Domain (mmd)	Resolution	Timesteps	Size (GB)
Spatial	Δt
2D	PB - Single Bubble	1	4.2 × 6.3	192 × 288	0.5	500	0.5
2D	PB - Saturated	13	11.2 × 11.2	512 × 512	1	200	24.2
2D	PB - Subcooled	10	8.4 × 8.4	384 × 384	1	200	10.3
2D	PB - Gravity	9	11.2 × 11.2	512 × 512	1	200	16.5
2D	FB - Inlet Velocity	7	29.4 × 3.5	1344 × 160	1	200	10.7
2D	FB - Gravity	6	35 × 3.5	1600 × 160	1	200	10.9
2D	PB - Subcooled0.1	15	8.4 × 8.4	384 × 384	0.1	2000	155.1
2D	PB - Gravity0.1	9	11.2 × 11.2	512 × 512	0.1	2000	163.8
2D	FB - Gravity0.1	6	35 × 3.5	1600 × 160	0.1	2000	108.6
3D	PB - Earth Gravity	1	8.753	4003	1	57	122.2
3D	PB - ISS Gravity	1	8.753	4003	1	29	62.6
3D	FB - Earth Gravity	1	35 × 3.52	1600 × 1602	1	55	93.9
BubbleML stores simulation output in HDF5 files. Each HDF5 file corresponds to the state of a simulation at a specific instant in time and can be directly loaded into popular tensor types (e.g., PyTorch tensors or NumPy arrays) using BoxKit. BoxKit is a custom Python API designed for efficient management and scalability of block-structured simulation datasets [49, 50]. It leverages multiprocessing and cache optimization techniques to improve the read/write efficiency of data between disk and memory. Figure 2 shows an example of a boiling dataset and the corresponding workflow for enabling downstream tasks like scientific machine learning and optical flow. By operating on simulation data in manageable chunks that fit into memory, BoxKit significantly improves computational performance, particularly when handling large datasets.
Figure 2: Dataset Curation and Workflow. Flash-X multiphase simulations are executed and converted into unblocked HDF5 formats using the BoxKit library. The resulting dataset is publicly available<sup>3</sup>, enabling downstream tasks like scientific machine learning and optical flow.