# Isoline Tracking in Particle-Based Fluids Using Level-Set Learning Representation
###### Abstract  
In this paper, we propose a learning model for tracking the isolines of fluid based on the physical properties of particles in particle-based fluid simulations. Our method involves analyzing which weights, closely related to surface tracking among the various physical properties of fluid particles, are significant. These weights are used as input values for the learning algorithm, enabling relatively accurate isoline tracking. In addition, compared to existing learning models such as linear regression, LSTM (long short-term memory), and learning representation (1-layer) models, our method obtained superior surface tracking results without accumulating errors. By using our proposed network structure to track the fluid surface, it learns and predicts values derived from existing fluid simulation algorithms, eliminating the need for computational processes for level-set values and enabling real-time surface tracking. As the scale of the simulation increases, our method significantly reduces the time and resources consumed compared to traditional methods and can track the fluid surface without additional resource consumption. Furthermore, due to our method's simple network structure, the time consumed in the initial process of loading the model into memory is faster than models such as CNN and LSTM. Our proposed model occupies less than 30 kb of storage space, making it suitable for use in middleware. Lastly, to verify the generality of our method, we conducted tests in a total of five scenes, and in all test scenes, visually natural fluid isolines were represented. isoline tracking; fluid simulation; fluid surfaces; level set; artificial neural network; particle-based fluids +
Footnote †: journal: Medical  
of extracting fluid surfaces. The reconstruction of fluid surfaces can only be done after calculations involving the fluid particles' position, density, viscosity, pressure, surface tension, and external forces are completed. The time and resources needed for simulation and surface extraction depend on the dimension of the space and the number of particles [9]. Unlike standard 3D models, which usually remain static over time, fluids continuously change their surfaces and interiors due to particle movement, requiring constant tracking of the surface in each frame. Consequently, these processes demand significant resources and computation time. Although advancements in hardware and CG technology have made realistic graphics widely accessible, mobile devices like smartphones, with limited resources, struggle to represent high-quality fluids in real time. The increased computation time due to limited resources forces a reduction in content quality to maintain real-time continuity in rendering. This quality reduction can decrease user engagement and make continuous use of the content challenging. Therefore, from a commercial perspective, it is essential to maximize graphics quality with limited resources to ensure sustained user engagement with the content. In this paper, we propose a learning model based on the physical properties of fluid particles obtained from SPH (Smoothed Particle Hydrodynamics)-based fluid simulations for tracking the surface of these particles. The proposed model reconstructs surfaces in real time with quality similar to ground truth in middleware environments. It learns physical properties such as position, density, the number of neighboring particles, and pressure used in SPH-based fluid simulations during preprocessing, thus avoiding additional resource consumption for surface tracking during runtime. Our method, by inferring level-set values used in surface tracking through the trained model, eliminates the level-set calculation process included in traditional methods, enabling real-time surface tracking of fluids in SPH-based simulations with fewer resources. To explore if similar quality can be achieved with fewer resources and a simpler structure than our proposed method, we implemented linear regression and learning models.