# Isoline Tracking in Particle-Based Fluids Using Level-Set Learning Representation
## 2 Related Work
### Fluid Simulation with Deep Learning  
With the significant advancements in various fields using deep learning, research has been conducted in fluid simulation to learn physical properties through it, aiming to gain benefits in memory efficiency and simulation acceleration [30]. To accelerate grid-based fluid simulations, the CFDNet (Computational Fluid Dynamics Network) [31], utilizing a CNN (Convolutional Neural Network), was proposed. This model inputs the initial and boundary conditions of fluid simulations, infers the fluid's dynamic movements, and achieves fast and accurate results using deep learning, outperforming traditional numerical analysis methods. Experimental results showed that CFDNet performs fluid simulations significantly faster than existing methods. This approach aimed to speed up simulations and minimize errors in the model, and demonstrated the potential of learning the physical properties of fluids through CNN.  
In Lagrangian fluid simulations, FluidMLP [32] was proposed to generate a model by learning particles' physical properties. This model, which learned and compared particles' positions, velocities, and accelerations, improved accuracy notably when using acceleration data. However, it faced accuracy issues during particle interactions, causing particles to escape the simulation boundaries. To resolve this, the FGN (Fluid Graph Networks) model [33] was designed with an Edge-focused network for learning particle interactionsand a Node-focused network for learning particles' physical properties. The model, created using GNN (Graph Neural Network), demonstrated error convergence within a certain range across various environments and confirmed its capability to learn physical properties of fluid simulations. FluidMLP and FGN, by leveraging models generated through deep learning, significantly reduced simulation computational time by bypassing traditional fluid simulation algorithms. However, due to the importance of accuracy in simulations, extensive research is ongoing to achieve a level of accuracy comparable to that of existing fluid simulation algorithms.  
Research applying deep learning to enhance memory efficiency and reduce computational time has been conducted for the surface reconstruction process in fluid simulations. To overcome the issue of losing sharp edge features in results from traditional MC, NMC (Neural Marching Cubes) [34] was proposed, utilizing mesh vertex positions and topology as training data. Although NMC provides more accurate surfaces than MC, it uses more complex tessellation templates than MC, leading to the generation of more triangles and requiring over 100 times more computational time for mesh reconstruction. Additionally, this method assumes the implicit function and signed distance field are provided together, so it only learns aspects related to the MC process.  
NDC (Neural Dual Contouring) [35] is a data-centric model based on DC. A common drawback of MC and DC is the need for surface normalization to calculate the optimal vertex position in each cell. However, NDC, as a data-centric model, bypasses this process and predicts vertex positions without it. The model, trained through CNN, results in 3 to 20 times faster inference times compared to NMC and generates 4 to 8 times fewer meshes, thus increasing memory efficiency. Based on such prior research, this study aims to replace traditional surface tracking algorithms in fluid simulations with learning models, thereby reducing computation time and enhancing memory usage efficiency.