Abstract : In this paper, we propose a projective grid model that enables learning representation of foam effects using artificial neural networks. In 3D fluid simulations, foam is one of the most representative secondary effects in water. Consequently, the processes of foam generation, advection, and dissolution are computationally expensive. However, no prior research has explored representing these processes using neural networks. This paper introduces a constitutive model for learning foam effects in projective space with neural networks. Learning 3D fluid simulation is a complex and multi-faceted challenge, but our approach simplifies the design of foam effects by leveraging a 2D projective space rather than a fully 3D space. The proposed projective grid model consists of the following components: 1) learning the conditions under which foam particles are generated in the projective shape, 2) distinguishing between surface foam and wave foam based on varying conditions instead of relying on a single foam texture, 3) learning the advection process of different foam types, and 4) learning the dissolution process through representation learning. As a result, our method enables efficient representation of 3D foam effects without the need for complex numerical calculations, demonstrating its effectiveness across various scenarios.

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