Lagrangian Neural Style Transfer for Fluids

Artistically controlling the shape, motion and appearance of fluid simulations pose major challenges in visual effects production. In this paper, we present a neural style transfer approach from images to 3D fluids formulated in a Lagrangian viewpoint. Using particles for style transfer has unique benefits compared to grid-based techniques. Attributes are stored on the particles and hence are trivially transported by the particle motion. This intrinsically ensures temporal consistency of the optimized stylized structure and notably improves the resulting quality. Simultaneously, the expensive, recursive alignment of stylization velocity fields of grid approaches is unnecessary, reducing the computation time to less than an hour and rendering neural flow stylization practical in production settings. Moreover, the Lagrangian representation improves artistic control as it allows for multi-fluid stylization and consistent color transfer from images, and the generality of the method enables stylization of smoke and liquids likewise.Comment: ACM Transaction on Graphics (SIGGRAPH 2020), additional materials: http://www.byungsoo.me/project/lnst/index.htm

Part I: Reconstruction of Missing Data in Social Networks Based on Temporal Patterns of Interactions Part II: Constitutive Modeling in Solid Mechanics for Graphics Applications

In Part I, the author presents a mathematical framework based on a self-exciting pointprocess aimed at analyzing temporal patterns in the series of interaction events betweenagents in a social network. We develop a reconstruction model formulated as a constraintoptimization problem that allows one to predict the unknown participants in a portion ofthose events. The results are used to predict the perpetrators of the unsolved crimes in theLos Angeles gang network.Part II discusses the work undertaken by the author in deformable solid body simulation.We first focus on purely elastic solids and develop a method for extending an arbitraryisotropic hyperelastic energy density function to inverted configurations. This energy basedextension is designed to improve robustness of elasticity simulations with extremely largedeformations typical in graphics applications and demonstrates significant improvementsover similar stress based techniques presented in [40, 86]. Moreover, it yields continuousstress and unambiguous stress derivatives in all inverted configurations. We also introducea novel concept of a hyper-elastic model's primary contour which can be used to predict itsrobustness and stability. We demonstrate that our invertible energy-density-based approachoutperforms the popular hyperelastic corotated model [13, 56] and show how to use theprimary contour methodology to improve the robustness of this model to large deformations.We further develop a novel snow simulation method utilizing a user-controllable consti-tutive model defined by an elasto-plastic energy density function integrated with a hybridEulerian/Lagrangian Material Point Method (MPM). The method is continuum based and itshybrid nature allows us to use a regular Cartesian grid to automate treatment of self-collisionand fracture. It also naturally allows us to derive a grid-based implicit integration schemethat has conditioning independent of the number of Lagrangian particles. We demonstratethe power of our method with a variety of snow phenomena

Part I: Reconstruction of Missing Data in Social Networks Based on Temporal Patterns of Interactions Part II: Constitutive Modeling in Solid Mechanics for Graphics Applications

In Part I, the author presents a mathematical framework based on a self-exciting pointprocess aimed at analyzing temporal patterns in the series of interaction events betweenagents in a social network. We develop a reconstruction model formulated as a constraintoptimization problem that allows one to predict the unknown participants in a portion ofthose events. The results are used to predict the perpetrators of the unsolved crimes in theLos Angeles gang network.Part II discusses the work undertaken by the author in deformable solid body simulation.We first focus on purely elastic solids and develop a method for extending an arbitraryisotropic hyperelastic energy density function to inverted configurations. This energy basedextension is designed to improve robustness of elasticity simulations with extremely largedeformations typical in graphics applications and demonstrates significant improvementsover similar stress based techniques presented in [40, 86]. Moreover, it yields continuousstress and unambiguous stress derivatives in all inverted configurations. We also introducea novel concept of a hyper-elastic model's primary contour which can be used to predict itsrobustness and stability. We demonstrate that our invertible energy-density-based approachoutperforms the popular hyperelastic corotated model [13, 56] and show how to use theprimary contour methodology to improve the robustness of this model to large deformations.We further develop a novel snow simulation method utilizing a user-controllable consti-tutive model defined by an elasto-plastic energy density function integrated with a hybridEulerian/Lagrangian Material Point Method (MPM). The method is continuum based and itshybrid nature allows us to use a regular Cartesian grid to automate treatment of self-collisionand fracture. It also naturally allows us to derive a grid-based implicit integration schemethat has conditioning independent of the number of Lagrangian particles. We demonstratethe power of our method with a variety of snow phenomena

Reconstruction of Missing Data in Social Networks Based on Temporal Patterns of Interactions

Abstract. We discuss a mathematical framework based on a self-exciting point process aimed at analyzing temporal patterns in the series of interaction events between agents in a social network. We then develop a reconstruction model that allows one to predict the unknown participants in a portion of those events. Finally, we apply our results to the Los Angeles gang network