youngMin

Projects

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Machine Learning Algorithms for Three-Dimensional Mean-Curvature Computation in the Level-Set Method

We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to 3D of our two-dimensional strategy in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of [DOI: 10.1016/j.jcp.2022.111291][2]. However, in contrast to [1,2], which built resolution-dependent neural-network dictionaries, here we develop a pair of models in 3D, regardless of the mesh size. Our feedforward networks ingest transformed level-set, gradient, and curvature data to fix numerical mean-curvature approximations selectively for interface nodes. To reduce the problem's complexity, we have used the Gaussian curvature to classify stencils and fit our models separately to non-saddle and saddle patterns. Non-saddle stencils are easier to handle because they exhibit a curvature error distribution characterized by monotonicity and symmetry. While the latter has allowed us to train only on half the mean-curvature spectrum, the former has helped us blend the data-driven and the baseline estimations seamlessly near flat regions. On the other hand, the saddle-pattern error structure is less clear; thus, we have exploited no latent information beyond what is known. In this regard, we have trained our models on not only spherical but also sinusoidal and hyperbolic paraboloidal patches. Our approach to building their data sets is systematic but gleans samples randomly while ensuring well-balancedness. We have also resorted to standardization and dimensionality reduction as a preprocessing step and integrated regularization to minimize outliers. In addition, we leverage curvature rotation/reflection invariance to improve precision at inference time. Several experiments confirm that our proposed system can yield more accurate mean-curvature estimations than modern particle-based interface reconstruction and level-set schemes around under-resolved regions.

J. Comput. Phys., 478: 111995, April 2023.

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Error-Correcting Neural Networks for Semi-Lagrangian Advection in the Level-Set Method

We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether we can compute on-the-fly, data-driven corrections to minimize numerical viscosity in the coarse-mesh evolution of an interface. The proposed system's starting point is the semi-Lagrangian formulation. And, to reduce numerical dissipation, we introduce an error-quantifying multilayer perceptron. The role of this neural network is to improve the numerically estimated surface trajectory. To do so, it processes localized level-set, velocity, and positional data in a single time frame for select vertices near the moving front. Our main contribution is thus a novel machine-learning-augmented transport algorithm that operates alongside selective redistancing and alternates with conventional advection to keep the adjusted interface trajectory smooth. Consequently, our procedure is more efficient than full-scan convolutional-based applications because it concentrates computational effort only around the free boundary. Also, we show through various tests that our strategy is effective at counteracting both numerical diffusion and mass loss. In simple advection problems, for example, our method can achieve the same precision as the baseline scheme at twice the resolution but at a fraction of the cost. Similarly, our hybrid technique can produce feasible solidification fronts for crystallization processes. On the other hand, tangential shear flows and highly deforming simulations can precipitate bias artifacts and inference deterioration. Likewise, stringent design velocity constraints can limit our solver's application to problems involving rapid interface changes. In the latter cases, we have identified several opportunities to enhance robustness without forgoing our approach's basic concept.

J. Comput. Phys., 471:111623, December 2022.

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Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method

We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-Cárdenas and Gibou, J. Comput. Phys., 463: 111291, August 2022, 10.1016/j.jcp.2022.111291] that relies on numerical schemes to enable machine-learning operations on demand. In particular, our routine features double predicting to harness curvature symmetry invariance in favor of precision and stability. The core of this solver is a multilayer perceptron trained on circular- and sinusoidal-interface samples. Its role is to quantify the error in numerical curvature approximations and emit corrected estimates for select grid vertices along the free boundary. These corrections arise in response to preprocessed context level-set, curvature, and gradient data. To promote neural capacity, we have adopted sample negative-curvature normalization, reorientation, and reflection-based augmentation. In the same manner, our system incorporates dimensionality reduction, well-balancedness, and regularization to minimize outlying effects. Our training approach is likewise scalable across mesh sizes. For this purpose, we have introduced dimensionless parametrization and probabilistic subsampling during data production. Together, all these elements have improved the accuracy and efficiency of curvature calculations around under-resolved regions. In most experiments, our strategy has outperformed the numerical baseline at twice the number of redistancing steps while requiring only a fraction of the cost.

J. Sci. Comput., 93(1):6, October 2022.

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Drag Reduction on Channel Flows over Superhydrophobic Surfaces

Graduate student research work supervised by Prof. Paolo Luzzatto-Fegiz and Prof. Frédéric Gibou at UCSB; Dr. Fernando Temprano-Coleto at Princeton University; Prof. Julien Landel, Prof. Oliver E. Jensen, and Dr. Samuel Tomlinson at University of Manchester; and Dr. François Peaudecerf at ETH Zurich.

Experimenting with high-Reynolds-number, high-gas-fraction channel-flow direct numerical simulations on three-dimensional superhydrophobic surfaces.

Heavy use of multicore, distributed, heterogenous compute systems accessed through XSEDE, such as Stampede2 at Texas Advanced Computing Center.

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A Hybrid Inference System for Improved Curvature Estimation in the Level-Set Method Using Machine Learning

We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks with standard numerical schemes to compute curvature more accurately. The core of our hybrid framework is a switching mechanism that relies on well established numerical techniques to gauge curvature. If the curvature magnitude is larger than a resolution-dependent threshold, it uses a neural network to yield a better approximation. Our networks are multilayer perceptrons fitted to synthetic data sets composed of sinusoidal- and circular-interface samples at various configurations. To reduce data set size and training complexity, we leverage the problem's characteristic symmetry and build our models on just half of the curvature spectrum. These savings lead to a powerful inference system able to outperform any of its numerical or neural component alone. Experiments with stationary, smooth interfaces show that our hybrid solver is notably superior to conventional numerical methods in coarse grids and along steep interface regions. Compared to prior research, we have observed outstanding gains in precision after training the regression model with data pairs from more than a single interface type and transforming data with specialized input preprocessing. In particular, our findings confirm that machine learning is a promising venue for reducing or removing mass loss in the level-set method.

J. Comput. Phys., 463:111291, August 2022.

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A Deep Learning Approach for the Computation of Curvature in the Level-Set Method

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from circular interfaces immersed in uniform grids of various resolutions. These multilayer perceptrons process the level-set values from mesh points next to the free boundary and output the dimensionless curvature at their closest locations on the interface. Accuracy analyses involving irregular interfaces, both in uniform and adaptive grids, show that our models are competitive with traditional numerical schemes in the L1 and L2 norms. In particular, our neural networks approximate curvature with comparable precision in coarse resolutions, when the interface features steep curvature regions, and when the number of iterations to reinitialize the level-set function is small. Although the conventional numerical approach is more robust than our framework, our results have unveiled the potential of machine learning for dealing with computational tasks where the level-set method is known to experience difficulties. We also establish that an application-dependent map of local resolutions to neural models can be devised to estimate mean curvature more effectively than a universal neural network.

SIAM J. Sci. Comput., 43(3):A1754-A1779, May 2021.

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NED: Collective Named Entity Disambiguation via Personalized Page Rank and Context Embeddings

In this work, we provide a solution to the disambiguation task by leveraging the traditional techniques of candidate mapping entity generation and local evaluation with some of the latest developments, such as word embeddings. We also consider a graph-based collective process to establish a topical relatedness metric that helps true mapping entities in a document to disambiguate one another through personalized PageRank. The final mapping entities for the given surface forms are obtained by heuristically reincorporating the candidates' local features with their resulting graph score and performing a maximal discriminant selection. The proposed methodology is capable of reaching up to 80% accuracy when it is evaluated against a well known dataset with around 18,000 named entity mentions.
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Reflective Shadow Maps

We have implemented Reflective Shadow Maps (RSM), together with Percentage-Closer Soft Shadows (PCSS) and Screen-Space Ambient Occlusion (SSAO) for added realism and details. Our approach works mostly with blurred textures and diffuse 3D objects shaded with the Blinn-Phong Reflectance Model. We have also resorted to Deferred Rendering to achieve interactive rates when RSM and SSAO are enabled, which are, by definition, very expensive tasks in terms of GPU resources. Finally, with regards to random sampling, we are using Poisson Disks which provide a good even distribution of 2D points without the artifacts that usually appear with uniformly distributed numbers in both PCSS and the importance driven sampling in RSM's indirect lighting.
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Precomputed Radiance Transfer

This OpenGL 4.1 project creates a GLFW window and renders on it a scene with geometries and a 3D object model. We currently support Precomputed Radiance Transfer on shadowed diffuse objects.
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Percentage Closer Soft Shadows

This OpenGL 4.1 project creates a GLFW window and renders on it a scene with geometric and textured 3D object models. The scene also has 3 colored area lights that make objects cast shadows using the Percentage Closer Soft Shadows procedure. We further support the Blinn-Phong Reflectance Model, and render text using FreeType and textures.
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WebGL Template

WebGL implementation using JSPs. This template uses the numeric.js library and other extensions to support drawing cubes, spheres, cylinders, prisms, dots, and paths. It also implements Phong shading for 3D bodies. Check the PHP template version now!
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Arthropoda

A physics-based simulation of a biomechanical model of an Araneous Diadematus specimen. The spider is able to walk by using ODE for dynamics emulation and OpenGL for rendering.
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Lisa - A Biomechanical Model of a Salamander

A physics-based simulation of a biomechanical model of a salamander, capable of walking and swimming. The system uses ODE for dynamics computation and OpenGL for rendering.
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Disambiguation of Named Entities in a Web List

System that yields the correct mapping for mentioned entities in a list by using optimization (simulated annealing). Our application utilizes Wikipedia (2012) as knowledge base to define the metrics and semantics used in the mapping process.
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2D Snow Simulation

2D physics-based simulation of snow by using the material point method. We emulate the mechanics, viscosity, and composition of snow as the latter is affected by external and internal forces. The system is developed in C++ and OpenGL.
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Face Classification and Generation

MATLAB application that uses Singular Value Decomposition and other image-processing machinery to classify male and female faces. Further statistical analysis allows to generate random faces given the intensity and geometry features extracted from the training set.
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A Symmetry-Seeking Model for 3D Object Reconstruction Using a Mesh of Particles

Our symmetry-seeking model allows construction of 3D objects from 2D input images, using a deformable tube made up of particles interconnected by damped-springs. This project is submitted as part of the CS269 Visual Modeling course at UCLA.
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Antarctica, Exploring the MAXSON Architecture

Simulation of an artificial ecosystem where virtual creatures learn to survive by eating food and avoiding poison, and to reproduce in order to maintain the continuity of their species. The agents emulate natural phenomena such as nuptial feeding and male brooding by resorting to a neural-based reinforcement learning.
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Auction Web Service

Web application that implements an auction website using Java, MySQL, Lucene, Apache Tomcat, Apache Axis2, JavaScript, and AJAX.
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Multi-Agent Simulation Using Continuum Crowds and the ClearPath Method

Crowd simulation where agent behavior resembles fluid motion. The displacement of agents depends on crowd densities at different locations in a discrete environment that represents a potential/velocity field.
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Darwinism, Lamarckism, and Knowledge Exchange among Animats

Simulation of an artificial ecosystem where animal-like creatures learn to survive from two evolutionary perspectives: Darwinism and Lamarckism. Agents have egocentric maps that allow them to acquire and share knowledge about the environment they live in.
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Spring Mass System

A simple spring mass, damped system simulating spheres bouncing off the ground.
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A 360-Degree Camera View of a Virtual World

A basic computer animation using (fixed-pipeline) OpenGL with textures and C++. This is project 2 of CS 164A: Introduction to Computer Graphics.
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Neural Model for Predicting Volcanic Events

Development of a neural network that prognosticates a volcanic eruption based on the input data and the historic information that was used as training set. This project fulfills the thesis requirement to acquire the degree of Bachelor's in Engineering.
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Drugstore Information System

Stock-management desktop application to control sales, purchases, and product reservations in a drugstore. Our system is written in Delphi and developed with the highest standards in software engineering.