Projects

We present a machine learning framework that blends image super-resolution technologies with 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 passive 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, highly deforming or lengthy simulations can precipitate bias artifacts and inference deterioration. Likewise, stringent design velocity constraints can impose certain limitations, especially for problems involving rapid interface changes. In the latter cases, we have identified several opportunity avenues to enhance robustness without forgoing our approach's basic concept.

Submitted.

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 static, 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.

Submitted.

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.

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.

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.

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.

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.

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!

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.

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.

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.

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.

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.

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.

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.

Web application that implements an auction website using Java, MySQL, Lucene, Apache Tomcat, Apache Axis2, JavaScript, and AJAX.

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.

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.

A simple spring mass, damped system simulating spheres bouncing off the ground.

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

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.

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.