Projects

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.
Submitted to SIAM Journal on Scientific Computing.

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

Reflective Shadow Maps

Precomputed Radiance Transfer

Percentage Closer Soft Shadows

WebGL Template

Arthropoda

Disambiguation of Named Entities in a Web List

Face Classification and Generation

A Symmetry-Seeking Model for 3D Object Reconstruction Using a Mesh of Particles

Antarctica, Exploring the MAXSON Architecture

Auction Web Service

Multi-Agent Simulation Using Continuum Crowds and the ClearPath Method

Darwinism, Lamarckism, and Knowledge Exchange among Animats

Spring Mass System

A 360-Degree Camera View of a Virtual World

Neural Model for Predicting Volcanic Events
