YoungMin Kai Ángel

Luis Ángel (영민 카이 앤절)

lal@cs.ucsb.edu

youngMin
 

My Portfolio

I am a computational scientist and software engineer interested in scientific computing and applied machine learning. Currently, I am an engineer at VideoAmp, helping build the future currency-grade ad data set. Prior to that, I was a graduate student researcher at the University of California, Santa Barbara, where I was a member of the Computational Applied Science Laboratory, advised by Prof. Frédéric Gibou.

Curriculum Vitae

Presentations

Machine-learning tools for curvature computation in the level-set method. Multidisciplinary University Research Initiatives (MURI) Program at UCSB/UMN. February, 2022.

A symmetry-seeking model for 3D object reconstruction using a mesh of particles. Information Technologies National Congress at ITCG. October 2012.

Latest 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.