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Articles by Simon Mak
QuIP: Experimental design for expensive simulators with many Qualitative factors via Integer Programming
Abstract The need to explore and/or optimize expensive simulators with many qualitative factors arises in broad scientific and engineering problems. Our motivating application lies in path planning – the exploration of feasible paths for navigation – which plays an important role in robotics and assembly planning. For complex settings, the parameter space for path exploration can be discrete and high-dimensional, and the evaluation of path feasibility requires expensive virtual simulations.
ProGress: Structured Music Generation via Graph Diffusion and Hierarchical Music Analysis
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Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma
Abstract The Quark-Gluon Plasma (QGP) is a unique phase of nuclear matter, theorized to have filled the Universe shortly after the Big Bang. A critical challenge in studying the QGP is that, to reconcile experimental observables with theoretical parameters, one requires many simulation runs of a complex physics model over a high-dimensional parameter space. Each run is computationally expensive, requiring thousands of CPU hours, thus limiting physicists to only several hundred runs.
Targeted Variance Reduction: Effective Bayesian Optimization of Black-Box Simulators with Noise Parameters
Abstract The optimization of a black-box simulator over control parameters x arises in a myriad of scientific applications. In such applications, the simulator often takes the form f(x,θ), where θ are parameters that are uncertain in practice. Stochastic optimization aims to optimize the objective E[f(x,Θ)], where Θ∼P is a random variable that models uncertainty on θ.
ProSpar-GP: scalable Gaussian process modeling with massive non-stationary datasets
Abstract Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data, existing methods typically rely on a stationary GP assumption for approximation, and can thus perform poorly when the underlying response surface is non-stationary, i.e., it has some regions of rapid change and other regions with little change.
eRPCA: Robust Principal Component Analysis for Exponential Family Distributions
Robust principal component analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low-rank background is critical for process monitoring and diagnosis.
A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions
Abstract With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of different fidelities to train an efficient predictive model which emulates the expensive simulator.
PERCEPT: A New Online Change-Point Detection Method using Topological Data Analysis
Abstract Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis.
Space Exploration and Data Science
By Simon Mak and C.F. Jeff Wu In his famous 1962 address at Rice University about U.S. space efforts to reach the moon, President John F. Kennedy declared that “the exploration of space will go ahead…and it is one of the great adventures of all time.” This adventure has become even more of a reality in recent years, as modern breakthroughs in mathematical modeling, scientific computing, and data science have inspired numerous pioneering achievements that were only dreams in the past.
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