Research |
Widely Applied Math
The MIGHTE Lab develops advanced mathematical models and machine learning algorithms to address complex problems in optimization, data processing, and the prediction of dynamic system behaviors. Our approach integrates mathematical analysis, statistics, and computational techniques to create efficient and scalable solutions in areas such as healthcare and data science. By leveraging methods like supervised and unsupervised learning and deep learning, we aim to uncover meaningful patterns from large datasets and improve data-driven decision-making.Additionally, the lab focuses on implementing mathematical models to interpret and enhance the performance of machine learning algorithms, ensuring their stability, robustness, and computational efficiency. We engage in research on convex optimization, probability theory, and stochastic processes to develop innovative methods for neural network training, dimensionality reduction, and uncertainty modeling. Through interdisciplinary collaboration, we aim to transform theoretical knowledge into practical applications that propel technological and scientific advancements.
Related publications
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Parameter Inference of Black Hole Images using Deep Learning in Visibility Space
Franc O, Pavlos Protopapas, Dominic W. Pesce, Angelo Ricarte, Sheperd S. Doeleman, Cecilia Garraffo, Lindy Blackburn, Mauricio Santillana arXiv:2504.21840 [astro-ph.GA] https://doi.org/10.48550/arXiv.2504.21840 Abstract
Using very long baseline interferometry, the Event Horizon Telescope (EHT) collaboration has resolved the shadows of two supermassive black holes. Model comparison is traditionally performed in image space, where imaging algorithms introduce uncertainties in the recovered structure. Here, we develop a deep learning framework to perform parameter inference in visibility space, directly using the data measured by the interferometer without introducing potential errors and biases from image recon- struction. First, we train and validate our framework on synthetic data derived from general relativistic magnetohydrodynamics (GRMHD) simulations that vary in magnetic field state, spin, and 𝑅high. Applying these models to the real data obtained during the 2017 EHT campaign, and only considering total intensity, we do not derive meaningful constraints on either of these parameters. At present, our method is limited both by theoretical uncertainties in the GRMHD simulations and variation between snapshots of the same underlying physical model. However, we demonstrate that spin and 𝑅high could be recovered using this framework through continuous monitoring of our sources, which mitigates variations due to turbulence. In future work, we anticipate that including spectral or polarimetric information will greatly improve the performance of this framework. |
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Unveiling individual and collective temporal patterns in the tanker shipping network
Kevin Teo, Naomi Arnold, Andrew Hone, Michael Coulon, Martin Ireland, Mauricio Santillana, István Z. Kiss. arXiv:2502.19957v1 [physics.soc-ph] https://doi.org/10.48550/arXiv.2502.19957 Abstract
The global shipping network, which moves over 80% of the world’s goods, is not only a vital backbone of the global economy but also one of the most polluting industries. Studying how this network operates is crucial for improving its efficiency and sustainability. While the transport of solid goods like packaged products and raw materials has been extensively researched, far less is known about the competitive trade of crude oil and petroleum, despite these commodities accounting for nearly 30% of the market. Using 4 years of high-resolution data on oil tanker movements, we employ sequential motif mining and dynamic mode decomposition to uncover global spatio-temporal patterns in the movement of individual ships. Across all ship classes, we demonstrate that maximizing the proportion of time ships spend carrying cargo –a metric of efficiency– is achieved through strategic diversification of routes and the effective use of intra-regional ports for trips without cargo. Moreover, we uncover a globally stable travel structure in the fleet, with pronounced seasonal variations linked to annual and semi-annual regional climate patterns and economic cycles. Our findings highlight the importance of integrating high-resolution data with innovative analysis methods not only to improve our understanding of the underlying dynamics of shipping patterns, but to design and evaluate strategies aimed at reducing their environmental impact. |
