Seminario de Matemáticas Aplicadas y Computacionales

El seminario es organizado por el Instituto de Ingeniería Matemática y Computacional (IMC) y reúne a investigadores y alumnos cada miércoles en un ambiente interdisciplinario.

2024-05-15
13:40hrs.

Mario Durán. Ingmat Centro I+D
Tópicos Teóricos y Aplicados de Fenómenos Complejos de Propagación de Ondas para Desafíos en Ingeniería y Alta Tecnología
Presencial en Auditorio Edificio San Agustín
Abstract:
Desde un punto de vista teórico y aplicado, nos proponemos entregar una visión global de algunos problemas estratégicos de gran escala para la sociedad y la industria en el ámbito de los fenómenos complejos de propagación de ondas. Muy en particular, abordaremos el tópico de Tecnologías Híbridas Avanzadas capaces de generar nueva y diferenciadora información geomecánica, geotécnica y geológica estructural para minería, obras civiles y otras industrias que contribuyan a enfrentar la dificultad en garantizar eficiencia y continuidad operacional en una faena, a través de una descripción optimizada del comportamiento mecánico espaciotemporal del suelo, subsuelo y/o macizo rocoso circundante.

2024-04-17
13:40hrs.

Nishant Mehta. Department of Computer Science, University of Victoria
Per-action regret bounds for adaptive sleeping bandits and beyond
Presencial en Auditorio Edificio San Agustín
Abstract:
The sleeping bandits problem is a variant of the classical multi-armed bandit problem. In each of a sequence of rounds: an adversary selects a set of arms (actions) which are available (unavailable arms are "asleep"), the learning algorithm (Learner) then pulls an arm, and finally the adversary sets the loss of each available arm. Learner suffers the loss of the selected arm and observes only that arm's loss. A standard performance measure for this type of problem with changing action sets is the per-action regret: the learning algorithm wishes, for all arms simultaneously, to have cumulative loss not much larger than the cumulative loss of the arm when considering only those rounds in which the arm was available. For this problem, we present the first algorithms which enjoy low per-action regret against reactive (i.e., adaptive) adversaries; moreover, the regret guarantees are near-optimal, unlike previous results which were far from optimal even for oblivious adversaries. Along the way, we will review the simpler, full-information version of the problem, known as sleeping experts. Time permitting, we will also mention various extensions of our results, including (i) new results for bandits with side information from sleeping experts; (ii) guarantees for the adaptive regret and tracking regret for standard (non-sleeping) bandits. This is joint work with my PhD student Quan Nguyen, who should be credited for nearly all the results in this work.

2024-04-03
13:40hrs.

Marcos Goycoolea. Escuela de Administración UC
Precedence constrained linear optimization and applications in scheduling & mining
Presencial en Auditorio Edificio San Agustín
Abstract:

We examine a class of mixed integer linear programming problems characterized by having a large set of precedence constraints and a small number of additional, “arbitrary” side constraints. These problems, which in a way are “almost” totally unimodular, are applicable in a wide array of scheduling tasks, including the well-known Resource-Constrained Project Scheduling Problem (RCPSP). RCPSPs and their variants are known to be extremely difficult to solve in practice. Moreover, they are of particular importance in the field of mining, where the scale of the problems can involve hundreds of millions of variables, posing a challenge for standard commercial solvers.

In this talk will describe these precedence-constrained optimization problems and discuss how understanding the optimal solution structure can inform the creation of specialized linear programming techniques that are more scalable than traditional algorithms. We will also describe new classes of cutting planes to strengthen linear relaxations. Applications of these methods will be showcased, ranging from scheduling for open pit and underground mines to adapting to uncertainties and integrating environmental objectives into scheduling practices.

This is joint work with Patricio Lamas, Eduardo Moreno and Orlando Rivera.

2024-03-27
13:40hrs.

Vamsi Potluru. Ai Research, Jp Morgan
Synthetic data in Finance
Presencial en Auditorio Edificio San Agustín
Abstract:

I will give a broad introduction to synthetic data and in particular their applications to Finance. I will focus on fair synthetic data based on creating a small coreset of the original dataset utilizing the Wasserstein distance while enforcing demographic parity. Experiments show the benefits of the approach and will also include reducing bias in LLMs. The talk will be broadly based on:

https://arxiv.org/abs/2401.00081

https://arxiv.org/abs/2311.05436

2024-03-25
13:40hrs.

Rashmi Vinayak. School of Computer Science, Carnegie Mellon University
Unlocking the Code: How Math Protects Our Data at Scale
Sala multiusos, primer piso Edificio Felipe Villanueva.
Abstract:
The massive data centers storing our information face constant challenges: hardware failures, unpredictable performance, and limited resources. How can we ensure our data stays safe and accessible in this ever-changing environment? This talk explores the surprising power of coding theory, a branch of mathematics that helps us store data efficiently and safely even when systems malfunction. I will start by delving into the basic principles behind coding theory and showing how it is used in modern storage systems. Finally, I will present a peek into cutting-edge research that's pushing the boundaries of data protection with even smarter codes.

2024-01-12
13:00hrs.

Brendan Keith. Division of Applied Mathematics, Brown University
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
Presencial en Auditorio Edificio San Agustín
Abstract:

The proximal Galerkin finite element method is a high-order, nonlinear numerical method that preserves the geometric and algebraic structure of bound constraints in infinite-dimensional function spaces. In this talk, we will introduce the proximal Galerkin method and apply it to solve free-boundary problems, enforce discrete maximum principles, and develop scalable, mesh-independent algorithms for optimal design. The proximal Galerkin framework is a natural consequence of the latent variable proximal point (LVPP) methodology, which is a stable and robust alternative to the interior point method that will also be introduced in this talk. LVPP can be viewed as a low-iteration complexity, infinite-dimensional optimization algorithm that may be viewed as having an adaptive barrier function that is updated with a new informative prior at each (outer loop) optimization iteration. One of the main benefits of this algorithm is witnessed when analyzing the classical obstacle problem. Therein, we find that the original variational inequality can be replaced by a sequence of semilinear partial differential equations (PDEs) that are readily discretized and solved with, e.g., high-order finite elements. Throughout the talk, we will arrive at several unexpected contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and an infinite-dimensional Lie group; and (3) a gradient-based, bound-preserving algorithm for two-field density-based topology optimization. The complete latent variable proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. This is joint work with T.M. Surowiec.

2024-01-10
13:30hrs.

Dr. Guido Kanschat. Decano de la Facultad de Ingeniería; Centro Interdisciplinario de Computación Científica (Iwr); Universidad de Heidelberg
Constructing Multigrid Solvers for Hybridized Finite Elements
Presencial en Auditorio Edificio San Agustín
Abstract:
We begin by reviewing the derivation and motivation of hybridized mixed finite element methods and hybridized discontinuous Galerkin (HDG) methods. In the second part of the talk, we discuss the benefits and inner workings of multigrid solvers. Then, we are ready to discuss multigrid solvers for HDG methods, where the focus is on the construction of intergrid operators. In particular, we show how the analysis of existing methods leads to the development of new schemes.

2023-12-14
15:30hrs.

Bernardo Subercaseaux. Carnegie Mellon University
El sorprendente poder de los SAT-solvers modernos aplicado a problemas matemáticos
Presencial en Auditorio Edificio San Agustín
Abstract:
Desde resolver Sudokus hasta demostrar teoremas matemáticos y pasando por verificar la correctitud de un programa, los SAT-solvers permiten resolver una amplia gama de problemas combinatoriales, y tienen aplicaciones en casi todas las áreas de la computación. Si bien los solvers modernos son altamente eficientes y sencillos de utilizar, usarlos para demostrar teoremas matemáticos que involucran millones de variables requiere de técnicas avanzadas de razonamiento automático. En esta charla presentaré una introducción al uso de SAT-solvers, pasando luego a explicar las técnicas utilizadas para resolver el problema del empaquetamiento cromático de la grilla infinita, un problema matemático abierto por 20 años que resolví junto a Marijn Heule.?

2023-12-12
13:00hrs.

Diego Paredes. Dim Universidad de Chile, Ci²Ma Universidad de Concepción
A Multiscale Hybrid (not Mixed) Method
Presencial en Auditorio Edificio San Agustín
Abstract:

In this talk, we introduce, analyze, and experimentally validate a novel multiscale finite element technique known as the Multiscale Hybrid (MH) method. This approach shares similarities with the established Multiscale Hybrid Mixed (MHM) method, but it distinguishes itself through a groundbreaking reinterpretation of the Lagrange multiplier.?

This reinterpretation leads to a significant practical advantage: both local problems for computing basis functions and the global problem become elliptic in nature. This stands in contrast to the MHM method (as well as other conventional approaches) where a mixed global problem is tackled, necessitating constrained local problem resolutions for the computation of local basis functions.?

Our error analysis of the MH method is grounded in a hybrid formulation, complemented by a discrete-level static condensation process. Consequently, the final global system exclusively involves the Lagrange multipliers.?

To validate the performance and efficiency of this method, we conduct a series of numerical experiments on problems characterized by multiscale coefficients. Additionally, we offer a comprehensive comparative analysis with the MHM method, assessing performance, accuracy, and memory requirements.?

2023-11-29
13:40hrs.

Thomas Führer. Facultad de Matemáticas, Pontificia Universidad Católica de Chile
Métodos de elementos finitos espacio-temporales
Presencial en Auditorio Edificio San Agustín
Abstract:

Las ecuaciones de calor son las representantes más famosas de problemas parabólicos e hiperbólicos, respectivamente. En la mayoría de los casos, resolver estos problemas de forma analítica es imposible. Por lo tanto, el diseño y análisis de métodos numéricos son extremadamente importantes.

Las discretizaciones clásicas involucran, por ejemplo, elementos finitos en el espacio, y discretizaciones temporales mediante diferencias finitas. En esta charla, exploraremos una perspectiva alternativa al tratar la variable temporal como cualquier otra variable en un dominio espacio-temporal. Discutiremos las ventajas y desventajas, basándonos en las ecuaciones de calor y onda. Además, presentaré resultados recientes sobre la discretización utilizando métodos de mínimos cuadrados, y abordaremos aplicaciones.

2023-11-22
13:40hrs.

Marcos Goycoolea. Escuela de Administración, Pontificia Universidad Católica de Chile
Precedence constrained linear optimization and applications in scheduling & mining
Presencial en Auditorio Edificio San Agustín
Abstract:

This is joint work with Patricio Lamas, Eduardo Moreno and Orlando Rivera.

2023-11-08
13:40hrs.

Sergio Rica. Instituto de Física, Pontificia Universidad Católica de Chile
Probable evidence of a finite-time singularity of the axisymmetric Euler equations for perfect fluids.
Presencial en Auditorio Edificio San Agustín
Abstract:
The search for singular solutions of the axisymmetric Euler equations is realized by expanding the vorticity and swirl velocity in the base of Legendre polynomials. This leads to an infinite non-linear hierarchy of ordinary differential equations (ODEs). In this seminar, we show the numerical robustness of solutions of the truncated hierarchy of the ODEs.

2023-10-11
13:55hrs.

Pablo Marquet. Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile
Ecología desde principios primarios (Ecology from first principles)
Presencial en Auditorio Edificio San Agustín
Abstract:
En esta charla se presentará un visión general del desarrollo de teorías en ecología, los problemas que se enfrentan y la importancia de desarrollar teorías basadas en principios primarios y expresables en el lenguaje de las matemáticas. Se mostrarán algunos ejemplos de teorías basadas en principios primarios (procesos de nacimiento y muerte) para el caso de la teoría de Biogeografía Insular y la teoría neutral de la biogeografía.

2023-08-23
13:40hrs.

Dardo Goyeneche. Facultad de Física, Pontificia Universidad Católica de Chile
Programación de estados cuánticos con pulsos
Presencial en Auditorio Edificio San Agustín
Abstract:
En esta charla autocontenida, presentaremos una introducción a los fundamentos de la mecánica cuántica y computación cuántica. Además, introduciremos la nueva forma de controlar computadores cuánticos superconductores, la cual reemplaza a las compuertas cuánticas tradicionales por pulsos electromagnéticos arbitrarios.

2023-05-31
13hrs.

Paul Escapil-Inchauspé. Data Observatory
New perspectives in artificial intelligence for computational engineering & data-centric paradigm
Presencial en Auditorio Edificio San Agustín.
Abstract:
Over the last 8 years, the usage of AI-based solutions such as deep learning in mathematical and computational engineering has experienced considerable growth in popularity, providing practitioners with new opportunities and approaches for performing simulations.

In this presentation, we analyze the data-centric paradigm outlined by Zha et al., with an emphasis on its implications for research and industry. We also consider what effects it may have on the fields of mathematical and computational engineering, along with the new prospects and trends it may create.

In particular, we present physics-informed machine learning (PIML) as a novel framework in computational mathematics and engineering. PIML couples observations with domain/physics knowledge in a single system, proving to be efficient for multi-physics, high-dimensional, and noisy problems. In particular, we explored physics-informed neural networks (PINNs) in greater detail.

We discuss the practical implementation of existing approaches, their strengths and limitations, and comment on current trends and future research opportunities in these areas.

2023-05-24
13hrs.

Felipe Huerta Pérez. Departamento de Ingeniería Química y Bioprocesos Uc.
Modelamiento de la evaporación de líquidos criogénicos en tanques de almacenamiento
Presencial en Auditorio Edificio San Agustín.
Abstract:
Los líquidos criogénicos se definen como sustancias con un punto normal de ebullición inferior a -150 °C. Entre los líquidos criogénicos, el gas natural licuado (GNL) y el hidrógeno líquido (LH2) destacan por su rol predominante en la transición energética. Los líquidos criogénicos son almacenados en tanques térmicamente aislados con el fin de minimizar el ingreso de calor desde los alrededores. El ingreso de calor produce la evaporación del líquido, así como también la convección natural y estratificación térmica del vapor generado. El vapor generado por la evaporación del líquido criogénico se denomina boil-off gas (BOG), y su manejo plantea desafíos tecno-económicos, ambientales y de seguridad de procesos. En este proyecto de investigación se han desarrollado nuevos modelos físico-matemáticos aplicables a la evaporación de líquidos criogénicos almacenados en tanques en condiciones isobáricas.

La principal aplicación de almacenamiento isobárico de líquidos criogénicos es el envejecimiento de GNL en tanques grandes. Para este sistema, un nuevo modelo de no-equilibrio unidimensional (1-D) se ha desarrollado. Este modelo incluye un submodelo realista de la transferencia de calor en la fase vapor, que considera el calentamiento por las murallas del tanque, conducción y advección. Los resultados de las simulaciones muestran que la advección es el mecanismo dominante de transferencia de calor. Los supuestos del modelo 1-D fueron validados numéricamente mediante el desarrollo un modelo bidimensional (2-D) de dinámica de fluidos computacional (CFD). Las simulaciones obtenidas con el modelo 2-D muestran que la estratificación térmica amortigua la convección natural en el vapor. Finalmente, soluciones analíticas del modelo 1-D fueron desarrolladas bajo el supuesto de estado pseudoestacionario. Las soluciones analíticas clarifican las fuerzas motrices que gobiernan la evaporación, y constituyen una herramienta que facilita el manejo del boil-off gas.

2023-01-24
13.30-15:30hrs.

Thomas Capelle. Weights & Biases
Desarrollo colaborativo de modelos de ML: cómo trabajar juntos para obtener mejores resultados
Presencial en Auditorio Edificio San Agustín.
Abstract:

La charla será dictada por Thomas Capelle, Machine Learning engineer de la empresa estadounidense Weights & Biases. Él es responsable de mantener activo y actualizado el repositorio WandB/Examples. Su experiencia es en planificación urbana, optimización combinatoria, economía del transporte y matemáticas aplicadas.

El evento incluirá una competencia de clasificación en Kaggle con premios para las mejores propuestas. Los y las participantes deben llevar sus laptops y deben tener acceso a WandB, Colab y Kaggle.

Inscripción gratuita: https://forms.gle/UVEBVJy3NpQHdYB29

2023-01-16
9.30hrs.

Varios. Instituto de Ingeniería Matemática y Computacional
Escuela de Verano SIAM-PUC
Campus San Joaquín
Abstract:
El Capítulo Estudiantil SIAM-PUC y el Instituto de Ingeniería Matemática y Computacional (IMC) los invitan a asistir en la semana del 16 al 20 de enero a la primera edición de la Escuela de Verano Capitulo SIAM PUC 2023 y al Ciclo de charlas Aniversario de Fourier, el cual se realizará en el Campus San Joaquín UC. Este evento será una instancia para conocer y acercarse al trabajo de profesores del IMC, conocer los temas que se desarrollan en el Magíster en Ingeniería Matemática y Computacional y conmemorar los 200 años de la teoría analítica del Calor de Fourier .

La Escuela está dirigida tanto a estudiantes como académicos/as e investigadores interesados/as en temas de ingeniería matemática y matemáticas aplicadas, y contempla las siguientes actividades:

Charlas de académicos de Ingeniería Matemática.
Cursos de los temas desarrollados por académicos del IMC.
Ciclo de charlas sobre Análisis de Fourier.
Coffee break durante los días que dure el evento.

Este evento es GRATUITO con CUPOS LIMITADOS. Formulario de postulación: https://form.jotform.com/223173577317661

Más información: https://sites.google.com/uc.cl/capitulosiampuc/escuela-de-verano

2022-11-28
13hrs.

Gianluca Iaccarino. Stanford University
What is Computational Mathematics and ICME for you?
Presencial en Auditorio Edificio San Agustín.
Abstract:

The Institute for Computational and Mathematical Engineering (ICME) at Stanford University is an interdisciplinary graduate program (granting Masters and PhDs) at the intersection of mathematics, computing, and science and engineering. ICME was established in 2004, is part of Stanford School of Engineering and provides a link between fundamental mathematics/statistical sciences, computer science and engineering applications. In ICME:

We design state-of-the-art mathematical and computational models, methods and algorithms.

We collaborate closely with engineers and scientists in academia and industry to develop improved computational approaches and advance disciplinary fields.

We train students and scholars in mathematical modeling, scientific computing and advanced computational algorithms.

In this talk I will give an overview of ICME, and give examples of recent research activities highlighting ICME students.

Link de inscripción: https://forms.gle/YcQYNVfWvMr4end29

2022-10-19
13hrs.

Carlos Spa. Computer Applications in Science and Engineering (Case) Department, Barcelona Supercomputing Center (Bsc-Cns)
Pseudo-spectral methods in room acoustics simulations
Presencial en Auditorio Edificio San Agustín.
Abstract:
Room acoustics is the science concerned to study the behavior of sound waves in enclosed rooms. The acoustic information of any room, the so-called impulse response, is expressed in terms of the acoustic field as a function of space and time. In general terms, it is nearly impossible to find analytical impulse responses of real rooms. Therefore, in recent years, the use of computers for solving this type of problems has emerged as a proper alternative to calculate these responses. In this talk, we focus on the analysis of the wave-based methods in the time-domain. More concretely, we study in detail the main formulations of Finite-Difference methods, which have been widely used in many room acoustics applications, and the recently proposed Fourier Pseudo-Spectral methods. Both methods are studied and compared in the three different contexts: the wave propagation, the source generation and the locally reacting boundary conditions.