Seminario de Matemáticas Aplicadas y Computacionales (SeMACs)

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.

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:
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.
 
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.
2022-10-14
13hrs.
Clement Lezane. University of Twente
Optimal Algorithms for Stochastic Complementary Composite Minimization
Presencial en Auditorio Edificio San Agustín.
Abstract:
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed with a stochastic first-order oracle, and a structured uniformly convex (possibly nonsmooth and non-Lipschitz) regularization term. Despite intensive work on closely related settings, prior to our work no complexity bounds for this problem were known. We close this gap by providing novel excess risk bounds, both in expectation and with high probability. Our algorithms are nearly optimal, which we prove via novel lower complexity bounds for this class of problems. We conclude by providing numerical results comparing our methods to the state of the art.
2022-09-28
13 horas.hrs.
Rodrigo Carrasco. Departamento de Ingeniería Industrial y de Sistemas e Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile
Energy storage management strategies under uncertain generation: combining prediction and optimization
Presencial en Auditorio Edificio San Agustín.
Abstract:
This work presents a novel approach to scheduling storage units in a photovoltaic generation system based on stochastic optimization. A common approach to take advantage of historical data for stochastic optimization has been to use machine learning techniques to compute relevant scenarios. Instead of this “predict THEN optimize” strategy, we show that using a combined “predict AND optimize” approach results in better recommendations. The resulting scenarios capture the relevant effects on the decision process and not just data features. We show experimental results applied to a real-life control system with limited computation capacity and further validate our results by testing the resulting schedules in an actual prototype.
 

 
 
2022-08-31
13 horas.hrs.
Rodrigo Carrasco. Departamento de Ingeniería Industrial y de Sistemas e Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile.
Energy storage management strategies under uncertain generation: combining prediction and optimization
Presencial en Auditorio Edificio San Agustín. (Link Zoom disponible escribiendo a imc@uc.cl)
Abstract:

Due to climate change concerns, many governments have pushed for higher penetration of intermittent renewable energy sources. Among these energy sources, photovoltaic (PV) generation is one of the most sought-off, particularly by domiciliary users and small industries. However, the main drawback of this energy source is its variability and intermittency, not being available for the whole day. One way of diminishing this drawback is to use energy storage systems like batteries. In Chile, as in several other countries, the new regulation allows selling excess household generation, albeit at a price significantly lower than the consumer price. With this new setting, the residential sector user, with solar panels installed in their home, can not only use the energy from that source and connect to the electrical distribution network when required. In addition, she can also sell the excess energy generated to the distribution network, getting an economic benefit from this sale. The decision becomes complex when storage capacity, like batteries, is added to the user. In this new case, the decision process must consider when and how much to store or sell to the grid; and whether energy should be used, sent to the network, or stored in the system.

This work presents a novel approach to scheduling these storage units in a PV generation system based on stochastic optimization. A common approach to using historical data for stochastic optimization has been to use machine learning techniques to compute relevant scenarios. Instead of this “predict then optimize” strategy, we show that using a combined “predict and optimize” approach results in better recommendations. The resulting scenarios capture the relevant effects on the decision process and not just data features. We show experimental results applied to a real-life control system with limited computation capacity and further validate our results by testing the resulting schedules in an actual prototype.

This is joint work with Helena García, Tito Homem-de-Mello, Gonzalo Ruz, Francisco Jara, and Carlos Silva. This work was partially funded by FONDEF grant ID19I10158. 

2022-08-24
13 horas.hrs.
Juan Reutter. Departamento de Ciencia de la Computación, Pontificia Universidad Católica de Chile
The power of graph neural networks
Presencial en Auditorio Edificio San Agustín.
Abstract:
The power of Graph Neural Networks (GNNs) is commonly measured in terms of their ability to separate graphs: a GNN is more powerful when it can recognize more graphs as being different. Studying this metric in GNNs helps in understanding the limitations of GNNs for graph learning tasks, but there are few general techniques for doing this, and most results in this direction are geared at specific GNN architectures.
 
In this talk I will review our recent work in studying the separation power of GNNs. Our approach is to view GNNs as expressions specified in procedural languages that describe the computations in the layers of the GNNs, and then analyze these expressions to obtain bounds on the separation power of said GNNs. As we see, this technique gives us an elegant way to easily obtain bounds on the separation power of GNNs in terms of the Weisfeiler-Leman (WL) tests, which have become the yardstick to measure the separation power of GNNs. If time permits, I will also review some of the by-products of our characterization, including connections to logic and approximation results for GNNs. 
2022-08-10
13 horas.hrs.
Nishant Mehta. Department of Computer Science, University of Victoria
Best-case lower bounds in online learning
Vía Zoom
Abstract:
I will begin by introducing an online learning problem motivated by group fairness considerations. It is standard in online learning to prove sublinear upper bounds on the regret, a key performance measure in online learning and online convex optimization. An alternative concept is a best-case lower bound — the largest improvement an algorithm can obtain relative to the single best action in hindsight. Best-case lower bounds have connections to fairness: it is known that best-case lower bounds are instrumental in obtaining algorithms for the popular decision-theoretic online learning (DTOL) setting that satisfy a notion of group fairness. A parallel motivation of this work is to better understand the adaptivity of a learning algorithm; while some algorithms provably exhibit certain types of adaptivity, we show that they are provably prohibited from obtaining another desirable form of adaptivity (related to what is known as the shifting regret). Our contributions are a general method to provide best-case lower bounds in Follow the Regularized Leader (FTRL) algorithms with time-varying regularizers, which we use to show that best-case lower bounds are often of the same order as existing upper regret bounds: this includes situations with a fixed learning rate, decreasing learning rates, and adaptive gradient methods. We also show that the popular linearized version of FTRL can attain negative linear regret and hence does not admit non-trivial best-case lower bounds in general.
 
This is joint work with Cristóbal Guzmán and Ali Mortazavi.

Link Zoom: https://us06web.zoom.us/j/81151863460?pwd=Z0RPTHZKd1hTTndrNHMwMkpJTjZlZz09 (Código: McJ80c)
2022-06-15
13 horas.hrs.
Benjamín Palacios. Departamento de Matemáticas, Pontificia Universidad Católica de Chile
The inverse problem of photoacoustic tomography: theoretical aspects and reconstruction methods
Presencial en Auditorio Edificio San Agustín.
Abstract:
Photoacoustic Tomography (PAT) is a promising hybrid medical imaging modality that is able to generate high-resolution and high-contrast images by exploiting the coupling of electromagnetic pulses (in the visible region) and ultrasound waves via de photoacoustic effect. The mathematical problem splits into two steps, one involving the inversion of boundary acoustic data to determine the initial source of waves, and the second step uses this internal information to retrieve optical properties of the medium and it is commonly known as Quantitative PAT.

In this talk, I will introduce the modality and focus on the ultrasound propagation component which is mathematically modeled as an inverse initial source problem for the wave equation. I will then discuss mathematical aspects of this inverse problem and present some recent theoretical results. The last part of the presentation will be devoted to addressing some open questions related to reconstruction methods and numerical implementations.
2022-06-01
13 horas.hrs.
Cristián Escauriaza. Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile
Transporte Turbulento en Zonas de Almacenamiento Superficial: Perspectivas Lagrangianas y Eulerianas
Presencial en Auditorio Edificio San Agustín.
Abstract:
Las zonas de almacenamiento superficial en ambientes fluviales y costeros se caracterizan por grandes regiones laterales de recirculación, dominadas por múltiples estructuras coherentes turbulentas que interactúan entre sí y con los bordes. Estos flujos que poseen velocidades más bajas, juegan un papel fundamental en el transporte de contaminantes y de sedimentos, y en la absorción de nutrientes en ríos y en la costa. Sin embargo, la dinámica de las estructuras coherentes en estas zonas es altamente compleja, con múltiples escalas espaciales y temporales. Modelos numéricos de alta resolución que capturan estos flujos a altos números de Reynolds proporcionan información sobre los mecanismos de transporte y los factores que influyen a escalas espaciales más grandes. En este trabajo estudiamos los procesos físicos utilizando simulaciones numéricas de las ecuaciones filtradas de Navier-Stokes junto con ecuaciones de transporte. Implementamos un modelo Lagrangiano de partículas para estudiar tiempos de residencia y realizar análisis estadísticos de trayectorias que permiten comprender los impactos a mayor escala, y sus implicancias en parametrizaciones de transporte.
2022-05-25
13 horas.hrs.
Pablo Barceló. Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile
The AGM Bound
Presencial en Auditorio Edificio San Agustín.
Abstract:
In several computer science applications one encounters the following problem: Given two edge-labeled graphs G and H, how many homomorphic images of H can be found in G? Atserias, Grohe, and Marx developed a tight bound for this number, denoted #Hom(H,G), which is now known as the AGM bound. The bound relates #Hom(H,G) with the fractional edge covers of H in a very elegant and direct way. We will present a self-contained and simple proof of this result using Holder's inequality.