Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Dirichlet-to-Neumann and Calderon operator via deep learning techniques.
Abstract: In this talk we consider the Dirichlet-to-Neumann operator and the Calderón mapping appearing in Calderon’s inverse problem. Using deep learning techniques, we prove that these maps are rigorously approximated by infinite-dimensional neural networks.
Long time asymptotics of large data in the Kadomtsev-Petviashvili models and geometrical aspects of its dynamics.
Abstract: In this talk we consider the Kadomtsev-Petviashvili equations posed on R2. For both models, we provide sequential in time asymptotic descriptions of solutions obtained from arbitrarily large initial data, inside and far regions of the plane not containing lumps or line solitons, and under minimal regularity assumptions. A geometrical description of the dynamics will be given in terms of parabolic regions.
Determinación de erosión costera con imágenes satelitales Sentinel-2 entre 2015 – 2022. Caso de estudio Bahía de Algarrobo, Chile Central
Resumen: En los últimos años, la erosión costera ha aumentado a nivel mundial por la frecuencia e intensidad de eventos de tormentas, convirtiéndose en una de las principales amenazas que afectan a la zona costera a diferentes escalas. En la Bahía de Algarrobo los eventos de marejadas frecuentes e intensas en las temporadas primavera-verano y las intervenciones antrópicas en humedales costeros, sobre la playa y las dunas han intensificado los procesos erosivos. El objetivo del trabajo es determinar las tasas de erosión costera a partir del...
Simplified Kalman filtering for non-linear models.
Abstract: We will discuss the problem of approximate statistical inference in the hidden Markov models where the observation equations are non-linear. We propose a Bayesian approach based on a Gaussian approximation as well as its versions suitable for “large” problems. The proposed approach may be seen as an approximate Kalman filter which is generic in the sense that it can be used for any non-linear relationship between the hidden state and the outcome. We show how the proposed simplified Kalman filter can be used in the...
On traveling waves for the Gross-Pitaevskii equations.
Abstract: In this talk, we will discuss some properties of traveling waves solutions for some variants of the classical Gross-Pitaevskii equation in the whole space, in order to include new physical models in Bose-Einstein condensates and nonlinear optics. We are interested in the existence of finite energy localized traveling waves solutions with nonvanishing conditions at infinity, i.e. dark solitons. After a review of the state of the art in the classical case, we will show some results for a family of Gross-Pitaevskii equations with...
Conjugacy classes of germs near a hyperbolic fixed point in dimension 1.
RESUMEN: A famous linearization theorem of Sternberg claims that, in dimension 1, near a hyperbolic fixed point (i.e. a fixed point where the derivative differs from 1), a germ of C^r diffeomorphism is C^r conjugate to its linear part when r is greater than or equal to 2. This result fails to be true in lower regularity, even for C^1 diffeomorphisms with absolutely continuous derivative. We will explain how to construct whole continuous families of such germs with the same derivative at a common fixed point but which are not pairwise...
Robust shape optimization with small uncertaintie.
Abstract: In this talk, we propose two approaches for dealing with small uncertainties in geometry and topology optimization of structures. Uncertainties occur in the loadings, the material properties, the geometry or the imposed vibration frequency. A first approach, in a worst-case scenario, amounts to linearize the considered cost function with respect to the uncertain parameters, then to consider the supremum function of the obtained linear approximation, which can be rewritten as a more `classical’ function of the design, owing to...
Cosmología Primordial.
Abstract: Nuestro entendimiento del origen del universo ha cambiado dramáticamente durante los últimos 40 años. Hoy sabemos que la estructura de gran escala del universo (compuesto por galaxias) debe su existencia a pequeñas fluctuaciones del espacio y el tiempo -fluctuaciones primordiales- ya presentes durante el Big-Bang. La teoría más aceptada para explicar el origen de estas fluctuaciones sostiene que ellas se deben a procesos cuánticos ocurridos antes del Big-Bang, durante una época conocida como inflación cósmica. Este cuadro lo hemos...
Neural Implicit Surface Evolution using Differential Equations.
Abstract: In this talk, we present a machine learning framework that uses smooth neural networks to model dynamic variations of implicit surfaces under partial differential equations. Examples include evolving an initial surface towards vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of implicit surfaces regularized by specific differential equations.
Análisis de Clusters para velocidades GNSS que revelan patrones de deformación del ciclo sísmico y de la estructura andina.
Resumen: A partir de técnicas de aprendizaje automático no supervisado se analizan los desplazamientos de la corteza a escala continental en áreas afectadas por el ciclo sísmico de grandes terremotos de subducción a lo largo de Chile. Particularmente, usamos algoritmos de clustering como una herramienta exploratoria para la investigación de patrones espaciales en velocidades GNSS regionales, sin incurrir en las complejidades de modelar una fuente física. Como datos utilizados, presentamos un campo de velocidad a escala continental que incluye...
