Simplified Kalman filtering for non-linear models.

Event Date: Jan 09, 2023 in Seminar CMM, Seminars

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 context of sport rating  where the skills of the...

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Determinación de erosión costera con imágenes satelitales Sentinel-2 entre 2015 – 2022. Caso de estudio Bahía de Algarrobo, Chile Central

Event Date: Jan 09, 2023 in Ciclo de Seminarios quincenales de la Alianza Copernicus-Chile, Seminars

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 uso de imágenes satelitales Sentinel-2 entre los...

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On traveling waves for the Gross-Pitaevskii equations.

Event Date: Jan 03, 2023 in Differential Equations, Seminars

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 nonlocal interactions in the potential energy, obtained...

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Conjugacy classes of germs near a hyperbolic fixed point in dimension 1.

Event Date: Dec 26, 2022 in Dynamical Systems, Seminars

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 bi-Lipschitz conjugate, or which are pairwise bi-Lipschitz...

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Robust shape optimization with small uncertaintie.

Event Date: Dec 21, 2022 in Optimization and Equilibrium, Seminars

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 standard adjoint techniques from optimal control...

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Neural Implicit Surface Evolution using Differential Equations.

Event Date: Dec 20, 2022 in Differential Equations, Seminars

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.

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