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We present a new method to obtain spatio-temporal information from aggregated data of stationary traffic detectors, the ``adaptive smoothing method''. In essential, a nonlinear spatio-temporal lowpass filter is applied to the input detector…
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers…
Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…
Wind speed retrieval at sea surface is of primary importance for scientific and operational applications. Besides weather models, in-situ measurements and remote sensing technologies, especially satellite sensors, provide complementary…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous meta-optimization problem for parameters; the…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
Wind speed at sea surface is a key quantity for a variety of scientific applications and human activities. Due to the non-linearity of the phenomenon, a complete description of such variable is made infeasible on both the small scale and…
Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for…
We formulate a strong equivalence between machine learning, artificial intelligence methods and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
The Adaptive Smoothing Method (ASM) is a data-driven approach for traffic state estimation. It interpolates unobserved traffic quantities by smoothing measurements along spatio-temporal directions defined by characteristic traffic wave…
Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice. The best solution usually lies between these extremes.…
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…
Several advances have been made in Data Assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, based on a…
Fine localization in autonomous driving platforms is a task of broad interest, receiving much attention in recent years. Some localization algorithms use the Euclidean distance as a similarity measure between the local image acquired by a…
There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…
For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…
This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of…