Mostafa Samir

Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi et al.

Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from data. We present two approaches: a two-step method that reconstructs trajectories before learning the Hamiltonian, and a one-step method that jointly infers both. Across several benchmark systems, including mass-spring dynamics, a nonlinear pendulum, and the Henon-Heiles system, we demonstrate that our framework achieves accurate, data-efficient predictions and outperforms two-step kernel-based baselines, particularly in scarce-data regimes, while preserving the conservation properties of Hamiltonian dynamics. Moreover, our methodology provides theoretical a priori error estimates, ensuring reliability of the learned models. We also provide a more general, problem-agnostic numerical framework that goes beyond Hamiltonian systems and can be used for data-driven learning of arbitrary dynamical systems.

Hamed Hamze Bajgiran, Pau Batlle Franch, Houman Owhadi et al.

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B) requires a prior, it is generally brittle and posterior estimations can be slow. Although (C) leads to the identification of an optimal prior, its approximation suffers from the curse of dimensionality and the notion of risk is one that is averaged with respect to the distribution of the data. We introduce a 4th kind which is a hybrid between (A), (B), (C), and hypothesis testing. It can be summarized as, after observing a sample $x$, (1) defining a likelihood region through the relative likelihood and (2) playing a minmax game in that region to define optimal estimators and their risk. The resulting method has several desirable properties (a) an optimal prior is identified after measuring the data, and the notion of risk is a posterior one, (b) the determination of the optimal estimate and its risk can be reduced to computing the minimum enclosing ball of the image of the likelihood region under the quantity of interest map (which is fast and not subject to the curse of dimensionality). The method is characterized by a parameter in $ [0,1]$ acting as an assumed lower bound on the rarity of the observed data (the relative likelihood). When that parameter is near $1$, the method produces a posterior distribution concentrated around a maximum likelihood estimate with tight but low confidence UQ estimates. When that parameter is near $0$, the method produces a maximal risk posterior distribution with high confidence UQ estimates. In addition to navigating the accuracy-uncertainty tradeoff, the proposed method addresses the brittleness of Bayesian inference by navigating the robustness-accuracy tradeoff associated with data assimilation.

Bashar Talafha, Mohammad Ali, Muhy Eddin Za'ter et al.

Arabic dialect identification is a complex problem for a number of inherent properties of the language itself. In this paper, we present the experiments conducted, and the models developed by our competing team, Mawdoo3 AI, along the way to achieving our winning solution to subtask 1 of the Nuanced Arabic Dialect Identification (NADI) shared task. The dialect identification subtask provides 21,000 country-level labeled tweets covering all 21 Arab countries. An unlabeled corpus of 10M tweets from the same domain is also presented by the competition organizers for optional use. Our winning solution itself came in the form of an ensemble of different training iterations of our pre-trained BERT model, which achieved a micro-averaged F1-score of 26.78% on the subtask at hand. We publicly release the pre-trained language model component of our winning solution under the name of Multi-dialect-Arabic-BERT model, for any interested researcher out there.