Related papers: Shadowing the rotating annulus. Part II: Gradient …
We perform a-priori validation tests of subgrid-scale (SGS) models for the turbulent transport of momentum, energy and passive scalars. To this end, we conduct two sets of high-resolution hydrodynamical simulations with a Lagrangian code:…
This paper proposes a novel model inference procedure to identify system matrix from a single noisy trajectory over a finite-time interval. The proposed inference procedure comprises an observation data processor, a redundant data processor…
Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. This fact is used to find a unique semiclassical representation without the…
Previous visual object tracking methods employ image-feature regression models or coordinate autoregression models for bounding box prediction. Image-feature regression methods heavily depend on matching results and do not utilize…
The paper proposes an alternative to the Foucault pendulum for detecting various movements of rotation of the Earth. Calculations suggest that if the duration of a "free" fall becomes longer the eastward deflection will be amplified in…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
We study the stochastic optimization problem from a continuous-time perspective, with a focus on the Stochastic Gradient Descent with Momentum (SGDM) method. We show that the trajectory of SGDM, despite its \emph{stochastic} nature,…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
Perception systems play a crucial role in autonomous driving, incorporating multiple sensors and corresponding computer vision algorithms. 3D LiDAR sensors are widely used to capture sparse point clouds of the vehicle's surroundings.…
Context. Recently our ability to study stars using asteroseismic techniques has increased dramatically, largely through the use of space based photometric observations. Work has also been done using ground based spectroscopic observations…
We provide a new perspective on shadow tomography by demonstrating its deep connections with the general theory of measurement frames. By showing that the formalism of measurement frames offers a natural framework for shadow tomography --…
Shadow art is a captivating form of sculptural expression where the projection of a sculpture in a specific direction reveals a desired shape with high precision. In this work, we introduce Neural Shadow Art, which leverages implicit…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
In this work, we introduce a novel gradient descent-based approach for optimizing control systems, leveraging a new representation of stable closed-loop dynamics as a function of two matrices i.e. the step size or direction matrix and value…
Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…
Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…
Machine learning (ML) systems are increasingly deployed in high-stakes domains where reliability is paramount. This thesis investigates how uncertainty estimation can enhance the safety and trustworthiness of ML, focusing on selective…
A game theory inspired methodology is proposed for finding a function's saddle points. While explicit descent methods are known to have severe convergence issues, implicit methods are natural in an adversarial setting, as they take the…
Model reduction techniques have emerged as a powerful paradigm across different fronts of scientific computing. Despite their success, the provided tools and methodologies remain limited if high-dimensional dynamical systems subject to…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…