Related papers: Shadowing the rotating annulus. Part II: Gradient …
Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…
Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…
The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…
Complex degradations like noise, blur, and low resolution are typical challenges in real world image fusion tasks, limiting the performance and practicality of existing methods. End to end neural network based approaches are generally…
Conventional imaging requires a line of sight to create accurate visual representations of a scene. In certain circumstances, however, obtaining a suitable line of sight may be impractical, dangerous, or even impossible. Non-line-of-sight…
A landmark result of non-smooth convex optimization is that gradient descent is an optimal algorithm whenever the number of computed gradients is smaller than the dimension $d$. In this paper we study the extension of this result to the…
This paper presents a novel methodology that uses surrogate models in the form of neural networks to reduce the computation time of simulation-based optimization of a reference trajectory. Simulation-based optimization is necessary when…
We present a novel method for estimating the circulations and positions of point vortices using trajectory data of passive particles in the presence of Gaussian noise. The method comprises two algorithms: the first one calculates the vortex…
We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and…
In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…
A didactic sequence of activities on some topics of Astronomy, related mainly with the length and orientation of shadows cast by a gnomon, the movement of shadows during daytime in different seasons of the year, and finding the true…
When machine learning models encounter data which is out of the distribution on which they were trained they have a tendency to behave poorly, most prominently over-confidence in erroneous predictions. Such behaviours will have disastrous…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency…
Nonintrusive shadowing algorithms efficiently compute $v$, the difference between shadowing trajectories, then use $v$ to compute derivatives of averaged objectives of chaos with respect to parameters of the dynamical system. However,…
Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…
We introduce a novel method for non-convex optimization, called Swarm-based Simulated Annealing (SSA), which is at the interface between the swarm-based gradient-descent (SBGD) [J. Lu et. al., ArXiv:2211.17157; E.Tadmor and A. Zenginoglu,…
We investigate the problem of persistent monitoring, where a mobile agent has to survey multiple targets in an environment in order to estimate their internal states. These internal states evolve with linear stochastic dynamics and the…
Specular reflection can be problematic for the determination of the cloud thermodynamic phase for near-nadir-pointing space LIDARs. A LIDAR system biased towards the specular contribution for backscatter, if near-concurrent to a…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…