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The ability of widely distributed radar systems to capture diverse spatial scattering properties substantially improves radar imaging performance. Traditional imaging methods leverage regularized optimization techniques to reconstruct…

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…

Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding…

In this work we propose a differential geometric motivation for Nesterov's accelerated gradient method (AGM) for strongly-convex problems. By considering the optimization procedure as occurring on a Riemannian manifold with a natural…

Diffusion models, as a type of generative model, have achieved impressive results in generating images and videos conditioned on textual conditions. However, the generation process of diffusion models involves denoising dozens of steps to…

Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…

It is common to manufacture an object by decomposing it into parts that can be assembled. This decomposition is often required by size limits of the machine, the complex structure of the shape, etc. To make it possible to easily assemble…

This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…

Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…

The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational…

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,…

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

Adaptive gradient methods have attracted much attention of machine learning communities due to the high efficiency. However their acceleration effect in practice, especially in neural network training, is hard to analyze, theoretically. The…

Deep learning methods for accelerated MRI achieve state-of-the-art results but largely ignore additional speedups possible with noncartesian sampling trajectories. To address this gap, we created a generative diffusion model-based…

Diffusion models achieve great success in generating diverse and high-fidelity images, yet their widespread application, especially in real-time scenarios, is hampered by their inherently slow generation speed. The slow generation stems…

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with…

Finite-difference time-domain (FDTD) simulations often involve physical quantities spanning multiple orders of magnitude, such as the speed of light or electromagnetic field amplitudes. The standard practice for maintaining numerical…

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…

Graph-based procedural materials are ubiquitous in content production industries. Procedural models allow the creation of photorealistic materials with parametric control for flexible editing of appearance. However, designing a specific…