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Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separate…
We study the fully dynamic All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. Given an $n$-vertex graph $G$ with non-negative edge lengths, that undergoes an online sequence of edge insertions and deletions, the…
Intracortical brain-machine interfaces demand low-latency, energy-efficient solutions for neural decoding. Spiking Neural Networks (SNNs) deployed on neuromorphic hardware have demonstrated remarkable efficiency in neural decoding by…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…
This work addresses the optimal control of multibody systems being actuated with control forces in order to find a dynamically feasible minimum-energy trajectory of the system. The optimal control problem and its constraints are integrated…
We show how to significantly reduce the number of energy bands required to model the interaction of light with crystalline solids in the velocity gauge. We achieve this by deriving analytical corrections to the electric current density.…
This paper investigates the energy savings that near-subthreshold processors can obtain in edge AI applications and proposes strategies to improve them while maintaining the accuracy of the application. The selected processors deploy…
Nature inspired algorithms has brought solutions to complex problems in optimization where the optimization and solution of complex problems is highly complex and nonlinear. There is a need to use proper design of the cost function or the…
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is…
A possible mechanism for the formation of a 90{\deg} misfit dislocation at the Ge/Si(001) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
$k$-Nearest Neighbor search on dense vector embeddings ($k$-NN retrieval) from pre-trained embedding models is the predominant retrieval method for text and images, as well as Retrieval-Augmented Generation (RAG) pipelines. In practice,…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
In real life, it is always an urge to reach our goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario is to represents…
Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or…
We investigate the differentiability of minimal average energy associated to the functionals $S_\ep (u) = \int_{\mathbb{R}^d} (1/2)|\nabla u|^2 + \ep V(x,u)\, dx$, using numerical and perturbative methods. We use the Sobolev gradient…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…
Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning…