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We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with…
The failure of 2D numerical cohesive granular steps collapsing under gravity are simulated for a large range of cohesion. Focussing on the cumulative displacement of the grains, and defining a displacement threshold, we establish a sensible…
In energy management, it is common that strategic investment decisions (storage capacity, production units) are made at a slow time scale, whereas operational decisions (storage, production) are made at a fast time scale: for such problems,…
Dynamical supersymmetry breaking is a fascinating theoretical problem. It is also of phenomenological significance. A better understanding of this phenomenon can help in model building, which in turn is useful in guiding the search for…
Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…
We define a second-order neural network stochastic gradient training algorithm whose block-diagonal structure effectively amounts to normalizing the unit activations. Investigating why this algorithm lacks in robustness then reveals two…
This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
This note deals with the mono-dimensional equation: $\d_t u -\d_x L(u_x) =f$ with $L(\cdot)$ merely monotone. The goal is to examine the features of facets -- flat regions of graphs of solutions appearing as $L(\cdot)$ suffers jumps. We…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
Cracks play a crucial role in assessing the safety and durability of manufactured buildings. However, the long and sharp topological features and complex background of cracks make the task of crack segmentation extremely challenging. In…
Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other…
Understanding the interplay between ordered structures and substrate curvature is an interesting problem with versatile applications, including functionalization of charged supramolecular surfaces and modern microfluidic technologies. In…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
With recent advances in both responsive materials and fabrication techniques it is now possible to construct integrated functional structures, composed of both structural and active materials. We investigate the robust design of such…