Related papers: Optimization Fabrics
Topology optimization is an important basis for the design of components. Here, the optimal structure is found within a design space subject to boundary conditions. Thereby, the specific material law has a strong impact on the final design.…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
Designing faster optimization algorithms is of ever-growing interest. In recent years, learning to learn methods that learn how to optimize demonstrated very encouraging results. Current approaches usually do not effectively include the…
Gradient-based methods successfully train highly overparameterized models in practice, even though the associated optimization problems are markedly nonconvex. Understanding the mechanisms that make such methods effective has become a…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
The paper addresses the underlying source of two forms of induced anisotropy in granular materials: contact orientation anisotropy and contact force anisotropy. A rational, mathematical structure is reviewed for the manner in which fabric…
Woven fabrics play an essential role in everyday textiles for clothing/sportswear, water filtration, and retaining walls, to reinforcements in stiff composites for lightweight structures like aerospace, sporting, automotive, and marine…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem.…
Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
The field of robotics faces inherent challenges in manipulating deformable objects, particularly in understanding and standardising fabric properties like elasticity, stiffness, and friction. While the significance of these properties is…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…
Sequential pulling policies to flatten and smooth fabrics have applications from surgery to manufacturing to home tasks such as bed making and folding clothes. Due to the complexity of fabric states and dynamics, we apply deep imitation…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
We develop a normative framework for hierarchical model-based policy optimization based on applying second-order methods in the space of all possible state-action paths. The resulting natural path gradient performs policy updates in a…
We introduce the Riemannian Motion Policy (RMP), a new mathematical object for modular motion generation. An RMP is a second-order dynamical system (acceleration field or motion policy) coupled with a corresponding Riemannian metric. The…
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This…