Related papers: Trade-offs in absorption and scattering by nanopho…

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…

In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…

Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…

Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…

Modern nanophotonic and meta-optical devices utilize a tremendous number of structural degrees of freedom to enhance light--matter interactions. A fundamental question is how large such enhancements can be. We develop an analytical…

Multi-task learning solves multiple correlated tasks. However, conflicts may exist between them. In such circumstances, a single solution can rarely optimize all the tasks, leading to performance trade-offs. To arrive at a set of optimized…

In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…

We derive and discuss general physical bounds on the electromagnetic scattering and absorption of passive structures. Our theory, based on passivity and power conservation, quantifies the minimum and maximum allowed scattering for an object…

For the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order, and its solution is the fixed…

The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…

Most approaches for designing self-assembled materials focus on the thermodynamic stability of a target structure or crystal polymorph. Yet in practice, the outcome of a self-assembly process is often controlled by kinetic pathways. Here we…

Optimization of accelerator performance parameters is limited by numerous trade-offs and finding the appropriate balance between optimization goals for an unknown system is challenging to achieve. Here we show that multi-objective Bayesian…

We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…

Multi-objective optimization (MOO) is a well-studied problem for several important recommendation problems. While multiple approaches have been proposed, in this work, we focus on using constrained optimization formulations (e.g., quadratic…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

We present a generalized formalism to describe the optical energy flow and spatially resolved absorption in arbitrarily anisotropic layered structures. The algorithm is capable of treating any number of layers of arbitrarily anisotropic,…

We study the problem of actively imaging a range-limited far-field scene using an antenna array. We describe how the range limit imposes structure in the measurements across multiple wavelengths. This structure allows us to introduce a…

Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel…

The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then…