相关论文: Another source of mesh dependence in topology opti…

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…

When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation,…

The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper,…

We introduce a simultaneous and meshfree topology optimization (TO) framework based on physics-informed Gaussian processes (GPs). Our framework endows all design and state variables via GP priors which have a shared, multi-output mean…

Policy optimization methods like Group Relative Policy Optimization (GRPO) and its variants have achieved strong results on mathematical reasoning and code generation tasks. Despite extensive exploration of reward processing strategies and…

Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper…

Large Language Models (LLMs) are known to exhibit social, demographic, and gender biases, often as a consequence of the data on which they are trained. In this work, we adopt a mechanistic interpretability approach to analyze how such…

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

Large Language Models (LLMs) are being applied in a wide array of settings, well beyond the typical language-oriented use cases. In particular, LLMs are increasingly used as a plug-and-play method for fitting data and generating…

We study a generic class of decentralized algorithms in which $N$ agents jointly optimize the non-convex objective $f(u):=1/N\sum_{i=1}^{N}f_i(u)$, while only communicating with their neighbors. This class of problems has become popular in…

Many resource allocation tasks are challenging global (i.e., non-convex) optimization problems. The main issue is that the computational complexity of these problems grows exponentially in the number of variables instead of polynomially as…

Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…

Performance of end-to-end neural networks on a given hardware platform is a function of its compute and memory signature, which in-turn, is governed by a wide range of parameters such as topology size, primitives used, framework used,…

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…

The scaling laws have become the de facto guidelines for designing large language models (LLMs), but they were studied under the assumption of unlimited computing resources for both training and inference. As LLMs are increasingly used as…

We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The…

Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…

This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…