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We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order…
Kernel design for Multi-output Gaussian Processes (MOGP) has received increased attention recently. In particular, the Multi-Output Spectral Mixture kernel (MOSM) arXiv:1709.01298 approach has been praised as a general model in the sense…
Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the…
Orthogonality constraints are ubiquitous in robust and probabilistic machine learning. Unfortunately, current optimizers are computationally expensive and do not scale to problems with hundreds or thousands of constraints. One notable…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
We here introduce a novel scheme for generating smoothly-varying infill graded microstructural (IGM) configurations from a given menu of generating cells. The scheme was originally proposed for essentially improving the variety of…
This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…
This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but…
In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
In topology optimization, the treatment of stress constraints for very large scale problems has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the…
Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as…
Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…
The demand for deploying large language models(LLMs) on mobile devices continues to increase, driven by escalating data security concerns and cloud costs. However, network bandwidth and memory limitations pose challenges for deploying…
We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…
Sketching algorithms have recently proven to be a powerful approach both for designing low-space streaming algorithms as well as fast polynomial time approximation schemes (PTAS). In this work, we develop new techniques to extend the…
In this paper we introduce the \emph{robust random number generation} problem where the goal is to design an abstract tile assembly system (aTAM system) whose terminal assemblies can be split into $n$ partitions such that a resulting…
Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…