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Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
An adaptive discretization refinement strategy for steady state discrete mesoscale models of coupled mechanics and mass transport in concrete is presented. Coupling is provided by two phenomena: the Biot's theory of poromechanics and an…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
Calibrating simulation models that take large quantities of multi-dimensional data as input is a hard simulation optimization problem. Existing adaptive sampling strategies offer a methodological solution. However, they may not sufficiently…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
Conforming hexahedral (hex) meshes are favored in simulation for their superior numerical properties, yet automatically decomposing a general 3D volume into a conforming hex mesh remains a formidable challenge. Among existing approaches,…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Control architectures and autonomy stacks for complex engineering systems are often divided into layers to decompose a complex problem and solution into distinct, manageable sub-problems. To simplify designs, uncertainties are often ignored…
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
We focus on modeling the relationship between an input feature vector and the predicted outcome of a trained decision tree using mixed-integer optimization. This can be used in many practical applications where a decision tree or tree…
The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…
This short communication discusses two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form…
High-performance multi-core software typically uses concurrent data structures. Tests for such data structures have significantly smaller state spaces than the entire software, making it feasible to model check them. However, dynamic memory…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…