Related papers: Adaptive shape optimization with NURBS designs and…

Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this…

We prove $hp$-optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) for the biharmonic problem with homogeneous essential boundary conditions. We consider tensor product-type meshes in two and three dimensions,…

We propose a simple drop-in noise-tolerant replacement for the standard finite difference procedure used ubiquitously in blackbox optimization. In our approach, parameter perturbation directions are defined by a family of structured…

A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…

This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural…

Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and…

We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…

Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…

We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…

We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…

In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…

In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…

A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local…

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…

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…

Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving partial differential equations, including the Helmholtz equation, due to their flexibility and mesh-free formulation. However, their low-frequency bias…

In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adaptive method generating a two-layer spline NN and a numerical…

Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…

Most Gaussian Splatting techniques that provide a 3D semantic representation of the scene do not optimize the underlying 3D geometry, making object-level editing or asset extraction challenging. Recent methods, such as COBGS, Trace3D,…