Related papers: Parametric solutions involving geometry integrated…
We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
We provide numerical evidence demonstrating the necessity of employing a superparametric geometry representation in order to obtain optimal convergence orders on two-dimensional domains with curved boundaries when solving the Euler…
Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…
This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems,…
Geometry problem solving (GPS) requires capacities of multi-modal understanding, multi-hop reasoning and theorem knowledge application. In this paper, we propose a neural-symbolic model for plane geometry problem solving (PGPS), named…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale…
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
Over the past years, there has been significant interest in understanding the implicit bias of gradient descent optimization and its connection to the generalization properties of overparametrized neural networks. Several works observed…
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we…
In this paper we introduce paraglide, a visualization system designed for interactive exploration of parameter spaces of multi-variate simulation models. To get the right parameter configuration, model developers frequently have to go back…