Neural Network Based Deep Learning Method for Multi-Dimensional Neutron Diffusion Problems with Novel Treatment to Boundary

In this paper, the artificial neural networks (ANN) based deep learning (DL) techniques were developed to solve the neutron diffusion problems for the continuous neutron flux distribution without domain discretization in advance. Due to its mesh-free property, the DL solution can easily be extended to complicated geometries. Two specific realizations of DL methods with different boundary treatments are developed and compared for accuracy and efficiency, including the boundary independent method (BIM) and boundary dependent method (BDM). The performance comparison on analytic benchmark indicates BDM being the preferred DL method. Novel constructions of trial function are proposed to generalize the application of BDM. For a more in-depth understanding of the BDM on diffusion problems, the influence of important hyper-parameters is further investigated. Numerical results indicate that the accuracy of BDM can reach hundreds of times higher than that of BIM on diffusion problems. This work can provide a new perspective for applying the DL method to nuclear reactor calculations.

Impact of domain discretization on the accuracy of a 2D model of PCM module for ventilation application

Optimal selection of domain discretization for numerical Phase Change Material (PCM) models is useful to establish confidence in model predictions and minimize the time consumption for conducting design analysis. Very detailed and geometrically complex models are usually applied utilizing several million cells. A 2D numerical PCM model of a climate module for thermal comfort ventilation is investigated. The mesh independence was conducted on 22 different mesh sizes ranging from 70 to 10.870 nodes. Convergence criteria was evaluated based on average air supply temperature and total heat transfer between the PCM and the air within the simulation time interval. Less than 0.1 % change in the air supply temperature and the heat transfer between the PCM and the air was achieved with 5250 and 9870 nodes, respectively. Thereby highlighting that a relatively small amount of nodes can be considered to achieve sufficient accuracy to conduct analysis of PCM applications.

Nearest Neighbors Search Using Multi-GPU

Meshless methods are increasingly gaining space in the study of electromagnetic phenomena as an alternative to traditional mesh-based methods. One of their biggest advantages is the absence of a mesh to describe the simulation domain. Instead, the domain discretization is done by spreading nodes along the domain and its boundaries. Thus, meshless methods are based on the interactions of each node with all its neighbors, and determining the neighborhood of the nodes becomes a fundamental task. The k-nearest neighbors (kNN) is a well-known algorithm used for this purpose, but it becomes a bottleneck for these methods due to its high computational cost. One of the alternatives to reduce the kNN high computational cost is to use spatial partitioning data structures (e.g., planar grid) that allow pruning when performing the k-nearest neighbors search. Furthermore, many of these strategies employed for kNN search have been adapted for graphics processing units (GPUs) and can take advantage of its high potential for parallelism. Thus, this paper proposes a multi-GPU version of the grid method for solving the kNN problem. It was possible to achieve a speedup of up to 1.99x and up to 3.94x using two and four GPUs, respectively, when compared against the single-GPU version of the grid method.

Coupled topology and shape optimization using an embedding domain discretization method

Density-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.

Elastic solution of a polyhedral particle with a polynomial eigenstrain and particle discretization

The paper extends the recent work (JAM, 88, 061002, 2021) of the Eshelby's tensors for polynomial eigenstrains from a two dimensional (2D) to three dimensional (3D) domain, which provides the solution to the elastic field with continuously distributed eigenstrain on a polyhedral inclusion approximated by the Taylor series of polynomials. Similarly, the polynomial eigenstrain is expanded at the centroid of the polyhedral inclusion with uniform, linear and quadratic order terms, which provides tailorable accuracy of the elastic solutions of polyhedral inhomogeneity by using Eshelby's equivalent inclusion method. However, for both 2D and 3D cases, the stress distribution in the inhomogeneity exhibits a certain discrepancy from the finite element results at the neighborhood of the vertices due to the singularity of Eshelby's tensors, which makes it inaccurate to use the Taylor series of polynomials at the centroid to catch the eigenstrain at the vertices. This paper formulates the domain discretization with tetrahedral elements to accurately solve for eigenstrain distribution and predict the stress field. With the eigenstrain determined at each node, the elastic field can be predicted with the closed-form domain integral of Green's function. The parametric analysis shows the performance difference between the polynomial eigenstrain by the Taylor expansion at the centroid and the 𝐶0 continuous eigenstrain by particle discretization. Because the stress singularity is evaluated by the analytical form of the Eshelby's tensor, the elastic analysis is robust, stable and efficient.

A Fully Meshless Approach to the Numerical Simulation of Heat Conduction Problems over Arbitrary 3D Geometries

One of the goals of new CAE (Computer Aided Engineering) software is to reduce both time and costs of the design process without compromising accuracy. This result can be achieved, for instance, by promoting a “plug and play” philosophy, based on the adoption of automatic mesh generation algorithms. This in turn brings about some drawbacks, among others an unavoidable loss of accuracy due to the lack of specificity of the produced discretization. Alternatively it is possible to rely on the so called “meshless” methods, which skip the mesh generation process altogether. The purpose of this paper is to present a fully meshless approach, based on Radial Basis Function generated Finite Differences (RBF-FD), for the numerical solution of generic elliptic PDEs, with particular reference to time-dependent and steady 3D heat conduction problems. The absence of connectivity information, which is a peculiar feature of this meshless approach, is leveraged in order to develop an efficient procedure that accepts as input any given geometry defined by a stereolithography surface (.stl file format). In order to assess its performance, the aforementioned strategy is tested over multiple geometries, selected for their complexity and engineering relevance, highlighting excellent results both in terms of accuracy and computational efficiency. In order to account for future extensibility and performance, both node generation and domain discretization routines are entirely developed using Julia, an emerging programming language that is rapidly establishing itself as the new standard for scientific computing.

Machine Learning-Based Detection of Graphene Defects with Atomic Precision

Defects in graphene can profoundly impact its extraordinary properties, ultimately influencing the performances of graphene-based nanodevices. Methods to detect defects with atomic resolution in graphene can be technically demanding and involve complex sample preparations. An alternative approach is to observe the thermal vibration properties of the graphene sheet, which reflects defect information but in an implicit fashion. Machine learning, an emerging data-driven approach that offers solutions to learning hidden patterns from complex data, has been extensively applied in material design and discovery problems. In this paper, we propose a machine learning-based approach to detect graphene defects by discovering the hidden correlation between defect locations and thermal vibration features. Two prediction strategies are developed: an atom-based method which constructs data by atom indices, and a domain-based method which constructs data by domain discretization. Results show that while the atom-based method is capable of detecting a single-atom vacancy, the domain-based method can detect an unknown number of multiple vacancies up to atomic precision. Both methods can achieve approximately a 90% prediction accuracy on the reserved data for testing, indicating a promising extrapolation into unseen future graphene configurations. The proposed strategy offers promising solutions for the non-destructive evaluation of nanomaterials and accelerates new material discoveries.