Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshes

Machine-learned surrogate models to accelerate lengthy computer simulations are becoming increasingly important as engineers look to streamline the product design cycle. In many cases, these approaches offer the ability to predict relevant quantities throughout a geometry, but place constraints on the form of the input data. In a world of diverse data types, a preferred approach would not restrict the input to a particular structure. In this paper, we propose Topology-Agnostic Graph U-Net (TAG U-Net), a graph convolutional network that can be trained to input any mesh or graph structure and output a prediction of a target scalar field at each node. The model constructs coarsened versions of each input graph and performs a set of convolution and pooling operations to predict the node-wise outputs on the original graph. By training on a diverse set of shapes, the model can make strong predictions, even for shapes unlike those seen during training. A 3-D additive manufacturing dataset is presented, containing Laser Powder Bed Fusion simulation results for thousands of parts. The model is demonstrated on this dataset, and it performs well, predicting both 2-D and 3-D scalar fields with a median R-squared > 0.85 on test geometries. Code and datasets are available online.

Scalar Field Prediction on Meshes Using Interpolated Multi-Resolution Convolutional Neural Networks

Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field prediction can be faster than traditional finite element methods. However, current data-driven techniques to predict scalar fields are limited to a fixed grid domain, instead of arbitrary mesh structures. In this work, we propose a method to predict scalar fields on arbitrary meshes. It uses a convolutional neural network whose feature maps at multiple resolutions are interpolated to node positions before being fed into a multilayer perceptron to predict solutions to partial differential equations at mesh nodes. The model is trained on finite element von Mises stress fields, and once trained it can estimate stress values at each node on any input mesh. Two shape datasets are investigated, and the model has strong performance on both, with a median R-squared value of 0.91. We also demonstrate the model on a temperature field in a heat conduction problem, where its predictions have a median R-squared value of 0.99. Our method provides a potential flexible alternative to finite element analysis in engineering design contexts. Code and datasets are available online.

Multi-scale Topology Optimization using Neural Networks

A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology optimization using neural networks. Our approach focuses on inverse homogenization that seamlessly maintains compatibility across neighboring microstructure cells. Our approach consists of a topology neural network that optimizes the microstructure shape and distribution across the design domain as a continuous field. Each microstructure cell is optimized based on a specified elasticity tensor that also accommodates in-plane rotations. The neural network takes as input the local coordinates within a cell to represent the density distribution within a cell, as well as the global coordinates of each cell to design spatially varying microstructure cells. As such, our approach models an n-dimensional multi-scale optimization problem as a 2n-dimensional inverse homogenization problem using neural networks. During the inverse homogenization of each unit cell, we extend the boundary of each cell by scaling the input coordinates such that the boundaries of neighboring cells are combined. Inverse homogenization on the combined cell improves connectivity. We demonstrate our method through the design and optimization of graded multi-scale structures.

Automating Style Analysis and Visualization With Explainable AI -- Case Studies on Brand Recognition

Incorporating style-related objectives into shape design has been centrally important to maximize product appeal. However, stylistic features such as aesthetics and semantic attributes are hard to codify even for experts. As such, algorithmic style capture and reuse have not fully benefited from automated data-driven methodologies due to the challenging nature of design describability. This paper proposes an AI-driven method to fully automate the discovery of brand-related features. Our approach introduces BIGNet, a two-tier Brand Identification Graph Neural Network (GNN) to classify and analyze scalar vector graphics (SVG). First, to tackle the scarcity of vectorized product images, this research proposes two data acquisition workflows: parametric modeling from small curve-based datasets, and vectorization from large pixel-based datasets. Secondly, this study constructs a novel hierarchical GNN architecture to learn from both SVG's curve-level and chunk-level parameters. In the first case study, BIGNet not only classifies phone brands but also captures brand-related features across multiple scales, such as the location of the lens, the height-width ratio, and the screen-frame gap, as confirmed by AI evaluation. In the second study, this paper showcases the generalizability of BIGNet learning from a vectorized car image dataset and validates the consistency and robustness of its predictions given four scenarios. The results match the difference commonly observed in luxury vs. economy brands in the automobile market. Finally, this paper also visualizes the activation maps generated from a convolutional neural network and shows BIGNet's advantage of being a more human-friendly, explainable, and explicit style-capturing agent. Code and dataset can be found on Github: 1. Phone case study: github.com/parksandrecfan/bignet-phone 2. Car case study: github.com/parksandrecfan/bignet-car

Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency

We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial field on the unoptimized domain, the efficiency of neural network based topology optimization can be further improved. Our approach consists of a topology neural network that is trained on a case by case basis to represent the geometry for a single topology optimization problem. It takes in domain coordinates as input to represent the density at each coordinate where the topology is represented by a continuous density field. The displacement is solved through a finite element solver. We employ the strain energy field calculated on the initial design domain as an additional conditioning field input to the neural network throughout the optimization. The addition of the strain energy field input improves the convergence speed compared to standalone neural network based topology optimization.

DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks

We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can give comparable results to conventional topology optimization techniques, with an added advantage of enabling seamless integration with post-processing software, and a potential of topology optimization with objectives where meshing and Finite Element Analysis (FEA) may be expensive or not suitable. Our approach (DMF-TONN) takes in as inputs the boundary conditions and domain coordinates and finds the optimum density field for minimizing the loss function of compliance and volume fraction constraint violation. The mesh-free nature is enabled by a physics-informed displacement field approximation neural network to solve the linear elasticity partial differential equation and replace the FEA conventionally used for calculating the compliance. We show that using a suitable Fourier Features neural network architecture and hyperparameters, the density field approximation neural network can learn the weights to represent the optimal density field for the given domain and boundary conditions, by directly backpropagating the loss gradient through the displacement field approximation neural network, and unlike prior work there is no requirement of a sensitivity filter, optimality criterion method, or a separate training of density network in each topology optimization iteration.

Target specific peptide design using latent space approximate trajectory collector

Despite the prevalence and many successes of deep learning applications in de novo molecular design, the problem of peptide generation targeting specific proteins remains unsolved. A main barrier for this is the scarcity of the high-quality training data. To tackle the issue, we propose a novel machine learning based peptide design architecture, called Latent Space Approximate Trajectory Collector (LSATC). It consists of a series of samplers on an optimization trajectory on a highly non-convex energy landscape that approximates the distributions of peptides with desired properties in a latent space. The process involves little human intervention and can be implemented in an end-to-end manner. We demonstrate the model by the design of peptide extensions targeting Beta-catenin, a key nuclear effector protein involved in canonical Wnt signalling. When compared with a random sampler, LSATC can sample peptides with $36\%$ lower binding scores in a $16$ times smaller interquartile range (IQR) and $284\%$ less hydrophobicity with a $1.4$ times smaller IQR. LSATC also largely outperforms other common generative models. Finally, we utilized a clustering algorithm to select 4 peptides from the 100 LSATC designed peptides for experimental validation. The result confirms that all the four peptides extended by LSATC show improved Beta-catenin binding by at least $20.0\%$, and two of the peptides show a $3$ fold increase in binding affinity as compared to the base peptide.

Component Segmentation of Engineering Drawings Using Graph Convolutional Networks

We present a data-driven framework to automate the vectorization and machine interpretation of 2D engineering part drawings. In industrial settings, most manufacturing engineers still rely on manual reads to identify the topological and manufacturing requirements from drawings submitted by designers. The interpretation process is laborious and time-consuming, which severely inhibits the efficiency of part quotation and manufacturing tasks. While recent advances in image-based computer vision methods have demonstrated great potential in interpreting natural images through semantic segmentation approaches, the application of such methods in parsing engineering technical drawings into semantically accurate components remains a significant challenge. The severe pixel sparsity in engineering drawings also restricts the effective featurization of image-based data-driven methods. To overcome these challenges, we propose a deep learning based framework that predicts the semantic type of each vectorized component. Taking a raster image as input, we vectorize all components through thinning, stroke tracing, and cubic bezier fitting. Then a graph of such components is generated based on the connectivity between the components. Finally, a graph convolutional neural network is trained on this graph data to identify the semantic type of each component. We test our framework in the context of semantic segmentation of text, dimension and, contour components in engineering drawings. Results show that our method yields the best performance compared to recent image, and graph-based segmentation methods.

Hierarchical Automatic Power Plane Generation with Genetic Optimization and Multilayer Perceptron

We present an automatic multilayer power plane generation method to accelerate the design of printed circuit boards (PCB). In PCB design, while automatic solvers have been developed to predict important indicators such as the IR-drop, power integrity, and signal integrity, the generation of the power plane itself still largely relies on laborious manual methods. Our automatic power plane generation approach is based on genetic optimization combined with a multilayer perceptron and is able to automatically generate power planes across a diverse set of problems with varying levels of difficulty. Our method GOMLP consists of an outer loop genetic optimizer (GO) and an inner loop multi-layer perceptron (MLP) that generate power planes automatically. The critical elements of our approach include contour detection, feature expansion, and a distance measure to enable island-minimizing complex power plane generation. We compare our approach to a baseline solution based on A*. The A* method consisting of a sequential island generation and merging process which can produce less than ideal solutions. Our experimental results show that on single layer power plane problems, our method outperforms A* in 71% of the problems with varying levels of board layout difficulty. We further describe H-GOMLP, which extends GOMLP to multilayer power plane problems using hierarchical clustering and net similarities based on the Hausdorff distance.

Concurrent build direction, part segmentation, and topology optimization for additive manufacturing using neural networks

We propose a neural network-based approach to topology optimization that aims to reduce the use of support structures in additive manufacturing. Our approach uses a network architecture that allows the simultaneous determination of an optimized: (1) part segmentation, (2) the topology of each part, and (3) the build direction of each part that collectively minimize the amount of support structure. Through training, the network learns a material density and segment classification in the continuous 3D space. Given a problem domain with prescribed load and displacement boundary conditions, the neural network takes as input 3D coordinates of the voxelized domain as training samples and outputs a continuous density field. Since the neural network for topology optimization learns the density distribution field, analytical solutions to the density gradient can be obtained from the input-output relationship of the neural network. We demonstrate our approach on several compliance minimization problems with volume fraction constraints, where support volume minimization is added as an additional criterion to the objective function. We show that simultaneous optimization of part segmentation along with the topology and print angle optimization further reduces the support structure, compared to a combined print angle and topology optimization without segmentation.