Generative Topology Optimization: Exploring Diverse Solutions in Structural Design

Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the exploration of alternative designs. To address this limitation, we introduce Generative Topology Optimization (GenTO) - a data-free method that trains a neural network to generate structurally compliant shapes and explores diverse solutions through an explicit diversity constraint. The network is trained with a solver-in-the-loop, optimizing the material distribution in each iteration. The trained model produces diverse shapes that closely adhere to the design requirements. We validate GenTO on 2D and 3D TO problems. Our results demonstrate that GenTO produces more diverse solutions than any prior method while maintaining near-optimality and being an order of magnitude faster due to inherent parallelism. These findings open new avenues for engineering and design, offering enhanced flexibility and innovation in structural optimization.

Simplified priors for Object-Centric Learning

Humans excel at abstracting data and constructing \emph{reusable} concepts, a capability lacking in current continual learning systems. The field of object-centric learning addresses this by developing abstract representations, or slots, from data without human supervision. Different methods have been proposed to tackle this task for images, whereas most are overly complex, non-differentiable, or poorly scalable. In this paper, we introduce a conceptually simple, fully-differentiable, non-iterative, and scalable method called SAMP Simplified Slot Attention with Max Pool Priors). It is implementable using only Convolution and MaxPool layers and an Attention layer. Our method encodes the input image with a Convolutional Neural Network and then uses a branch of alternating Convolution and MaxPool layers to create specialized sub-networks and extract primitive slots. These primitive slots are then used as queries for a Simplified Slot Attention over the encoded image. Despite its simplicity, our method is competitive or outperforms previous methods on standard benchmarks.

Geometry-Informed Neural Networks

We introduce the concept of geometry-informed neural networks (GINNs), which encompass (i) learning under geometric constraints, (ii) neural fields as a suitable representation, and (iii) generating diverse solutions to under-determined systems often encountered in geometric tasks. Notably, the GINN formulation does not require training data, and as such can be considered generative modeling driven purely by constraints. We add an explicit diversity loss to mitigate mode collapse. We consider several constraints, in particular, the connectedness of components which we convert to a differentiable loss through Morse theory. Experimentally, we demonstrate the efficacy of the GINN learning paradigm across a range of two and three-dimensional scenarios with increasing levels of complexity.