Eric Volkmann

Arturs Berzins, Andreas Radler, Eric Volkmann et al.

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) -- a framework for training shape-generative neural fields without data by leveraging user-specified design requirements in the form of objectives and constraints. By adding diversity as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several problems spanning physics, geometry, and engineering design, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.

Eric Volkmann, Alena Brändle, Daniel Durstewitz et al.

Data-driven inference of the generative dynamics underlying a set of observed time series is of growing interest in machine learning and the natural sciences. In neuroscience, such methods promise to alleviate the need to handcraft models based on biophysical principles and allow to automatize the inference of inter-individual differences in brain dynamics. Recent breakthroughs in training techniques for state space models (SSMs) specifically geared toward dynamical systems (DS) reconstruction (DSR) enable to recover the underlying system including its geometrical (attractor) and long-term statistical invariants from even short time series. These techniques are based on control-theoretic ideas, like modern variants of teacher forcing (TF), to ensure stable loss gradient propagation while training. However, as it currently stands, these techniques are not directly applicable to data modalities where current observations depend on an entire history of previous states due to a signal's filtering properties, as common in neuroscience (and physiology more generally). Prominent examples are the blood oxygenation level dependent (BOLD) signal in functional magnetic resonance imaging (fMRI) or Ca$^{2+}$ imaging data. Such types of signals render the SSM's decoder model non-invertible, a requirement for previous TF-based methods. Here, exploiting the recent success of control techniques for training SSMs, we propose a novel algorithm that solves this problem and scales exceptionally well with model dimensionality and filter length. We demonstrate its efficiency in reconstructing dynamical systems, including their state space geometry and long-term temporal properties, from just short BOLD time series.

Andreas Radler, Eric Volkmann, Johannes Brandstetter et al.

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 Topology Optimization using Modulated Neural Fields (TOM) - 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 TOM on 2D and 3D TO problems. Our results show that TOM generates more diverse solutions than any previous method, all while maintaining near-optimality and without relying on a dataset. These findings open new avenues for engineering and design, offering enhanced flexibility and innovation in structural optimization.