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Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state., Comment: Published at ICLR 2024

Autoregressive neural networks within the temporal point process (TPP) framework have become the standard for modeling continuous-time event data. Even though these models can expressively capture event sequences in a one-step-ahead fashion, they are inherently limited for long-term forecasting applications due to the accumulation of errors caused by their sequential nature. To overcome these limitations, we derive ADD-THIN, a principled probabilistic denoising diffusion model for TPPs that operates on entire event sequences. Unlike existing diffusion approaches, ADD-THIN naturally handles data with discrete and continuous components. In experiments on synthetic and real-world datasets, our model matches the state-of-the-art TPP models in density estimation and strongly outperforms them in forecasting.

Machine learning for molecules holds great potential for efficiently exploring the vast chemical space and thus streamlining the drug discovery process by facilitating the design of new therapeutic molecules. Deep generative models have shown promising results for molecule generation, but the benefits of specific inductive biases for learning distributions over small graphs are unclear. Our study aims to investigate the impact of subgraph structures and vocabulary design on distribution learning, using small drug molecules as a case study. To this end, we introduce Subcover, a new subgraph-based fragmentation scheme, and evaluate it through a two-step variational auto-encoder. Our results show that Subcover's improved identification of chemically meaningful subgraphs leads to a relative improvement of the FCD score by 30%, outperforming previous methods. Our findings highlight the potential of Subcover to enhance the performance and scalability of existing methods, contributing to the advancement of drug discovery., Comment: Accepted for publication at the MLDD workshop, ICLR 2023

Statistical shape modeling aims at capturing shape variations of an anatomical structure that occur within a given population. Shape models are employed in many tasks, such as shape reconstruction and image segmentation, but also shape generation and classification. Existing shape priors either require dense correspondence between training examples or lack robustness and topological guarantees. We present FlowSSM, a novel shape modeling approach that learns shape variability without requiring dense correspondence between training instances. It relies on a hierarchy of continuous deformation flows, which are parametrized by a neural network. Our model outperforms state-of-the-art methods in providing an expressive and robust shape prior for distal femur and liver. We show that the emerging latent representation is discriminative by separating healthy from pathological shapes. Ultimately, we demonstrate its effectiveness on two shape reconstruction tasks from partial data. Our source code is publicly available (https://github.com/davecasp/flowssm).

Statistical shape models learn to capture the most characteristic geometric variations of anatomical structures given samples from their population. Accordingly, shape models have become an essential tool for many medical applications and are used in, for example, shape generation, reconstruction, and classification tasks. However, established statistical shape models require precomputed dense correspondence between shapes, often lack robustness, and ignore the global surface topology. This thesis presents a novel neural flow-based shape model that does not require any precomputed correspondence. The proposed model relies on continuous flows of a neural ordinary differential equation to model shapes as deformations of a template. To increase the expressivity of the neural flow and disentangle global, low-frequency deformations from the generation of local, high- frequency details, we propose to apply a hierarchy of flows. We evaluate the performance of our model on two anatomical structures, liver, and distal femur. Our model outperforms state-of-the-art methods in providing an expressive and robust shape prior, as indicated by its generalization ability and specificity. More so, we demonstrate the effectiveness of our shape model on shape reconstruction tasks and find anatomically plausible solutions. Finally, we assess the quality of the emerging shape representation in an unsupervised setting and discriminate healthy from pathological shapes., Statistische Formmodelle lernen, die geometrische Variation anatomischer Strukturen anhand von Stichproben zu modellieren. Als solches sind Formmodelle ein essenzielles Werkzeug für viele medizinische Anwendungen geworden und werden zum Beispiel bei Formerzeugungs-, Rekonstruktions- und Klassifikationsaufgaben verwendet. Etablierte statistische Formmodelle erfordern jedoch eine vorberechnete dichte Korrespondenz zwischen Formen, sind oftmals nicht robust und ignorieren die Topologie der modellierten Oberfläche. Diese Arbeit stellt ein neuartiges Formmodell vor, das keine vorberechnete Korrespondenz erfordert und durch ein neuronales Netzwerk parametrisiert wird. Das vorgeschlagene Modell beruht auf einer gewöhnlichen Differentialgleichung, die Formen durch die Deformation einer Vorlage modelliert. Es wird eine Hierarchie von Deformationen angewandt, die globale, niederfrequente Deformationen von der Erzeugung lokaler, hochfrequenter Formdetails separiert. In der experimentellen Evaluation des Modells werden zwei anatomische Strukturen verwendet, die Leber und der Oberschenkelknochen. Das vorgestellte Modell übertrifft etablierte Methoden in Generalisierbarkeit und Spezifität und präsentiert ein ausdrucksstarkes und robustes Formmodell. Des Weiteren wird die Wirksamkeit des Formmodells demonstriert, indem anatomisch plausible und akkurate Rekonstruktionen für Formrekonstruktionsaufgaben gefunden werden. Schließlich wird die Qualität der emergenten, latenten Repräsentation durch die Klassifikation von pathologische Formen evaluiert.