arXiv subjects

Hanno Gottschalk

Publications and source records attributed to Hanno Gottschalk.

At least 19 recordsLinked to original sources

arXiv2026

Diffuse2Seg: Diffusion Models Can Segment Anything Without Supervision

Open-world entity segmentation aims to predict masks for arbitrary objects across domains and at multiple granularities, from parts to whole objects. In this setting, SAM sets a strong standard: trained on SA-1B, comprising 11M images and over 1B carefully annotated masks, it achieves remarkable zero-shot performance. Collecting such labels is expensive and time-consuming, however, which limits how far this recipe can scale. Text-to-image diffusion models offer a way around this. Their intermediate features transfer well across perception tasks, and since object structure emerges as the model denoises a noise sample into an image conditioned on a text prompt, that structure is already encoded in these representations. They can therefore be exploited for open-world entity segmentation without retraining or supervision. Building on this observation, we introduce Diffuse2Seg, which repurposes generative diffusion models for automatic mask generation by propagating a grid of point prompts through their self-attention representations in an edge-preserving manner. Diffuse2Seg produces multi-granular instance masks and outperforms prior state-of-the-art label generators by 4.3-7.1 p.p. in AR_1000 across five domains. Training an instance segmentation model on these generated masks advances detector-free open-world segmentation by 7.4 and 7.7 p.p. on "things" and "stuff+things" datasets and surpasses the detector-based UnSAM on "stuff+things" by 2.1 p.p. in AR_1000. Finally, we show that a model trained on Diffuse2Seg labels provides a strong initialization for semi-supervised learning, outperforming its fully supervised counterpart with already 5k labeled images.

cs.CV↗

arXiv2026

RoG-DAgger: Rollout-Guided Post-Training for End-to-End Driving

Recent end-to-end driving systems demonstrate strong performance on closed-loop benchmarks, yet are still predominantly trained on fixed expert-collected data using open-loop imitation learning. This training-inference mismatch leaves the policy vulnerable in policy-induced states, where accumulated errors can lead to safety-critical failures. A promising post-training approach to overcome this issue is Dataset Aggregation (DAgger), which gathers expert demonstrations in policy-induced states and subsequently fine-tunes the policy on the resulting aggregated dataset. Existing driving DAgger pipelines, however, face three challenges: i) the expert is restricted to a limited trajectory-and-speed solution space, ii) takeover may occur too early or too late relative to impending failures, and iii) privileged expert decisions may rely on information unavailable to the student. To address this, we introduce RoG-DAgger, a post-training framework that uses short-horizon kinematic rollouts to construct high-quality expert demonstrations in safety-critical states. Specifically, RoG-DAgger expands the expert's trajectory-and-speed solution space and evaluates candidate plans through rollout to construct preventive supervision. Moreover, it uses rollout solvability to time the takeover near the estimated point of no return. Lastly, it aligns the expert's field of view with that of the student to provide student-compatible supervision. Across in-distribution (including long-horizon) and out-of-distribution evaluations, RoG-DAgger improves the end-to-end model SimLingo by 5.3 driving-score points and 6.2 percentage points in success rate on Bench2Drive, doubles its driving score from 22 to 44 on Longest6 v2, and improves out-of-distribution success rate from 55\% to 66\% on Fail2Drive.

cs.RO↗

arXiv2026

Extended Field of View Analysis for VideoGAN-based Trajectory Generation

Realistic and diverse trajectory generation is central to enabling higher levels of vehicle automation. While rule-based and classical learning-based methods may struggle to capture the complexity of traffic behavior, generative models have already demonstrated in other fields that they can handle a comparable level of complexity. In this paper, we build upon previous work on generative adversarial network (GAN)-based semantic bird's-eye-view traffic generation and extend the proposed framework in several key aspects. We improve the semantic representation, replace the trajectory extraction procedure with a graph-based association method, and systematically investigate increasingly larger fields of view. In addition, we introduce a quantitative evaluation framework to assess hallucinations and object permanence in generated videos. Our experiments demonstrate that the framework generalizes to larger and more complex traffic scenes while maintaining statistically realistic trajectories and coherent spatial relationships between traffic participants. Within 150GPU hours of training and with inference times below 20ms for scenes of up to 20s, our results demonstrate that video-based GANs remain an efficient and scalable approach for realistic trajectory generation, even in substantially larger traffic scenes, making them well suited for downstream tasks such as prediction, planning, and simulation in automated driving.

cs.CV↗

arXiv2026

Consistency of Learned Sparse Grid Quadrature Rules using NeuralODEs

We prove consistency of a recently proposed scheme that evaluates expected values by composing a learned transport map with Clenshaw--Curtis sparse-grid quadrature on a tractable product source. Our analysis hinges on the structural fact that composition of a $C^k_{\mathrm{mix}}$-regular function -- which carries the fast quadrature rate $m^{-k}(\log m)^{(d-1)(k+1)}$ -- with a $C^1$-diffeomorphism can only be guaranteed to be $C^k_{\mathrm{mix}}$ itself, if the diffeomorphism is diagonal up to a permutation of coordinates. The fast rate is therefore available exclusively for product targets, and the analysis splits into two regimes. In the general regime of arbitrary targets, we learn the transport as the time-one flow of a $\mathrm{ReLU}^{k+1}$-neural ODE trained by maximum likelihood. The resulting flow lies in the isotropic space $C^k$ and yields the rate $m^{-k/d}(\log m)^{(d-1)(k/d+1)}$, with raising the density smoothness $k$ and the matched activation order $k+1$ mitigating the curse of dimensionality at the cost of harder optimization. In the diagonal regime of product targets, the Knothe--Rosenblatt map is itself diagonal and we estimate it pointwise via empirical quantile transport, a lightweight alternative that recovers the full mixed-regularity rate. In both regimes, the resulting LtI estimator is PAC (probably approximately correct) consistent. With high probability the numerical integral approximates the true value to arbitrary accuracy as both the sample size $n$ and the quadrature budget $m$ tend to infinity.

math.NA↗

arXiv2026

Generative Adversarial Learning from Deterministic Processes

Physical AI is being successfully applied to data which does not follow the traditional paradigm of independent and identically distributed (i.i.d.) samples. In fact, physical AI is often trained on data which is not random at all, and is instead derived from chaotic dynamical systems like turbulence. We aim to explain the empirical success of these methods using the example of generative adversarial networks (GANs), whose statistical learning theory under the i.i.d. assumption is generally well understood. We prove that it is possible, using an infinite-dimensional model of generative adversarial learning (GAL), to learn the invariant distribution of a sufficiently chaotic dynamical system from a single deterministically evolving time series of its states or measurements thereof, and give explicit rates for the convergence to the solution in terms of the Jensen-Shannon divergence.

cs.LG↗

arXiv2026

Generative Design of a Gas Turbine Combustor Using Invertible Neural Networks

The need to burn 100% H2 in high efficient gas turbines featuring low NOx combustion in premix mode require the complete redesign of the combustion system to ensure stable operation without any flashback. Since all engine frames featuring a power range from 4 MW up to 600 MW are affected, a huge design effort is expected. To reduce this effort, especially to transfer knowledge between the different engine classes, generative design methods using latest AI technology will provide promising potential. In this work, this challenge is approached utilizing the current advances in generative artificial intelligence. We train an Invertible Neural Network (INN) on an expandable database of geometrically parameterized combustor designs with simulated performance labels. Utilizing the INN in its inverse direction, multiple design proposals are generated which fulfill specified performance labels.

cs.AI↗

arXiv2026

Regularity of Solutions to Beckmann's Parametric Optimal Transport

Beckmann's problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann's problem in optimal transport is developed utilizing an unconstrained Lagrangian formulation and solving the variational first order optimality conditions. It turns out that the Lagrangian multiplier that enforces Beckmann's divergence constraint fulfills a Poisson equation and the flux vector field is obtained as the potential's gradient. Utilizing Schauder estimates from elliptic regularity theory, the exact Hölder regularity of the potential, the flux and the flow generating is derived on the basis of Hölder regularity of source and target densities on a bounded, regular domain. If the target distribution depends on parameters, as is the case in conditional (``promptable'') generative learning, we provide sufficient conditions for separate and joint Hölder continuity of the resulting vector field in the parameter and the data dimension. Following a recent result by Belomnestny et al., one can thus approximate such vector fields with deep ReQu neural networks in C^(k,alpha)-Hölder norm. We also show that this approach generalizes to other probability paths, like Fisher-Rao gradient flows.

math.AP↗

arXiv2026

Generative Inverse Design with Abstention via Diagonal Flow Matching

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to $P{=}784$, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.

cs.LG↗

arXiv2026

Towards Reliable Detection of Empty Space: Conditional Marked Point Processes for Object Detection

Deep neural networks have set the state-of-the-art in computer vision tasks such as bounding box detection and semantic segmentation. Object detectors and segmentation models assign confidence scores to predictions, reflecting the model's uncertainty in object detection or pixel-wise classification. However, these confidence estimates are often miscalibrated, as their architectures and loss functions are tailored to task performance rather than probabilistic foundation. Even with well calibrated predictions, object detectors fail to quantify uncertainty outside detected bounding boxes, i.e., the model does not make a probability assessment of whether an area without detected objects is truly free of obstacles. This poses a safety risk in applications such as automated driving, where uncertainty in empty areas remains unexplored. In this work, we propose an object detection model grounded in spatial statistics. Bounding box data matches realizations of a marked point process, commonly used to describe the probabilistic occurrence of spatial point events identified as bounding box centers, where marks are used to describe the spatial extension of bounding boxes and classes. Our statistical framework enables a likelihood-based training and provides well-defined confidence estimates for whether a region is drivable, i.e., free of objects. We demonstrate the effectiveness of our method through calibration assessments and evaluation of performance.

cs.CV↗

arXiv2026

How well do generative models solve inverse problems? A benchmark study

Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a traditional Bayesian inverse approach based on a forward regression model and a prior sampled with the Markov Chain Monte Carlo method with three state of the art generative learning models, namely conditional Generative Adversarial Networks, Invertible Neural Networks and Conditional Flow Matching. We apply them to a problem of gas turbine combustor design where we map six independent design parameters to three performance labels. We propose several metrics for the evaluation of this inverse design approaches and measure the accuracy of the labels of the generated designs along with the diversity. We also study the performance as a function of the training dataset size. Our benchmark has a clear winner, as Conditional Flow Matching consistently outperforms all competing approaches.

cs.LG↗

arXiv2026

Generative Design of Ship Propellers using Conditional Flow Matching

In this paper, we explore the use of generative artificial intelligence (GenAI) for ship propeller design. While traditional forward machine learning models predict the performance of mechanical components based on given design parameters, GenAI models aim to generate designs that achieve specified performance targets. In particular, we employ conditional flow matching to establish a bidirectional mapping between design parameters and simulated noise that is conditioned on performance labels. This approach enables the generation of multiple valid designs corresponding to the same performance targets by sampling over the noise vector. To support model training, we generate data using a vortex lattice method for numerical simulation and analyze the trade-off between model accuracy and the amount of available data. We further propose data augmentation using pseudo-labels derived from less data-intensive forward surrogate models, which can often improve overall model performance. Finally, we present examples of distinct propeller geometries that exhibit nearly identical performance characteristics, illustrating the versatility and potential of GenAI in engineering design.

cs.LG↗

arXiv2026

Learning Transient Convective Heat Transfer with Geometry Aware World Models

Partial differential equation (PDE) simulations are fundamental to engineering and physics but are often computationally prohibitive for real-time applications. While generative AI offers a promising avenue for surrogate modeling, standard video generation architectures lack the specific control and data compatibility required for physical simulations. This paper introduces a geometry aware world model architecture, derived from a video generation architecture (LongVideoGAN), designed to learn transient physics. We introduce two key architecture elements: (1) a twofold conditioning mechanism incorporating global physical parameters and local geometric masks, and (2) an architectural adaptation to support arbitrary channel dimensions, moving beyond standard RGB constraints. We evaluate this approach on a 2D transient computational fluid dynamics (CFD) problem involving convective heat transfer from buoyancy-driven flow coupled to a heat flow in a solid structure. We demonstrate that the conditioned model successfully reproduces complex temporal dynamics and spatial correlations of the training data. Furthermore, we assess the model's generalization capabilities on unseen geometric configurations, highlighting both its potential for controlled simulation synthesis and current limitations in spatial precision for out-of-distribution samples.

physics.flu-dyn↗

arXiv2026

Comparison of Generative Learning Methods for Turbulence Surrogates

Numerical simulations of turbulent flows present significant challenges in fluid dynamics due to their complexity and high computational cost. High resolution techniques such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are generally not computationally affordable, particularly for technologically relevant problems. Recent advances in machine learning, specifically in generative probabilistic models, offer promising alternatives as surrogates for turbulence. This paper investigates the application of three generative models - Variational Autoencoders (VAE), Deep Convolutional Generative Adversarial Networks (DCGAN), and Denoising Diffusion Probabilistic Models (DDPM) - in simulating a von Kármán vortex street around a fixed cylinder projected into 2D, as well as a real-world experimental dataset of the wake flow of a cylinder array. Training data was obtained by means of LES in the simulated case and Particle Image Velocimetry (PIV) in the experimental case. We evaluate each model's ability to capture the statistical properties and spatial structures of the turbulent flow. Our results demonstrate that DDPM and DCGAN effectively replicate all flow distributions, highlighting their potential as efficient and accurate tools for turbulence surrogacy. We find a strong argument for DCGAN, as although they are more difficult to train (due to problems such as mode collapse), they show the fastest inference and training time, require less data to train compared to VAE and DDPM, and provide the results most closely aligned with the input stream. In contrast, VAE train quickly (and can generate samples quickly) but do not produce adequate results, and DDPM, whilst effective, are significantly slower at both, inference and training time.

physics.flu-dyn↗

arXiv2025

New advances in universal approximation with neural networks of minimal width

We prove several universal approximation results at minimal or near-minimal width for approximation of $L^p(\mathbb{R}^{d_x}, \mathbb{R}^{d_y})$ and $C^0(\mathbb{R}^{d_x}, \mathbb{R}^{d_y})$ on compact sets. Our approach uses a unified coding scheme that yields explicit constructions relying only on standard analytic tools. We show that feedforward neural networks with two leaky ReLU activations $σ_α$, $σ_{-α}$ achieve the optimal width $\max\{d_x, d_y\}$ for $L^p$ approximation, while a single leaky ReLU $σ_α$ achieves width $\max\{2, d_x, d_y\}$, providing an alternative proof of the results of Cai et al. (2023). By generalizing to stepped leaky ReLU activations, we extend these results to uniform approximation of continuous functions while identifying sets of activation functions compatible with gradient-based training. Since our constructions pass through an intermediate dimension of one, they imply that autoencoders with a one-dimensional feature space are universal approximators. We further show that squashable activations combined with FLOOR achieve width $\max\{3, d_x, d_y\}$ for uniform approximation. We also establish a lower bound of $\max\{d_x, d_y\} + 1$ for networks when all activations are continuous and monotone and $d_y \leq 2d_x$. Moreover, we extend our results to invertible LU-decomposable networks, proving distributional universal approximation for LU-Net normalizing flows and providing a constructive proof of the classical theorem of Brenier and Gangbo on $L^p$ approximation by diffeomorphisms.

cs.NE↗

arXiv2025

When do World Models Successfully Learn Dynamical Systems?

In this work, we explore the use of compact latent representations with learned time dynamics ('World Models') to simulate physical systems. Drawing on concepts from control theory, we propose a theoretical framework that explains why projecting time slices into a low-dimensional space and then concatenating to form a history ('Tokenization') is so effective at learning physics datasets, and characterise when exactly the underlying dynamics admit a reconstruction mapping from the history of previous tokenized frames to the next. To validate these claims, we develop a sequence of models with increasing complexity, starting with least-squares regression and progressing through simple linear layers, shallow adversarial learners, and ultimately full-scale generative adversarial networks (GANs). We evaluate these models on a variety of datasets, including modified forms of the heat and wave equations, the chaotic regime 2D Kuramoto-Sivashinsky equation, and a challenging computational fluid dynamics (CFD) dataset of a 2D Kármán vortex street around a fixed cylinder, where our model is successfully able to recreate the flow.

math.NA↗

arXiv2025

FOCUS: Internal MLLM Representations for Efficient Fine-Grained Visual Question Answering

While Multimodal Large Language Models (MLLMs) offer strong perception and reasoning capabilities for image-text input, Visual Question Answering (VQA) focusing on small image details still remains a challenge. Although visual cropping techniques seem promising, recent approaches have several limitations: the need for task-specific fine-tuning, low efficiency due to uninformed exhaustive search, or incompatibility with efficient attention implementations. We address these shortcomings by proposing a training-free visual cropping method, dubbed FOCUS, that leverages MLLM-internal representations to guide the search for the most relevant image region. This is accomplished in four steps: first, we identify the target object(s) in the VQA prompt; second, we compute an object relevance map using the key-value (KV) cache; third, we propose and rank relevant image regions based on the map; and finally, we perform the fine-grained VQA task using the top-ranked region. As a result of this informed search strategy, FOCUS achieves strong performance across four fine-grained VQA datasets and three types of MLLMs. It outperforms three popular visual cropping methods in both accuracy and efficiency, and matches the best-performing baseline, ZoomEye, while requiring 3 - 6.5 x less compute.

cs.CV↗

arXiv2025

On the Influence of Shape, Texture and Color for Learning Semantic Segmentation

Recent research has investigated the shape and texture biases of pre-trained deep neural networks (DNNs) in image classification. Those works test how much a trained DNN relies on specific image cues like texture. The present study shifts the focus to understanding the cue influence during training, analyzing what DNNs can learn from shape, texture, and color cues in absence of the others; investigating their individual and combined influence on the learning success. We analyze these cue influences at multiple levels by decomposing datasets into cue-specific versions. Addressing semantic segmentation, we learn the given task from these reduced cue datasets, creating cue experts. Early fusion of cues is performed by constructing appropriate datasets. This is complemented by a late fusion of experts which allows us to study cue influence location-dependent on pixel level. Experiments on Cityscapes, PASCAL Context, and a synthetic CARLA dataset show that while no single cue dominates, the shape + color expert predominantly improves the prediction of small objects and border pixels. The cue performance order is consistent for the tested convolutional and transformer architecture, indicating similar cue extraction capabilities, although pre-trained transformers are said to be more biased towards shape than convolutional neural networks.

cs.CV↗

arXiv2025

Domain Generalization for Semantic Segmentation: A Survey

The generalization of deep neural networks to unknown domains is a major challenge despite their tremendous progress in recent years. For this reason, the dynamic area of domain generalization (DG) has emerged. In contrast to unsupervised domain adaptation, there is no access to or knowledge about the target domains, and DG methods aim to generalize across multiple different unseen target domains. Domain generalization is particularly relevant for the task semantic segmentation which is used in several areas such as biomedicine or automated driving. This survey provides a comprehensive overview of the rapidly evolving topic of domain generalized semantic segmentation. We cluster and review existing approaches and identify the paradigm shift towards foundation-model-based domain generalization. Finally, we provide an extensive performance comparison of all approaches, which highlights the significant influence of foundation models on domain generalization. This survey seeks to advance domain generalization research and inspire scientists to explore new research directions.

cs.CV↗