Martin Spitznagel

Martin Spitznagel, Janis Keuper

Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g. differential equations, to improve the modeling of complex systems. Over two decades later, while Cellular Automata have still been waiting for a substantial breakthrough in scientific applications, recent research showed new and promising approaches which combine Wolfram's ideas with learnable Artificial Neural Networks: So-called Neural Cellular Automata (NCA) are able to learn the complex update rules of CA from data samples, allowing them to model complex, self-organizing generative systems. The aim of this paper is to review the existing work on NCA and provide a unified modular framework and notation, as well as a reference implementation in the open-source library NCAtorch.

Martin Spitznagel, Janis Keuper

Data-driven modeling of complex physical systems is receiving a growing amount of attention in the simulation and machine learning communities. Since most physical simulations are based on compute-intensive, iterative implementations of differential equation systems, a (partial) replacement with learned, 1-step inference models has the potential for significant speedups in a wide range of application areas. In this context, we present a novel benchmark for the evaluation of 1-step generative learning models in terms of speed and physical correctness. Our Urban Sound Propagation benchmark is based on the physically complex and practically relevant, yet intuitively easy to grasp task of modeling the 2d propagation of waves from a sound source in an urban environment. We provide a dataset with 100k samples, where each sample consists of pairs of real 2d building maps drawn from OpenStreetmap, a parameterized sound source, and a simulated ground truth sound propagation for the given scene. The dataset provides four different simulation tasks with increasing complexity regarding reflection, diffraction and source variance. A first baseline evaluation of common generative U-Net, GAN and Diffusion models shows, that while these models are very well capable of modeling sound propagations in simple cases, the approximation of sub-systems represented by higher order equations systematically fails. Information about the dataset, download instructions and source codes are provided on our website: https://www.urban-sound-data.org.

Martin Spitznagel, Jan Vaillant, Janis Keuper

The image-to-image translation abilities of generative learning models have recently made significant progress in the estimation of complex (steered) mappings between image distributions. While appearance based tasks like image in-painting or style transfer have been studied at length, we propose to investigate the potential of generative models in the context of physical simulations. Providing a dataset of 300k image-pairs and baseline evaluations for three different physical simulation tasks, we propose a benchmark to investigate the following research questions: i) are generative models able to learn complex physical relations from input-output image pairs? ii) what speedups can be achieved by replacing differential equation based simulations? While baseline evaluations of different current models show the potential for high speedups (ii), these results also show strong limitations toward the physical correctness (i). This underlines the need for new methods to enforce physical correctness. Data, baseline models and evaluation code http://www.physics-gen.org.

Achim Eckerle, Martin Spitznagel, Janis Keuper

Accurate and fast urban noise prediction is pivotal for public health and for regulatory workflows in cities, where the Environmental Noise Directive mandates regular strategic noise maps and action plans, often needed in permission workflows, right-of-way allocation, and construction scheduling. Physics-based solvers are too slow for such time-critical, iterative "what-if" studies. We evaluate conditional Normalizing Flows (Full-Glow) for generating for generating standards-compliant urban sound-pressure maps from 2D urban layouts in real time per 256x256 map on a single RTX 4090), enabling interactive exploration directly on commodity hardware. On datasets covering Baseline, Diffraction, and Reflection regimes, our model accelerates map generation by >2000 times over a reference solver while improving NLoS accuracy by up to 24% versus prior deep models; in Baseline NLoS we reach 0.65 dB MAE with high structural fidelity. The model reproduces diffraction and interference patterns and supports instant recomputation under source or geometry changes, making it a practical engine for urban planning, compliance mapping, and operations (e.g., temporary road closures, night-work variance assessments).