Thomas Richter

The antagonistic interplay between canonical Wnt signalling and Dickkopf (Dkk) proteins is fundamental to tissue organisation, including stem cell differentiation and body-axis formation. Disruptions in this interaction are linked to various human diseases, yet the mechanisms by which β -catenin/Wnt–Dkk interactions give rise to robust spatial patterning remain unclear. A key model system for Wnt-driven pattern formation is the pre-bilaterian organism Hydra , where two ancestral Dkk proteins interact with Wnt signalling to self-organise the body axis. While Hydra patterning has been extensively studied within the activator–inhibitor framework, a model that directly integrates experimentally identified molecular components has been lacking. Here, we introduce a mathematical model incorporating both Dkk molecules and their experimentally established interactions with Wnt signalling. Numerical simulations and analytical results show that the Wnt–Dkk network alone is sufficient to drive de novo body-axis formation across a broad parameter range. The model provides a biologically grounded realisation of the general local activation–long-range inhibition (LALI) principle, in which effective local activation emerges from mutual inhibition rather than molecular self-activation. In contrast to previous Hydra models, it explicitly links experimentally characterised Wnt–Dkk interactions to pattern formation, accounts for the experimentally observed role of injury-induced activation, and exhibits robust behaviour under perturbations.

Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and boundary conditions. The Deep Ritz method can be interpreted as a particular variational form of a PINN, where the loss corresponds to the minimization of an energy functional associated with a symmetric positive definite problem. In this work, we study the approximation of the Laplace equation using both the classical PINN formulation and its variational counterpart, the Deep Ritz method, with the objective of accurately estimating prescribed goal functionals. When standard sampling strategies, such as uniform or loss-based sampling, are employed during training, the convergence of the functional error and the attained minimal functional value can be slow. To address this issue, we introduce a functional-oriented importance sampling strategy that can be applied to both PINNs and the Deep Ritz method. The key ingredient is the construction of a reliable and accurate estimator for the error in a given quantity of interest. This estimator is derived using concepts from the Dual Weighted Residual (DWR) framework and is implemented entirely within the neural network setting. It is then used to adaptively guide the sampling of training points in the computational domain, focusing computational effort on regions that have the strongest influence on the functional value. Numerical experiments demonstrate that the proposed adaptive sampling strategy significantly accelerates the convergence of the functional error and improves the minimization of the target functional during training for both PINN and Deep Ritz formulations.

Hydrodynamic journal bearings are essential machine parts that are used for applications with high rotational speeds. Their precise simulation requires the consideration of thermomechanical interactions between solids and fluid. During operation, the shear stresses in the fluid (lubricant film heights: 5–100 ), lead to significant friction losses, acting as a considerable heat source. Such a heating not only causes a nonlinear change in the fluid viscosity but also influences the temperature distribution. Consequently, deformations in adjacent solid bodies are induced, influencing the pressure in the fluid film due to the thermomechanical coupling. These coupling effects dynamically change the geometry of the lubricating film and significantly influence the load‐carrying capacity as well as the dynamic properties of the bearing. This contribution investigates the thermomechanical interactions within a cylindrical radial journal bearing consisting of a shaft and bearing shell, including suitable boundary conditions. For this purpose, a temperature model for the solids is developed and implemented to solve the heat conduction equation and is coupled with a mechanical model. To achieve a high numerical efficiency, the p ‐finite element method is utilized for the solid parts and studied concerning its numerical behavior. In contrast, the fluid temperature is described by the energy equation, which is approximated using the finite volume method. After verifying the model, it is applied to the thermomechanical analysis of a bearing to gain a deeper understanding of the coupling effects as well as their impact on the bearing's performance including numerical effort and solution quality.

We perform analytical and numerical analyses of the propulsion of a rigid body in a viscous fluid subjected to a periodic force with zero average over a period. This general formulation specifically addresses the significant case where propulsion is generated by the oscillation of a mass located in an internal cavity of the body. We provide a rigorous proof of the necessary and sufficient conditions for propulsion at the second order of magnitude of the force. These conditions are implemented and confirmed by numerical tests for bodies without fore-and-aft symmetry, while they are silent for bodies with such symmetry, like round ellipsoids. Consequently, in this case, propulsion can only occur at an order higher than the second. This problem is investigated by numerically integrating the entire set of equations, and the result shows that, in fact, propulsion does occur, thus opening new avenues for further analytical studies.

NeXtSIM-DG is a novel sea ice model developed as part of the Scale Aware Sea Ice Project (SASIP).The continum model supports both the established viscous plastic rheology (mEVP) and the Brittle Bingham-Maxwell rheology (BBM). The discretization is based on higher-order discontinuous and continuous finite elements to accurately represent the sharp features of sea ice. Quadrilateral parametric meshes with regular topology are used to allow for easy coupling with ocean models and a highly efficient implementation.Following best practices in software engineering, the C++ code is designed to be maintainable and easily extendable, with a modular design that allows users to add new physics implementations.In this poster, we give an overview of neXtSIM-DG and present recent developments regarding its usability and performance. We demonstrate our model's heterogeneous compute capabilities, supporting shared-memory parallelization with OpenMP, full GPU acceleration through Kokkos and scaling across multiple CPUs via MPI.

Long-term models for ice-sheets and glaciers are in general modeled as very slow, viscous fluids, which allows for large time steps on the order of years. However, over the past few decades, observations and theoretical studies have shown that ice streams exhibit short-term responses when it comes to external forcing due to ocean tides, which induce for example non-linear velocity variations.Short-term models typically apply viscous-elastic ice rheologies to capture these effects. However, resolving tidal dynamics requires very small time steps on the order of minutes, making long-term simulations computationally challenging.To address this, we propose a temporal averaging approach to include short-term tidal effects into efficient, long-term simulations. We present initial results based on a two-component modeling framework. The long-term component models the ice sheet as a viscous fluid governed by the p-Stokes equations with free surfaces. The short-term component describes the elastic response of the ice to tidal forcing, modeled by an elasticity problem driven by variations in hydro-static pressure due to ocean tides. This leads to a variational inequality of Signorini type, reflecting intermittent contact between the ice and the bedrock. As the tidal cycle causes the ice–bedrock contact zone to evolve in time, the basal boundary condition alternates between frictional contact and floating due to ocean-pressure. By exploiting the periodic nature of the tidal forcing, we derive effective, tidally averaged basal traction coefficients based on the varying grounding line position. These effective coefficients can be incorporated into the basal friction law of the viscous, long-term ice-flow model. The averaged friction coefficients are updated after a time step in the long-term model to take the geometric deformation of the ice sheet into account. This approach allows for efficient simulations that capture the influence of short-term tidal dynamics on ice-streams effectively, and relies on a clear separation between the short tidal time scale and the long-term viscous dynamics of the ice sheet.

Stratification strongly influences lake circulation, oxygenation, and biogeochemical exchange. In stably stratified lakes, deep and surface waters can differ markedly in chemical composition. Changes in mixing intensity or overturn events can therefore alter oxygen levels and water quality by redistributing reduced or nutrient-rich deep water.Accurate modelling of circulation and air-water oxygen exchange in deep, low-salinity lakes requires thermobaric effects, i.e. the pressure-temperature dependence of water density. In such systems, density differences at depth can be small enough that thermobaricity becomes a primary driver of vertical exchange and renewal.We investigate thermobaricity-driven circulation in a simplified setting using a 2D Boussinesq Navier-Stokes framework in which the buoyancy term is derived from the approximate equation of state for freshwater by Farmer and Carmack (1981). To assess deep water renewal and stratification persistence, we introduce a passive “water age” tracer. We first compute a time-periodic solution for the flow and temperature fields, and then transport the age tracer over many cycles using this periodic state. This approach enables efficient long-term estimates of water renewal time scales and their sensitivity to thermobaric forcing, providing a simplified assessment of physical stability in deep-lake stratification.

The deep neural network multigrid solver (DNN-MG) combines a coarse-grid finite element simulation with a deep neural network that corrects the solution on finer grid levels, thereby improving the computational efficiency. In this work, we discuss various design choices for the DNN-MG method and demonstrate significant improvements in accuracy and generalizability when applied to the solution of the instationary Navier-Stokes equations.We investigate the stability of the hybrid simulation and show how the neural networks can be made more robust with the help of replay buffers. By retraining on data derived from the hybrid simulation, the error caused by the neural network over multiple time-steps can be minimized without the need for a differentiable numerical solver.Furthermore, we compare multiple neural network architectures, including recurrent neural networks and Transformers, and study their ability to utilize more information from an increased temporal and spatial receptive field. Transformers allow us to make use of information from cells outside the predicted patch even with unstructured meshes while maintaining the locality of our approach. This can further improve the accuracy of DNN-MG without a significant impact on performance.

Contactless and non-invasive estimation of mechanical properties of physical media from optical observations is of interest for manifold engineering and biomedical applications, where direct physical measurements are not possible. Conventional approaches to the assessment of image displacement and non-contact material probing typically rely on time-consuming iterative algorithms for non-rigid image registration and constitutive modelling using discretization and iterative numerical solving techniques, such as Finite Element Method (FEM) and Finite Difference Method (FDM), which are not suitable for high-throughput data processing. Here, we present an efficient deep learning based end-to-end approach for the estimation of continuum displacement and material compressibility directly from the image series. Based on two deep neural networks for image registration and material compressibility estimation, this framework outperforms conventional approaches in terms of efficiency and accuracy. In particular, our experimental results show that the deep learning model trained on a set of reference data can accurately determine the material compressibility even in the presence of substantial local deviations of the mapping predicted by image registration from the reference displacement field. Our findings suggest that the remarkable accuracy of the deep learning end-to-end model originates from its ability to assess higher-order cognitive features, such as the vorticity of the vector field, rather than conventional local features of the image displacement.