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Dominik L. Michels

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Machine Learning Computer Vision math.AP eess.IV math.CA math.DG math.RA math.SP physics.comp-ph

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preprint2026arXiv

Climate-based Pre-screening of Self-sustaining Regreening Opportunities in Drylands: A Case Study for Saudi Arabia

Large-scale restoration in drylands is widely promoted to address land degradation and biodiversity loss, yet many efforts rely on long-term irrigation, limiting sustainability in water-scarce regions. A key challenge is identifying locations where native vegetation can persist without intensive management while minimizing costly field campaigns. A scalable pre-screening framework is presented that integrates climate and remote sensing data to enable cost-efficient site selection in arid environments using Saudi Arabia as a case study. A Climate Suitability Score (CSS), derived from machine learning models trained on expert-curated reference sites, captures complex climatic dependencies on vegetation persistence. Using multi-year ERA5-Land data for Saudi Arabia, national-scale prediction maps are generated and combined with vegetation indices to identify areas where climate is favorable, but vegetation remains underdeveloped. Multi-criteria screening reduces candidates to thirteen priority locations. Climatically analogous intact ecosystems provide benchmarks for restoration targets and indicate that an average 2.5 fold increase in vegetation coverage is a realistic target for restoration efforts. Overall, this approach narrows the search space, reduces costs, and supports resilient ecosystem recovery planning in water-limited regions.

preprint2022arXiv

On Helical Surfaces with a Constant Ratio of Principal Curvatures

We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio $a:=κ_1/κ_2$ of principal curvatures (CRPC surfaces), thus providing the first explicit CRPC surfaces beyond the known rotational ones. A key ingredient in the successful determination of these surfaces is the proper choice of generating profiles. We employ the contours for parallel projection orthogonal to the helical axis. This has the advantage that the CRPC property can be nicely expressed with the help of the involution of conjugate surface tangents. The arising ordinary differential equation has an explicit parametric solution, which forms the basis for a further study and classification of the possible shapes and the singularities arising for $a>0$.

preprint2022arXiv

RLSS: A Deep Reinforcement Learning Algorithm for Sequential Scene Generation

We present RLSS: a reinforcement learning algorithm for sequential scene generation. This is based on employing the proximal policy optimization (PPO) algorithm for generative problems. In particular, we consider how to effectively reduce the action space by including a greedy search algorithm in the learning process. Our experiments demonstrate that our method converges for a relatively large number of actions and learns to generate scenes with predefined design objectives. This approach is placing objects iteratively in the virtual scene. In each step, the network chooses which objects to place and selects positions which result in maximal reward. A high reward is assigned if the last action resulted in desired properties whereas the violation of constraints is penalized. We demonstrate the capability of our method to generate plausible and diverse scenes efficiently by solving indoor planning problems and generating Angry Birds levels.

preprint2021arXiv

Accurately Solving Physical Systems with Graph Learning

Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. Finally, to illustrate the scalability of our approach, we simulate complex 3D tree models composed of over a thousand individual branch segments swaying in wind fields. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at http://computationalsciences.org/publications/shao-2021-physical-systems-graph-learning.html .

preprint2020arXiv

Domain Adaptation with Morphologic Segmentation

We present a novel domain adaptation framework that uses morphologic segmentation to translate images from arbitrary input domains (real and synthetic) into a uniform output domain. Our framework is based on an established image-to-image translation pipeline that allows us to first transform the input image into a generalized representation that encodes morphology and semantics - the edge-plus-segmentation map (EPS) - which is then transformed into an output domain. Images transformed into the output domain are photo-realistic and free of artifacts that are commonly present across different real (e.g. lens flare, motion blur, etc.) and synthetic (e.g. unrealistic textures, simplified geometry, etc.) data sets. Our goal is to establish a preprocessing step that unifies data from multiple sources into a common representation that facilitates training downstream tasks in computer vision. This way, neural networks for existing tasks can be trained on a larger variety of training data, while they are also less affected by overfitting to specific data sets. We showcase the effectiveness of our approach by qualitatively and quantitatively evaluating our method on four data sets of simulated and real data of urban scenes. Additional results can be found on the project website available at http://jonathank.de/research/eps/ .

preprint2020arXiv

On Ambarzumyan-type Inverse Problems of Vibrating String Equations

We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is shown that there is a curve in the boundary parameters' domain on which no analog of it is possible. Necessary conditions of the $n$-th eigenvalue are identified, which allows to state the theorems. In addition, several properties of the first eigenvalue are examined. Lower and upper bounds are identified, and the areas are described in the boundary parameters' domain on which the sign of the first eigenvalue remains unchanged. This paper contributes to inverse spectral theory as well as to direct spectral theory.

preprint2015arXiv

On the Partial Analytical Solution of the Kirchhoff Equation

We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.

preprint2014arXiv

Lie Symmetry Analysis for Cosserat Rods

We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary functions in t. Assuming analyticity of the arbitrary functions in a domain under consideration, we prove that the obtained solution is analytic and general. The Special Cosserat Theory of Rods describes the dynamic equilibrium of 1-dimensional continua, i.e. slender structures like fibers, by means of a system of partial differential equations.