​​​​Selected Publications (since Sept. 2016)

Springer Science+Business Media

Geometric-Integration Tools for the Simulation of Musical Sounds

A. Ishikawa, D. L. Michels, and T. Yaguchi.
Japan Journal of Industrial and Applied Mathematics, Springer (2018).

During the last decade, much attention has been given to sound rendering and the simulation of acoustic phenomena by solving appropriate models described by Hamiltonian partial differential equations. In this contribution, we introduce a procedure to develop appropriate tools inspired from geometric integration in order to simulate musical sounds. Geometric integrators are numerical integrators of excellent quality that are designed exclusively for Hamiltonian ordinary differential equations. The introduced procedure is a combination of two techniques in geometric integration: the semi-discretization method by Celledoni et al. (J Comput Phys 231:6770–6789, 2012) and symplectic partitioned Runge–Kutta methods. This combination turns out to be a right procedure that derives numerical schemes that are effective and suitable for computation of musical sounds. By using this procedure we derive a series of explicit integration algorithms for a simple model describing piano sounds as a representative example for virtual instruments. We demonstrate the advantage of the numerical methods by evaluating a variety of numerical test cases.

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Springer Science+Business Media

Über Konzeption und Methodik computergestützter Simulationen

D. L. Michels.
Human and Technology in the Digital Age, Springer (2018).

Die computergestützte Simulation hat sich im Zuge steigender konzeptioneller und technischer Möglichkeiten zu einer zentralen Kulturtechnik herausgebildet. Neben klassischer Theorie und Experiment stellt sie nunmehr einen gleichberechtigten digitalen Methodenapparat zu Analyse und Vorhersage und schließlich zur Schaffung wissenschaftlicher Erkenntnisse dar. Die Auslagerung schwieriger Problemstellungen in die digitale Welt ermöglicht in vielen Fällen deren effiziente Lösung und läßt in ihrer inversen Formulierung die Bewältigung komplexer Optimierungsprobleme zu. Umgekehrt erlaubt sie die Steuerung digitaler Systeme sowie deren Reaktion im Hinblick auf sensorische Dateneingaben und läßt dadurch eine adäquate Interaktion dieser Systeme mit ihrer realen Umwelt zu. Dieser Beitrag führt unter konzeptionellen Gesichtspunkten in die Grundlagen computergestützter Simulationen ein und diskutiert Möglichkeiten und Grenzen des resultierenden technischen Methodenapparats.

(to appear)


Multi-Scale Terrain Texturing using Generative Adversarial Networks

J. Klein, S. Hartmann, M. Weinmann, and D. L. Michels.
Image and Vision Computing New Zealand (IVCNZ 2017), IEEE Xplore Digital Library (2017).

We propose a novel, automatic generation process for detail maps that allows the reduction of tiling artifacts in real-time terrain rendering. This is achieved by training a generative adversarial network (GAN) with a single input texture and subsequently using it to synthesize a huge texture spanning the whole terrain. The low-frequency components of the GAN output are extracted, down-scaled and combined with the high-frequency components of the input texture during rendering. This results in a terrain texture that is both highly detailed and non-repetitive, which eliminates the tiling artifacts without decreasing overall image quality. The rendering is efficient regarding both memory consumption and computational costs. Furthermore, it is orthogonal to other techniques for terrain texture improvements such as texture splatting and can directly be combined with them.

(to appear)


Interactive Wood Combustion for Botanical Tree Models

S. Pirk, M. Jarząbek, T. Hädrich, D. L. Michels, and W. Pałubicki.
ACM Transactions on Graphics (SIGGRAPH Asia 2017), ACM (2017).

We present a novel method for the combustion of botanical tree models. Tree models are represented as connected particles for the branching structure and a polygonal surface mesh for the combustion. Each particle stores biological and physical attributes that drive the kinetic behavior of a plant and the exothermic reaction of the combustion. Coupled with realistic physics for rods, the particles enable dynamic branch motions. We model material properties, such as moisture and charring behavior, and associate them with individual particles. The combustion is efficiently processed in the surface domain of the tree model on a polygonal mesh. A user can dynamically interact with the model by initiating fires and by inducing stress on branches. The flames realistically propagate through the tree model by consuming the available resources. Our method runs at interactive rates and supports multiple tree instances in parallel. We demonstrate the effectiveness of our approach through numerous examples and evaluate its plausibility against the combustion of real wood samples.

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Springer Science+Business Media

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

D. A. Lyakhov, V. P. Gerdt, A. G. Weber, and D. L. Michels.
Computer Algebra in Scientific Computing (CASC 2017), Springer (2017).

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized α-method illustrating the computational efficiency of our approach for problems in structural mechanics.

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Teaching UAVs to Race Using UE4Sim

M. Mueller, V. Casser, N. Smith, D. L. Michels, and B. Ghanem.
arXiv:1708.05884, Cornell University Library (2017).

Automating the navigation of unmanned aerial vehicles (UAVs) in diverse scenarios has gained much attention in the recent years. However, teaching UAVs to fly in challenging environments remains an unsolved problem, mainly due to the lack of data for training. In this paper, we develop a photo-realistic simulator that can afford the generation of large amounts of training data (both images rendered from the UAV camera and its controls) to teach a UAV to autonomously race through challenging tracks. We train a deep neural network to predict UAV controls from raw image data for the task of autonomous UAV racing. Training is done through imitation learning enabled by data augmentation to allow for the correction of navigation mistakes. Extensive experiments demonstrate that our trained network (when sufficient data augmentation is used) outperforms state-of-the-art methods and flies more consistently than many human pilots.



A Stiffly Accurate Integrator for Elastodynamic Problems

D. L. Michels, V. T. Luan, and M. Tokman.
ACM Transactions on Graphics (SIGGRAPH 2017), ACM (2017).

We present a new integration algorithm for the accurate and efficient solution of stiff elastodynamic problems governed by the second-order ordinary differential equations of structural mechanics. Current methods have the shortcoming that their performance is highly dependent on the numerical stiffness of the underlying system that often leads to unrealistic behavior or a significant loss of efficiency. To overcome these limitations, we present a new integration method which is based on a mathematical reformulation of the underlying differential equations, an exponential treatment of the full nonlinear forcing operator as opposed to more standard partially implicit or exponential approaches, and the utilization of the concept of stiff accuracy which ensures that the efficiency of the simulations is significantly less sensitive to increased stiffness. As a consequence, we are able to tremendously accelerate the simulation of stiff systems compared to established integrators and significantly increase the overall accuracy. The advantageous behavior of this approach is demonstrated on a broad spectrum of complex examples like deformable bodies, textiles, bristles, and human hair. Our easily parallelizable integrator enables more complex and realistic models to be explored in visual computing without compromising efficiency.

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Algorithmic Verification of Linearizability for Ordinary Differential Equations

D. A. Lyakhov, V. P. Gerdt, and D. L. Michels.
ACM International Symposium on Symbolic and Algebraic Computation (ISSAC 2017), ACM 2017.

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of both algorithms is discussed and their application is illustrated using several examples.

ACM SIGSAM Distinguished Paper Award.

ACM Library arXiv SIGSAM Awards


On Strongly Consistent Finite Difference Approximations to the Navier-Stokes Equations

D. A. Lyakhov, V. P. Gerdt, and D. L. Michels.
Foundations of Computational Mathematics (FoCM 2017), Symbolic Analysis Workshop (Poster), FoCM 2017.

The finite difference method is widely used for solving partial differential equations in the computational sciences. The decisive factor for its successful application is the quality of the underlying finite difference approximations. In this contribution, we present a computer algebra assisted approach to generate appropriate finite difference approximations to systems of polynomially nonlinear partial differential equations on regular Cartesian grids. The generated approximations satisfy the major quality criterion – strong consistency – which implies the preservation of fundamental algebraic properties of the system at the discrete level. This criterion admits a verification algorithm. We apply our approach to the Navier-Stokes equations and construct strongly consistent approximations. Moreover, we construct two approximations which are not only strongly consistent but also fully conservative.

Symbolic Analysis Workshop


Discrete Computational Mechanics for Stiff Phenomena

D. L. Michels and J. P. T. Mueller.
ACM SIGGRAPH Asia 2016, Course Notes, ACM (2016).

Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.

ACM Library WWW

Springer Science+Business Media

On the General Analytical Solution of the Kinematic Cosserat Equations

D. L. Michels, D. A. Lyakhov, V. P. Gerdt, Z. Hossain, I. H. Riedel-Kruse, and A. G. Weber.
Computer Algebra in Scientific Computing (CASC 2016), Springer (2016).

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

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