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Michael Günther

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Published work

19 published item(s)

preprint2026arXiv

jina-embeddings-v5-omni: Geometry-preserving Embeddings via Locked Aligned Towers

In this work, we introduce GELATO (Geometry-preserving Embeddings via Locked Aligned TOwers), a novel approach to multimodal embedding models. We build on the VLM-style architecture, in which non-text encoders are adapted to produce input for a language model, which in turn generates embeddings for all varieties of input. We present the result: the jina-embeddings-v5-omni suite, a pair of models that encode text, image, audio, and video input into a single semantic embedding space. GELATO extends the two Jina Embeddings v5 Text models to support additional modality by adding encoders for images and audio. The backbone text embedding models and the added non-text modality encoders remain frozen. We only trained the connecting components, representing 0.35% of the total weights of the joint model. Training is therefore much more efficient than full-parameter retraining. Additionally, the language model remains effectively unaltered, producing exactly the same embeddings for text inputs as the Jina Embeddings v5 Text models. Our evaluations show that GELATO produces results that are competitive with the state-of-the-art, yielding nearly equal performance to larger multimodal embedding models.

preprint2023arXiv

Microphone Utility Estimation in Acoustic Sensor Networks using Single-Channel Signal Features

In multichannel signal processing with distributed sensors, choosing the optimal subset of observed sensor signals to be exploited is crucial in order to maximize algorithmic performance and reduce computational load, ideally both at the same time. In the acoustic domain, signal cross-correlation is a natural choice to quantify the usefulness of microphone signals, i.e., microphone utility, for array processing, but its estimation requires that the uncoded signals are synchronized and transmitted between nodes. In resource-constrained environments like acoustic sensor networks, low data transmission rates often make transmission of all observed signals to the centralized location infeasible, thus discouraging direct estimation of signal cross-correlation. Instead, we employ characteristic features of the recorded signals to estimate the usefulness of individual microphone signals. In this contribution, we provide a comprehensive analysis of model-based microphone utility estimation approaches that use signal features and, as an alternative, also propose machine learning-based estimation methods that identify optimal sensor signal utility features. The performance of both approaches is validated experimentally using both simulated and recorded acoustic data, comprising a variety of realistic and practically relevant acoustic scenarios including moving and static sources.

preprint2023arXiv

Port-Hamiltonian Systems Modelling in Electrical Engineering

The port-Hamiltonian modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as port-Hamiltonian systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a port-Hamiltonian system (PHS), too, which preserves the properties of the underlying subsystems. If the coupling is given by a skew-symmetric matrix, as usual in many applications, the overall system can be easily derived from the subsystems without the need of introducing dummy variables and therefore artificially increasing the complexity of the system. Hence the PHS framework is especially suitable for modelling multi-physical systems. In this paper, we show that port-Hamiltonian systems are a natural generalization of Hamiltonian systems, define coupled port-Hamiltonian systems as ordinary and differential-algebraic equations. To highlight the suitability for electrical engineering applications, we derive PHS models for MNA network equations, electromagnetic devices and coupled systems thereof.

preprint2023arXiv

Structure-preserving identification of port-Hamiltonian systems -- a sensitivity-based approach

We present a gradient-based calibration algorithm to identify a port-Hamiltonian system from given time-domain input-output data. The gradient is computed with the help of sensitivities and the algorithm is tailored such that the structure of the system matrices of the port-Hamiltonian system (skew-symmetry and positive semi-definiteness) is preserved in each iteration of the algorithm. As we only require input-output data, we need to calibrate the initial condition of the internal state of the port-Hamiltonian system as well. Numerical results with synthetic data show the feasibility of the approach.

preprint2022arXiv

Electromagnetic Quasistatic Field Formulations of Darwin Type

Electromagnetic quasistatic (EMQS) fields, where radiation effects are neglected, while Ohmic losses and electric and magnetic field energies are considered, can be modeled using Darwin-type field models as an approximation to the full Maxwell equations. Commonly formulated in terms of magnetic vector and electric scalar potentials, these EMQS formulations are not gauge invariant. Several EMQS formulations resulting from different gauge equations are considered and analyzed in terms of their structural properties and their modeling capabilities and limitations. Associated discrete field formulations in the context of the Maxwell-grid equations of the Finite Integration Technique are considered in frequency and time domain and are studied with respect to their algebraic properties. A comparison of numerical simulation results w.r.t. reference solutions obtained with established formulations for the full Maxwell equations are presented.

preprint2021arXiv

Enhanced fifth order WENO Shock-Capturing Schemes with Deep Learning

In this paper we enhance the well-known fifth order WENO shock-capturing scheme by using deep learning techniques. This fine-tuning of an existing algorithm is implemented by training a rather small neural network to modify the smoothness indicators of the WENO scheme in order to improve the numerical results especially at discontinuities. In our approach no further post-processing is needed to ensure the consistency of the method, which simplifies the method and increases the effect of the neural network. Moreover, the convergence of the resulting scheme can be theoretically proven. We demonstrate our findings with the inviscid Burgers' equation, the Buckley-Leverett equation and the 1-D Euler equations of gas dynamics. Hereby we investigate the classical Sod problem and the Lax problem and show that our novel method outperforms the classical fifth order WENO schemes in simulations where the numerical solution is too diffusive or tends to overshoot at shocks.

preprint2021arXiv

Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups

In this paper we present a general procedure for designing higher strong order methods for Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge-Kutta--Munthe-Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge-Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.

preprint2020arXiv

Constrained Hybrid Monte Carlo algorithms for gauge-Higgs models

We develop Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge- Higgs models and introduce a new observable for the constraint effective Higgs potential. We use an extension of the so-called Rattle algorithm to general Hamiltonians for constrained systems, which we adapt to the 4D Abelian-Higgs model and the 5D SU(2) gauge theory on the torus and on the orbifold. The derivative of the potential is measured via the expectation value of the Lagrange multiplier for the constraint condition and allows a much more precise determination of the effective potential than conventional histogram methods. With the new method, we can access the potential over the full domain of the Higgs variable, while the histogram method is restricted to a short region around the expectation value of the Higgs field in unconstrained simulations, and the statistical precision does not deteriorate when the volume is increased. We further verify our results by comparing to the one-loop Higgs potential of the 4D Abelian-Higgs model in unitary gauge and find good agreement. To our knowledge, this is the first time this problem has been addressed for theories with gauge fields. The algorithm can also be used in four dimensions to study finite temperature and density transitions via effective Polyakov loop actions.

preprint2020arXiv

Dynamic iteration schemes and port-Hamiltonian formulation in coupled DAE circuit simulation

Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within dynamic iteration procedures. To this end, we introduce new classes of port-Hamiltonian differential-algebraic equations. Thereby, we additionally allow for nonlinear dissipation on a subspace of the state space. Both, each subsystem and the overall system, possess a port-Hamiltonian structure. A structural analysis is performed for the new setups. Dynamic iteration schemes are investigated and we show that the Jacobi approach as well as an adapted Gauss-Seidel approach lead to port-Hamiltonian differential-algebraic equations.

preprint2020arXiv

GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks

This paper describes the project GivEn that develops a novel multicriteria optimization process for gas turbine blades and vanes using modern "adjoint" shape optimization algorithms. Given the many start and shut-down processes of gas power plants in volatile energy grids, besides optimizing gas turbine geometries for efficiency, the durability understood as minimization of the probability of failure is a design objective of increasing importance. We also describe the underlying coupling structure of the multiphysical simulations and use modern, gradient based multicriteria optimization procedures to enhance the exploration of Pareto-optimal solutions.

preprint2020arXiv

Inter/extrapolation-based multirate schemes -- a dynamic-iteration perspective

Multirate behavior of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) is characterized by widely separated time constants in different components of the solution or different additive terms of the right-hand side. Here, classical multirate schemes are dedicated solvers, which apply (e.g.) micro and macro steps to resolve fast and slow changes in a transient simulation accordingly. The use of extrapolation and interpolation procedures is a genuine way for coupling the different parts, which are defined on different time grids. This paper contains for the first time, to the best knowledge of the authors, a complete convergence theory for inter/extrapolation-based multirate schemes for both ODEs and DAEs of index one, which are based on the fully-decoupled approach, the slowest-first and the fastest-first approach. The convergence theory is based on linking these schemes to multirate dynamic iteration schemes, i.e., dynamic iteration schemes without further iterations. This link defines naturally stability conditions for the DAE case.

preprint2020arXiv

Linearly implicit GARK schemes

Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness and characteristic time scales. The multimethod approach discretizes each physical process with an appropriate numerical method; the methods are coupled appropriately such that the overall solution has the desired accuracy and stability properties. The authors developed the general-structure additive Runge-Kutta (GARK) framework, which constructs multimethods based on Runge-Kutta schemes. This paper constructs the new GARK-ROS/GARK-ROW families of multimethods based on linearly implicit Rosenbrock/Rosenbrock-W schemes. For ordinary differential equation models, we develop a general order condition theory for linearly implicit methods with any number of partitions, using exact or approximate Jacobians. We generalize the order condition theory to two-way partitioned index-1 differential-algebraic equations. Applications of the framework include decoupled linearly implicit, linearly implicit/explicit, and linearly implicit/implicit methods. Practical GARK-ROS and GARK-ROW schemes of order up to four are constructed.

preprint2020arXiv

RETRO: Relation Retrofitting For In-Database Machine Learning on Textual Data

There are massive amounts of textual data residing in databases, valuable for many machine learning (ML) tasks. Since ML techniques depend on numerical input representations, word embeddings are increasingly utilized to convert symbolic representations such as text into meaningful numbers. However, a naive one-to-one mapping of each word in a database to a word embedding vector is not sufficient and would lead to poor accuracies in ML tasks. Thus, we argue to additionally incorporate the information given by the database schema into the embedding, e.g. which words appear in the same column or are related to each other. In this paper, we propose RETRO (RElational reTROfitting), a novel approach to learn numerical representations of text values in databases, capturing the best of both worlds, the rich information encoded by word embeddings and the relational information encoded by database tables. We formulate relation retrofitting as a learning problem and present an efficient algorithm solving it. We investigate the impact of various hyperparameters on the learning problem and derive good settings for all of them. Our evaluation shows that the proposed embeddings are ready-to-use for many ML tasks such as classification and regression and even outperform state-of-the-art techniques in integration tasks such as null value imputation and link prediction.

preprint2020arXiv

Tracing Contacts to Control the COVID-19 Pandemic

The control of the COVID-19 pandemic requires a considerable reduction of contacts mostly achieved by imposing movement control up to the level of enforced quarantine. This has lead to a collapse of substantial parts of the economy. Carriers of the disease are infectious roughly 3 days after exposure to the virus. First symptoms occur later or not at all. As a consequence tracing the contacts of people identified as carriers is essential for controlling the pandemic. This tracing must work everywhere, in particular indoors, where people are closest to each other. Furthermore, it should respect people's privacy. The present paper presents a method to enable a thorough traceability with very little risk on privacy. In our opinion, the latter capabilities are necessary to control the pandemic during a future relaunch of our economy.

preprint2016arXiv

Adapted nested force-gradient integrators: the Schwinger model case

We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a well known benchmark problem. We derive the analytical basis of nested force-gradient type methods and demonstrate the advantage of the proposed approach, namely reduced computational costs compared with other numerical integration schemes in HMC.

preprint2016arXiv

The Wilson Flow and the finite temperature phase transition

We consider the determination of the finite temperature phase transition in the Yang--Mills SU(3) gauge theory. We compute the difference of the spatial and temporal energy density at a physical Wilson flow time. This difference is zero in the confined phase and becomes non zero in the deconfined phase. We locate the phase transition by using a new technique based on an exponential smoothing spline. This method is an alternative to the determination of the phase transition based on the Polyakov loop susceptibility and can also be used with dynamical fermions.

preprint2013arXiv

Force-Gradient Nested Multirate Methods for Hamiltonian System

Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential can be exploited by coupling force-gradient decomposition methods with splitting techniques for multi-time scale problems to further increase the accuracy of the scheme and reduce the computational costs. In this paper, we derive novel force-gradient nested methods and test them numerically. Such methods can be used to increase the acceptance rate for the molecular dynamics step of the Hybrid Monte Carlo algorithm (HMC) and hence improve its computational efficiency.

preprint2011arXiv

Accuracy of Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie-Groups

Computer simulations in QCD are based on the discretization of the theory on a Euclidean lattice. To compute the mean value of an observable, usually the Hybrid Monte Carlo method is applied. Here equations of motion, derived from an Hamiltonian, have to be solved numerically. Commonly the Leapfrog (Stoermer-Verlet) method or splitting methods with multiple timescales à la Sexton-Weingarten are used to integrate the dynamical system, defined on a Lie group. Here we formulate time-reversible higher order integrators based on implicit partitioned Runge-Kutta schemes and show that they allow for larger step-sizes than the Leapfrog method. Since these methods are based on an infinite series of exponential functions, we concentrate on the truncation of this series with respect to the global error and accuracy. Finally, we see that the global error of a SPRK scheme is always even such that a convergence order of one is gained for methods with odd convergence order.

preprint2011arXiv

Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie Groups

In this paper, we develop a higher order symmetric partitioned Runge-Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge-Kutta methods on Lie groups of arbitrary order. As symmetry is not met for higher orders, we generalize the method to a symmetric partitioned Runge-Kutta (SPRK) scheme. Furthermore, we derive a set of coefficients for convergence order 4. The SPRK integration method can be used, for example, in simulations of quantum field theories. Finally, we compare the new SPRK scheme numerically with the Störmer-Verlet scheme, one of the state-of-the-art schemes used in this subject.