arXiv subjects

Markus Abel

Publications and source records attributed to Markus Abel.

At least 19 recordsLinked to original sources

arXiv2025

Transition of AI Models in dependence of noise

We investigate the dependence of the score on noise in the data, and on the network size. As a result, we obtain the so-called "cognition transition" from good performance to zero with increasing noise. The understanding of this transition is of fundamental scientific and practical interest. We use concepts from statistical mechanics to understand how a changing finite size of models affects the cognition ability under the presence or corrupted data. On one hand, we study if there is a universal aspect in the transition to several models, on the other hand we go into detail how the approach of the cognition transition point can be captured quantitatively. Therefore, we use the so-called scaling approach from statistical mechanics and find a power-law behaviour of the transition width with increasing model size. Since our study is aimed at universal aspects we use well-know models and data for image classification. That way we avoid uncertainties in data handling or model setup. The practical implication of our results is a tool to estimate model sizes for a certain "universality class" of models, without the need to investigate large sizes, just by extrapolating the scaling results. In turn, that allows for cost reduction in hyperparameter studies. Here, we present first results on a concrete setup; we think that the understanding the mechanics of large system sizes is of fundamental interest for a further exploration of even larger models.

physics.data-an↗

arXiv2025

Private GPTs for LLM-driven testing in software development and machine learning

In this contribution, we examine the capability of private GPTs to automatically generate executable test code based on requirements. More specifically, we use acceptance criteria as input, formulated as part of epics, or stories, which are typically used in modern development processes. This gives product owners, or business intelligence, respectively, a way to directly produce testable criteria through the use of LLMs. We explore the quality of the so-produced tests in two ways: i) directly by letting the LLM generate code from requirements, ii) through an intermediate step using Gherkin syntax. As a result, it turns out that the two-step procedure yields better results -where we define better in terms of human readability and best coding practices, i.e. lines of code and use of additional libraries typically used in testing. Concretely, we evaluate prompt effectiveness across two scenarios: a simple "Hello World" program and a digit classification model, showing that structured prompts lead to higher-quality test outputs.

cs.SE↗

arXiv2024

Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint maximum \textit{a~posteriori} (JMAP) and variational Bayesian approximation (VBA), are compared to the {LASSO, ridge regression and SINDy algorithms for sparse} regression, by application to several dynamical systems with added {Gaussian or Laplace} noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or ``Gaussian norm'' $||\vec{y}-\hat{\vec{y}}||^2_{M^{-1}} = (\vec{y}-\hat{\vec{y}})^\top {M^{-1}} (\vec{y}-\hat{\vec{y}})$, where $\vec{y}$ is a vector variable, $\hat{\vec{y}}$ is its estimator and $M$ is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection {for the different systems and noise models examined.}

stat.ME↗

arXiv2020

Explainable Machine Learning Control -- robust control and stability analysis

Recently, the term explainable AI became known as an approach to produce models from artificial intelligence which allow interpretation. Since a long time, there are models of symbolic regression in use that are perfectly explainable and mathematically tractable: in this contribution we demonstrate how to use symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In previous publications, network control was achieved by automatized machine learning control using genetic programming. Here, we focus on the subsequent analysis of the analytical expressions which result from the machine learning. In particular, we use AUTO to analyze the stability properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable models over less accessible neural networks.

cs.LG↗

arXiv2019

On the Dynamics of the Flow and the Sound Field of an Organ Pipes's Mouth Region

The dynamics of an organ pipe's mouth region has been studied by numerical simulations. The investigations presented here were carried out by solving the compressible Navier-Stokes equations under suitable initial and boundary conditions using parts of the open source C++ toolbox OpenFOAM. The focus of the study is on the examination of the velocity field close to the jet. The components of the velocity field sampled at a cross-section spanning the mouth were analyzed by using methods of coarse-graining. It is shown that the dynamics of the sampled velocity field can be separated into two fractions, a velocity component mainly comprising the jet's flow velocity and a component that essentially carries particle velocity caused by back-propagating sound waves inside the resonator. The SPL-spectra calculated of the data sets of the numerical simulations are compared with the measurements on real organ pipes. The phase-space representations of sound pressure and particle velocity indicate the presence of nonlinearities in the organ pipes's mouth region. The numerical results are consistent with measurements on real organ pipes.

physics.flu-dyn↗

arXiv2019

Inferring the dynamics of oscillatory systems using recurrent neural networks

We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system, but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay and chaotic systems. Furthermore, with a statistical analysis we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit.

nlin.AO↗

arXiv2018

Sparse Identification of Nonlinear Dynamics for Rapid Model Recovery

Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change. In this work, we propose a conceptual framework to recover parsimonious models of a system in response to abrupt changes in the low-data limit. First, the abrupt change is detected by comparing the estimated Lyapunov time of the data with the model prediction. Next, we apply the sparse identification of nonlinear dynamics (SINDy) regression to update a previously identified model with the fewest changes, either by addition, deletion, or modification of existing model terms. We demonstrate this sparse model recovery on several examples for abrupt system change detection in periodic and chaotic dynamical systems. Our examples show that sparse updates to a previously identified model perform better with less data, have lower runtime complexity, and are less sensitive to noise than identifying an entirely new model. The proposed abrupt-SINDy architecture provides a new paradigm for the rapid and efficient recovery of a system model after abrupt changes.

physics.data-an↗

arXiv2018

Glyph: Symbolic Regression Tools

We present Glyph - a Python package for genetic programming based symbolic regression. Glyph is designed for usage let by numerical simulations let by real world experiments. For experimentalists, glyph-remote provides a separation of tasks: a ZeroMQ interface splits the genetic programming optimization task from the evaluation of an experimental (or numerical) run. Glyph can be accessed at http://github.com/ambrosys/glyph . Domain experts are be able to employ symbolic regression in their experiments with ease, even if they are not expert programmers. The reuse potential is kept high by a generic interface design. Glyph is available on PyPI and Github.

cs.MS↗

arXiv2017

Synchronization of organ pipes

We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interaction is highly complex and nonlinear, however, we show that two delay-coupled Van-der-Pol oscillators appear to be a good model for the occurring dynamical phenomena. Here the coupling is realized as distance-dependent, or time-delayed, equivalently. Analytically, we investigate the synchronization frequency and bifurcation scenarios which occur at the boundaries of the Arnold tongues. We successfully compare our results to experimental data.

nlin.AO↗

arXiv2016

Learning Optimal Control of Synchronization in Networks of Coupled Oscillators using Genetic Programming-based Symbolic Regression

Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice-versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly-effective and interpretable control functions for such systems.

nlin.AO↗

arXiv2016

Prediction of Dynamical Systems by Symbolic Regression

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.

physics.data-an↗

arXiv2015

Optimized Setup for 2D Convection Experiments in Thin Liquid Films

We present a novel experimental setup to investigate two-dimensional thermal convection in a freestanding thin liquid film. We develop a setup for the reproducible generation of freestanding thin liquid films. Such films can be produced in a controlled way on the scale of 5 to 1000 nanometers. Our primary goal is to investigate the statistics of reversals in Rayleigh-Bénard convection with varying aspect ratio; here numerical works are quite expensive and 3D experiments prohibitively complicated and costly. However, as well questions regarding the physics of liquid films under controlled conditions can be investigated, like surface forces, or stability under varying thermodynamical parameters. The thin liquid film has a well-defined and -chosen chemistry in order to fit our particular requirements, it has a thickness to area ratio of approximately 10^8 and is supported by a frame which is adjustable in height and width to vary the aspect ratio from 0.16 to 10. The top and bottom frame elements can be set to specific temperature within T= 15-55°C. The ambient parameters of the thin film are carefully controlled to achieve reproducible results and allow a comparison to experimental and numerical data.

physics.ins-det↗

arXiv2015

Small- and Large-scale Characterization and Mixing Properties in a Thermally Driven Thin Liquid Film

Thin liquid films are nanoscopic elements of foams, emulsions and suspensions, and form a paradigm for nanochannel transport that eventually test the limits of hydrodynamic descriptions. Here we use classical dynamical systems characteristics to study the complex interplay of thermal convection, interface and gravitational forces which yields turbulent mixing and transport: Lyapunov exponents and entropies. We induce a stable two eddy convection in an extremely thin liquid film by applying a temperature gradient. Experimentally, we determine the small-scale dynamics using the motion and deformation of spots of equal size/equal color, we dubbed that technique "color imaging velocimetry". The large-scale dynamics is captured by encoding the left/right motion of the liquid directed to the left or right of the separatrix between the two rolls. This way, we characterize chaos of course mixing in this peculiar fluid geometry of a thin, free-standing liquid film.

physics.flu-dyn↗

arXiv2015

Feedback Control of Turbulent Shear Flows by Genetic Programming

Turbulent shear flows have triggered fundamental research in nonlinear dynamics, like transition scenarios, pattern formation and dynamical modeling. In particular, the control of nonlinear dynamics is subject of research since decades. In this publication, actuated turbulent shear flows serve as test-bed for a nonlinear feedback control strategy which can optimize an arbitrary cost function in an automatic self-learning manner. This is facilitated by genetic programming providing an analytically treatable control law. Unlike control based on PID laws or neural networks, no structure of the control law needs to be specified in advance. The strategy is first applied to low-dimensional dynamical systems featuring aspects of turbulence and for which linear control methods fail. This includes stabilizing an unstable fixed point of a nonlinearly coupled oscillator model and maximizing mixing, i.e.\ the Lyapunov exponent, for forced Lorenz equations. For the first time, we demonstrate the applicability of genetic programming control to four shear flow experiments with strong nonlinearities and intrinsically noisy measurements. These experiments comprise mixing enhancement in a turbulent shear layer, the reduction of the recirculation zone behind a backward facing step, and the optimized reattachment of separating boundary layers. Genetic programming control has outperformed tested optimized state-of-the-art control and has even found novel actuation mechanisms.

physics.flu-dyn↗

arXiv2014

Closed-loop control of an experimental mixing layer using machine learning control

A novel framework for closed-loop control of turbulent flows is tested in an experimental mixing layer flow. This framework, called Machine Learning Control (MLC), provides a model-free method of searching for the best function, to be used as a control law in closed-loop flow control. MLC is based on genetic programming, a function optimization method of machine learning. In this article, MLC is benchmarked against classical open-loop actuation of the mixing layer. Results show that this method is capable of producing sensor-based control laws which can rival or surpass the best open-loop forcing, and be robust to changing flow conditions. Additionally, MLC can detect non-linear mechanisms present in the controlled plant, and exploit them to find a better type of actuation than the best periodic forcing.

physics.flu-dyn↗

arXiv2014

Cluster-based reduced-order modelling of a mixing layer

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.

physics.flu-dyn↗

arXiv2014

Closed-loop separation control using machine learning

A novel, model free, approach to experimental closed-loop flow control is implemented on a separated flow. Feedback control laws are generated using genetic programming where they are optimized using replication, mutation and cross-over of best performing laws to produce a new generation of candidate control laws. This optimization process is applied automatically to a backward-facing step flow at Re=1350, controlled by a slotted jet, yielding an effective control law. Convergence criterion are suggested. The law is able to produce effective action even with major changes in the flow state, demonstrating its robustness. The underlying physical mechanisms leveraged by the law are analyzed and discussed. Contrary to traditional periodic forcing of the shear layer, this new control law plays on the physics of the recirculation area downstream the step. While both control actions are fundamentally different they still achieve the same level of effectiveness. Furthermore the new law is also potentially easier and cheaper to implement actuator wise.

physics.flu-dyn↗

arXiv2014

Closed-Loop Turbulence Control Using Machine Learning

We propose a general model-free strategy for feedback control design of turbulent flows. This strategy called 'machine learning control' (MLC) is capable of exploiting nonlinear mechanisms in a systematic unsupervised manner. It relies on an evolutionary algorithm that is used to evolve an ensemble of feedback control laws until minimization of a targeted cost function. This methodology can be applied to any non-linear multiple-input multiple-output (MIMO) system to derive an optimal closed-loop control law. MLC is successfully applied to the stabilization of nonlinearly coupled oscillators exhibiting frequency cross-talk, to the maximization of the largest Lyapunov exponent of a forced Lorenz system, and to the mixing enhancement in an experimental mixing layer flow. We foresee numerous potential applications to most nonlinear MIMO control problems, particularly in experiments.

physics.flu-dyn↗