arXiv subjects

Nils Müller

Publications and source records attributed to Nils Müller.

11 recordsLinked to original sources

arXiv2025

Optimization of Sums of Bivariate Functions: An Introduction to Relaxation-Based Methods for the Case of Finite Domains

We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing sums of bivariates is shown to be NP-equivalent and it is shown that there exists free lunch in the optimization of sums of bivariates. Based on measure-valued extensions of the objective function, so-called relaxations, $\ell^2$-approximation, and entropy-regularization, we derive several tractable problem formulations solvable with linear programming, coordinate ascent as well as with closed-form solutions. The limits of applying tractable versions of such relaxations to sums of bivariates are investigated using general results for reconstructing measures from their bivariate marginals. Experiments in which the derived algorithms are applied to random functions, vertex coloring, and signal reconstruction problems provide insights into qualitatively different function classes that can be modeled as sums of bivariates.

math.OC↗

arXiv2023

A Principle for Global Optimization with Gradients

This work demonstrates the utility of gradients for the global optimization of certain differentiable functions with many suboptimal local minima. To this end, a principle for generating search directions from non-local quadratic approximants based on gradients of the objective function is analyzed. Experiments measure the quality of non-local search directions as well as the performance of a proposed simplistic algorithm, of the covariance matrix adaptation evolution strategy (CMA-ES), and of a randomly reinitialized Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

math.OC↗

arXiv2023

CyPhERS: A Cyber-Physical Event Reasoning System providing real-time situational awareness for attack and fault response

Cyber-physical systems (CPSs) constitute the backbone of critical infrastructures such as power grids or water distribution networks. Operating failures in these systems can cause serious risks for society. To avoid or minimize downtime, operators require real-time awareness about critical incidents. However, online event identification in CPSs is challenged by the complex interdependency of numerous physical and digital components, requiring to take cyber attacks and physical failures equally into account. The online event identification problem is further complicated through the lack of historical observations of critical but rare events, and the continuous evolution of cyber attack strategies. This work introduces and demonstrates CyPhERS, a Cyber-Physical Event Reasoning System. CyPhERS provides real-time information pertaining the occurrence, location, physical impact, and root cause of potentially critical events in CPSs, without the need for historical event observations. Key novelty of CyPhERS is the capability to generate informative and interpretable event signatures of known and unknown types of both cyber attacks and physical failures. The concept is evaluated and benchmarked on a demonstration case that comprises a multitude of attack and fault events targeting various components of a CPS. The results demonstrate that the event signatures provide relevant and inferable information on both known and unknown event types.

cs.CR↗

arXiv2023

Long-range fiber-optic earthquake sensing by active phase noise cancellation

We present a long-range fiber-optic environmental deformation sensor based on active phase noise cancellation (PNC) in metrological frequency dissemination. PNC sensing exploits recordings of a compensation frequency that is commonly discarded. Without the need for dedicated measurement devices, it operates synchronously with metrological services, suggesting that existing phase-stabilized metrological networks can be co-used effortlessly as environmental sensors. The compatibility of PNC sensing with inline amplification enables the interrogation of cables with lengths beyond 1000 km, making it a potential contributor to earthquake detection and early warning in the oceans. Using spectral-element wavefield simulations that accurately account for complex cable geometry, we compare observed and computed recordings of the compensation frequency for a magnitude 3.9 earthquake in south-eastern France and a 123 km fiber link between Bern and Basel, Switzerland. The match in both phase and amplitude indicates that PNC sensing can be used quantitatively, for example, in earthquake detection and characterization.

physics.geo-ph↗

arXiv2023

Threat Scenarios and Monitoring Requirements for Cyber-Physical Systems of Flexibility Markets

The ongoing integration of renewable generation and distributed energy resources introduces new challenges to distribution network operation. Due to the increasing volatility and uncertainty, distribution system operators (DSOs) are seeking concepts to enable more active management and control. Flexibility markets (FMs) offer a platform for economically efficient trading of electricity flexibility between DSOs and other participants. The integration of cyber, physical and market domains of multiple participants makes FMs a system of cyber-physical systems (CPSs). While cross-domain integration sets the foundation for efficient deployment of flexibility, it introduces new physical and cyber vulnerabilities to participants. This work systematically formulates threat scenarios for the CPSs of FMs, revealing several remaining security challenges across all domains. Based on the threat scenarios, unresolved monitoring requirements for secure participation of DSOs in FMs are identified, providing the basis for future works that address these gaps with new technical concepts.

eess.SY↗

arXiv2023

Assessment of Cyber-Physical Intrusion Detection and Classification for Industrial Control Systems

The increasing interaction of industrial control systems (ICSs) with public networks and digital devices introduces new cyber threats to power systems and other critical infrastructure. Recent cyber-physical attacks such as Stuxnet and Irongate revealed unexpected ICS vulnerabilities and a need for improved security measures. Intrusion detection systems constitute a key security technology, which typically monitors cyber network data for detecting malicious activities. However, a central characteristic of modern ICSs is the increasing interdependency of physical and cyber network processes. Thus, the integration of network and physical process data is seen as a promising approach to improve predictability in real-time intrusion detection for ICSs by accounting for physical constraints and underlying process patterns. This work systematically assesses machine learning-based cyber-physical intrusion detection and multi-class classification through a comparison to its purely network data-based counterpart and evaluation of misclassifications and detection delay. Multiple supervised detection and classification pipelines are applied on a recent cyber-physical dataset, which describes various cyber attacks and physical faults on a generic ICS. A key finding is that the integration of physical process data improves detection and classification of all considered attack types. In addition, it enables simultaneous processing of attacks and faults, paving the way for holistic cross-domain root cause identification.

cs.CR↗

arXiv2022

A Proof of Kirchhoff's First Law for Hyperbolic Conservation Laws on Networks

Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on networks may capture shared concepts, and provide a setting for deriving abstract properties. To this end, we develop a calculus for networks modeled as abstract metric spaces and derive an analog of Kirchhoff's first law for hyperbolic conservation laws. In dynamical systems on networks, Kirchhoff's first law connects the study of abstract global objects, and that of a computationally-beneficial edgewise-Euclidean perspective by stating its equivalence. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions.

math.AP↗

arXiv2022

Unsupervised detection and open-set classification of fast-ramped flexibility activation events

The continuous electrification of the mobility and heating sectors adds much-needed flexibility to the power system. However, flexibility utilization also introduces new challenges to distribution system operators (DSOs), who need mechanisms to supervise flexibility activations and monitor their effect on distribution network operation. Flexibility activations can be broadly categorized to those originating from electricity markets and those initiated by the DSO to avoid constraint violations. Simultaneous electricity market driven flexibility activations may cause voltage quality or temporary overloading issues, and the failure of flexibility activations initiated by the DSO might leave critical grid states unresolved. This work proposes a novel data processing pipeline for automated real-time identification of fast-ramped flexibility activation events. Its practical value is twofold: i) potentially critical flexibility activations originating from electricity markets can be detected by the DSO at an early stage, and ii) successful activation of DSO-requested flexibility can be verified by the operator. In both cases the increased awareness would allow the DSO to take counteractions to avoid potentially critical grid situations. The proposed pipeline combines techniques from unsupervised detection and open-set classification. For both building blocks feasibility is systematically evaluated and proofed on real load and flexibility activation data.

eess.SY↗

arXiv2021

Uncertainty Quantification in LV State Estimation Under High Shares of Flexible Resources

The ongoing electrification introduces new challenges to distribution system operators (DSOs). Controllable resources may simultaneously react to price signals, potentially leading to network violations. DSOs require reliable and accurate low-voltage state estimation (LVSE) to improve awareness and mitigate such events. However, the influence of flexibility activations on LVSE has not been addressed yet. It remains unclear if flexibility-induced uncertainty can be reliably quantified to enable robust DSO decision-making. In this work, uncertainty quantification in LVSE is systematically investigated for multiple scenarios of input availability and flexibility utilization, using real data. For that purpose, a Bayesian neural network (BNN) is compared to quantile regression. Results show that frequent flexibility activations can significantly deteriorate LVSE performance, unless secondary substation measurements are available. Moreover, it is demonstrated that the BNN captures flexibility-induced voltage drops by dynamically extending the prediction interval during activation periods, and that it improves interpretability regarding the cause of uncertainty.

eess.SY↗

arXiv2021

Non-local Optimization: Imposing Structure on Optimization Problems by Relaxation

In stochastic optimization, particularly in evolutionary computation and reinforcement learning, the optimization of a function $f: Ω\to \mathbb{R}$ is often addressed through optimizing a so-called relaxation $θ\in Θ\mapsto \mathbb{E}_θ(f)$ of $f$, where $Θ$ resembles the parameters of a family of probability measures on $Ω$. We investigate the structure of such relaxations by means of measure theory and Fourier analysis, enabling us to shed light on the success of many associated stochastic optimization methods. The main structural traits we derive and that allow fast and reliable optimization of relaxations are the consistency of optimal values of $f$, Lipschitzness of gradients, and convexity. We emphasize settings where $f$ itself is not differentiable or convex, e.g., in the presence of (stochastic) disturbance.

math.OC↗

arXiv2018

Challenges in High-dimensional Reinforcement Learning with Evolution Strategies

Evolution Strategies (ESs) have recently become popular for training deep neural networks, in particular on reinforcement learning tasks, a special form of controller design. Compared to classic problems in continuous direct search, deep networks pose extremely high-dimensional optimization problems, with many thousands or even millions of variables. In addition, many control problems give rise to a stochastic fitness function. Considering the relevance of the application, we study the suitability of evolution strategies for high-dimensional, stochastic problems. Our results give insights into which algorithmic mechanisms of modern ES are of value for the class of problems at hand, and they reveal principled limitations of the approach. They are in line with our theoretical understanding of ESs. We show that combining ESs that offer reduced internal algorithm cost with uncertainty handling techniques yields promising methods for this class of problems.

cs.NE↗