arXiv subjects

Michael Lindner

Publications and source records attributed to Michael Lindner.

16 recordsLinked to original sources

arXiv2026

Learning Dynamic Stability Landscapes in Synchronization Networks

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

cs.LG↗

arXiv2026

Managing the Mismatch: The Role of Flexibility on the Path to a Carbon-Neutral Energy System

A rapid expansion of system flexibility is essential to integrate increasing shares of renewable energy into future energy systems. However, flexibility needs and technology-specific contributions to flexibility remain poorly quantified in energy system modelling. Existing methods are not widely applied, leaving key questions unanswered: which flexibility technologies are critical for climate neutrality, and what are the cost implications of alternative deployment strategies? To address this gap, we apply a correlation-based flexibility metric to a high-resolution, sector-coupled model of the German energy system, covering its transformation towards climate neutrality. For our default scenario, we find that daily flexibility needs increase by a factor of 3.7 between 2025 and 2045, driven primarily by the expansion of solar PV. By 2045, stationary batteries provide 38% of daily flexibility, while flexible electric vehicle charging contributes 30%. Systems with constrained flexibility increase system costs by 6.9%, electricity prices by 14 EUR/MWh and trigger 47% higher hydrogen and e-fuel imports compared to an unconstrained system in 2045. In contrast, scenarios with high shares of flexible electric vehicle charging, vehicle-to-grid, and industrial demand-side management achieve system cost reductions of 3.3%, while also reducing import dependence. Higher flexibility also reduces electricity price ranges, decreases average electricity prices by 3 EUR/MWh, and reduces backup capacity by 22% (22 GW). Overall, our results highlight the decisive role of specific flexibility technologies in achieving cost-efficient and energy-secure climate-neutral energy systems, providing quantitative guidance for policy and investment decisions.

physics.soc-ph↗

arXiv2025

PyPSA-DE: Open-source German energy system model reveals savings from integrated planning

Germany has set an ambitious target of reaching net zero greenhouse gas emissions by 2045. We explore how integrated cross-sectoral planning can reduce costs compared to existing national plans. Our new linear optimization model PyPSA-DE simulates the electricity and hydrogen transmission networks, as well as supply, demand, and storage in all sectors of the energy system in Germany and its neighboring countries with high spatial and temporal resolution. While our new model shows strong electricity transmission grid development, total expansion is one third lower than in the national grid development plan, lowering costs by 92 billion EUR$_{2020}$ to 191 billion EUR$_{2020}$ and average grid tariffs by 7.5 EUR$_{2020}$ / MWh. These savings are mainly due to integrated planning and operation, a market design with regional prices, and a system-optimal usage of offshore wind. PyPSA-DE is open-source and can readily be adapted to study related issues around the energy transition.

physics.soc-ph↗

arXiv2025

Price Formation in a Highly-Renewable, Sector-Coupled Energy System

As variable renewable energy increases and more demand is electrified, we expect price formation in wholesale electricity markets to transition from being dominated by fossil fuel generators to being dominated by the opportunity costs of storage and demand management. In order to analyse this transition, we introduce a new method to investigate price formation based on a mapping from the dual variables of the energy system optimisation problem to the bids and asks of electricity suppliers and consumers. This allows us to build the full supply and demand curves in each hour. We use this method to analyse price formation in a sector-coupled, climate-neutral energy system model for Germany, PyPSA-DE, with high temporal resolution and myopic foresight in 5-year steps from 2020 until full decarbonisation in 2045. We find a clear transition from distinct price levels, corresponding to fossil fuels, to a smoother price curve set by variable renewable energy sources, batteries and electrolysis. Despite higher price volatility, the fully decarbonised system clears with non-zero prices in 75% of all hours. Our results suggest that flexibility and cross-sectoral demand bidding play a vital role in stabilising electricity prices in a climate-neutral future. These findings are highly relevant for guiding investment decisions and informing policy, particularly in support of dynamic pricing, the expansion of energy storage across multiple timescales, and the coordinated development of renewable and flexibility technologies.

econ.GN↗

arXiv2025

Spin wave propagation in a ring-shaped magnonic waveguide

We experimentally investigate frequency-selective spin wave (SW) transmission in a micrometre-scale, ring-shaped magnonic resonator integrated with a linear Yttrium Iron Garnet (YIG) stripe. Using super-Nyquist-sampling magneto-optical Kerr effect microscopy (SNS-MOKE) and micro-focused Brillouin light scattering ({\mu}-BLS), we probe SW dynamics in the dipolar regime under in-plane magnetisation. Spatially resolved measurements reveal a sharp transmission peak at 3.92 GHz for an external field of 74 mT, demonstrating strong frequency selectivity. Our results show that this selectivity arises from scattering and interference between multiple SW modes within the ring. These modes are governed by the anisotropic dispersion relation, transverse mode quantisation due to geometric confinement, and inhomogeneities of the effective magnetic field. In addition, the anisotropy enforces fixed group velocity directions, leading to caustic-like propagation that limits efficient out-coupling. Fourier analysis reveals discrete wavevector components consistent with quantised transverse eigenmodes. Additional {\mu}-BLS measurements at 70 mT show a shift of the transmission peak, confirming that the filtering characteristics are tunable by external parameters.

cond-mat.mes-hall↗

arXiv2024

Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions

The geometry of a graph is encoded in dynamical processes on the graph. Many graph neural network (GNN) architectures are inspired by such dynamical systems, typically based on the graph Laplacian. Here, we introduce Dirac--Bianconi GNNs (DBGNNs), which are based on the topological Dirac equation recently proposed by Bianconi. Based on the graph Laplacian, we demonstrate that DBGNNs explore the geometry of the graph in a fundamentally different way than conventional message passing neural networks (MPNNs). While regular MPNNs propagate features diffusively, analogous to the heat equation, DBGNNs allow for coherent long-range propagation. Experimental results showcase the superior performance of DBGNNs over existing conventional MPNNs for long-range predictions of power grid stability and peptide properties. This study highlights the effectiveness of DBGNNs in capturing intricate graph dynamics, providing notable advancements in GNN architectures.

cs.LG↗

arXiv2024

Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning

Due to the increasing share of renewables, the analysis of the dynamical behavior of power grids gains importance. Effective risk assessments necessitate the analysis of large number of fault scenarios. The computational costs inherent in dynamic simulations impose constraints on the number of configurations that can be analyzed. Machine Learning (ML) has proven to efficiently predict complex power grid properties. Hence, we analyze the potential of ML for predicting dynamic stability of future power grids with large shares of inverters. For this purpose, we generate a new dataset consisting of synthetic power grid models and perform dynamical simulations. As targets for the ML training, we calculate the fault-ride-through probability, which we define as the probability of staying within a ride-through curve after a fault at a bus has been cleared. Importantly, we demonstrate that ML models accurately predict the fault-ride-through probability of synthetic power grids. Finally, we also show that the ML models generalize to an IEEE-96 Test System, which emphasizes the potential of deploying ML methods to study probabilistic stability of power grids.

eess.SY↗

arXiv2024

Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning

A central question of network science is how functional properties of systems emerge from their structure. For networked dynamical systems, structure is typically captured through network measures. We investigate the relationship between these measures and stability metrics across non-linear and linear oscillators, as well as real-world power grid topologies and dynamics. We find that this relationship is highly sensitive to the underlying ensemble: minor changes in the networks considered, such as going from mean degree 6 to mean degree 8, can invert the correlation between a network measure and stability. We also investigate network measures as inputs for machine learning, as well as Graph Neural Networks (GNNs) as predictors of stability. Both GNNs and the non-linear combination of many network measures can accurately predict stability within a given ensemble, yet both can fail when the ensemble changes. We conclude that neither approach reliably identifies the underlying structural causes of instability.

nlin.AO↗

arXiv2022

Towards dynamic stability analysis of sustainable power grids using graph neural networks

To mitigate climate change, the share of renewable needs to be increased. Renewable energies introduce new challenges to power grids due to decentralization, reduced inertia and volatility in production. The operation of sustainable power grids with a high penetration of renewable energies requires new methods to analyze the dynamic stability. We provide new datasets of dynamic stability of synthetic power grids and find that graph neural networks (GNNs) are surprisingly effective at predicting the highly non-linear target from topological information only. To illustrate the potential to scale to real-sized power grids, we demonstrate the successful prediction on a Texan power grid model.

cs.LG↗

arXiv2022

Toward Dynamic Stability Assessment of Power Grid Topologies using Graph Neural Networks

To mitigate climate change, the share of renewable energies in power production needs to be increased. Renewables introduce new challenges to power grids regarding the dynamic stability due to decentralization, reduced inertia, and volatility in production. Since dynamic stability simulations are intractable and exceedingly expensive for large grids, graph neural networks (GNNs) are a promising method to reduce the computational effort of analyzing the dynamic stability of power grids. As a testbed for GNN models, we generate new, large datasets of dynamic stability of synthetic power grids, and provide them as an open-source resource to the research community. We find that GNNs are surprisingly effective at predicting the highly non-linear targets from topological information only. For the first time, performance that is suitable for practical use cases is achieved. Furthermore, we demonstrate the ability of these models to accurately identify particular vulnerable nodes in power grids, so-called troublemakers. Last, we find that GNNs trained on small grids generate accurate predictions on a large synthetic model of the Texan power grid, which illustrates the potential for real-world applications.

cs.LG↗

arXiv2022

Information-theoretic analyses of neural data to minimize the effect of researchers' assumptions in predictive coding studies

Studies investigating neural information processing often implicitly ask both, which processing strategy out of several alternatives is used and how this strategy is implemented in neural dynamics. A prime example are studies on predictive coding. These often ask if confirmed predictions about inputs or predictions errors between internal predictions and inputs are passed on in a hierarchical neural system--while at the same time looking for the neural correlates of coding for errors and predictions. If we do not know exactly what a neural system predicts at any given moment, this results in a circular analysis--as has been criticized correctly. To circumvent such circular analysis, we propose to express information processing strategies (such as predictive coding) by local information-theoretic quantities, such that they can be estimated directly from neural data. We demonstrate our approach by investigating two opposing accounts of predictive coding-like processing strategies, where we quantify the building blocks of predictive coding, namely predictability of inputs and transfer of information, by local active information storage and local transfer entropy. We define testable hypotheses on the relationship of both quantities to identify which of the assumed strategies was used. We demonstrate our approach on spiking data from the retinogeniculate synapse of the cat. Applying our local information dynamics framework, we are able to show that the synapse codes for predictable rather than surprising input. To support our findings, we apply measures from partial information decomposition, which allow to differentiate if the transferred information is primarily bottom-up sensory input or information transferred conditionally on the current state of the synapse. Supporting our local information-theoretic results, we find that the synapse preferentially transfers bottom-up information.

q-bio.NC↗

arXiv2021

An Open Source Software Stack for Tuning the Dynamical Behavior of Complex Power Systems

BlockSystems.jl and NetworkDynamics.jl are two novel software packages which facilitate highly efficient transient stability simulations of power networks. Users may specify inputs and power system design in a convenient modular and equation-based manner without compromising on speed or model detail. Written in the high-level, high-performance programming language Julia a rich open-source package ecosystem is available, which provides state-of-the-art solvers and machine learning algorithms. Motivated by the recent interest in the Nordic inertia challenge we have implemented the Nordic5 test case and tuned its control parameters by making use of the machine learning and automatic differentiation capabilities of our software stack.

eess.SY↗

arXiv2021

Predicting Basin Stability of Power Grids using Graph Neural Networks

The prediction of dynamical stability of power grids becomes more important and challenging with increasing shares of renewable energy sources due to their decentralized structure, reduced inertia and volatility. We investigate the feasibility of applying graph neural networks (GNN) to predict dynamic stability of synchronisation in complex power grids using the single-node basin stability (SNBS) as a measure. To do so, we generate two synthetic datasets for grids with 20 and 100 nodes respectively and estimate SNBS using Monte-Carlo sampling. Those datasets are used to train and evaluate the performance of eight different GNN-models. All models use the full graph without simplifications as input and predict SNBS in a nodal-regression-setup. We show that SNBS can be predicted in general and the performance significantly changes using different GNN-models. Furthermore, we observe interesting transfer capabilities of our approach: GNN-models trained on smaller grids can directly be applied on larger grids without the need of retraining.

physics.soc-ph↗

arXiv2020

NetworkDynamics.jl -- Composing and simulating complex networks in Julia

NetworkDynamics.jl is an easy-to-use and computationally efficient package for working with heterogeneous dynamical systems on complex networks, written in Julia, a high-level, high-performance, dynamic programming language. By combining state of the art solver algorithms from DifferentialEquations.jl with efficient data structures, NetworkDynamics.jl achieves top performance while supporting advanced features like events, algebraic constraints, time-delays, noise terms and automatic differentiation.

cs.MS↗

arXiv2018

Stochastic basins of attraction and generalized committor functions

We generalize the concept of basin of attraction of a stable state in order to facilitate the analysis of dynamical systems with noise and to assess stability properties of metastable states and long transients. To this end we examine the notions of mean sojourn times and absorption probabilities for Markov chains and study their relation to the basins of attraction. Our approach is applicable to a large variety of problems since in most cases the transfer operator associated to a dynamical system can be approximated by a Markov chain.

math.DS↗

arXiv2016

Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: a Lagrangian flow network perspective

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that characterizes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic (ROC) analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.

nlin.CD↗