arXiv subjects

Daniel Köglmayr

Publications and source records attributed to Daniel Köglmayr.

6 recordsLinked to original sources

arXiv2026

Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systems

Machine learning methods predict many real-world systems with remarkable accuracy, but they are typically treated as black boxes that offer no insight into which interactions drive the dynamics. Causal discovery methods reconstruct the interaction network from observational data, but without regard to whether the inferred structure supports prediction. Existing approaches combining both tasks rely on a single global hyperparameter, such as a causal threshold or a fixed neighborhood size, which cannot recover the structure of heterogeneous systems. Here we introduce causal local states (CLS), a framework that simultaneously infers an approximate Granger-causal interaction network and forecasts the system dynamics. For each node independently, we select the smallest set of neighbors that allows a predictive model to forecast the node near-optimally, and the resulting neighborhoods are then combined for a forecast of the full system. On three benchmarks of increasing difficulty, we achieve reconstruction of the underlying networks with high fidelity and forecasts on par with a model that is supplied with the true network, providing a step toward explainable and scalable forecasting of complex systems.

cs.LG↗

arXiv2026

Controlling Dynamical Systems into Unseen Target States Using Machine Learning

We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware realization of next-generation reservoir computing (NGRC), our approach accurately predicts system behavior in unobserved parameter regimes, enabling control over transitions to arbitrary target states utilizing a new prediction evaluation and selection scheme. Crucially, this includes states with dynamics that differ fundamentally from known regimes, such as shifts from periodic to intermittent or chaotic behavior. The method's parameter awareness facilitates non-stationary control with which control scenarios are generated and evaluated on the basis of predefined control objective. In addition to proving the method for transient-free control to extrapolated chaotic target states over transition times, we demonstrate the method's effectiveness on a nonlinear power system model. Our method successfully navigates transitions even in scenarios where system collapse is observed frequently, while ensuring fast transitions and avoiding prolonged transient behavior. By extending the applicability of machine learning-based control mechanisms to previously inaccessible target dynamics, the methodology opens the door to new control applications while maintaining exceptional efficiency.

nlin.CD↗

arXiv2026

Two-shot learning of multiple strange attractors

The brain combines short- and long-term memory to process, store, and recall multiple different pieces of information. Inspired by this and recent results on multifunctional and parameter-aware learning, we extend a new machine learning technique that combines short- and long-term memory units, specifically, a system consisting of a next-generation reservoir computer (NGRC) and extremely randomized trees (ERT), to process, store, and recall multiple different strange attractors. We train the combined NGRC+ERT system using a two-shot learning approach which significantly improves performance by filtering out unnecessary features, thereby avoiding extensive hyperparameter optimization. We first show that an NGRC+ERT system achieves highly accurate reconstruction of the short- and long-term dynamics of both the Lorenz and Halvorsen chaotic attractors when using an exponential filtering scheme. We validate these finding by training the NGRC+ERT system to reconstruct different pairs of attractors and also a greater number of attractors. We focus on the task of training a single NGRC+ERT system to reconstruct 16 different attractors and show that sufficient index-based separation in feature space suppresses unwanted switching dynamics, thus stabilizing long-term memory recall. Finally, we identify that defects in short-term memory processing can provoke failure modes in long-term memory recall resulting in confabulation.

nlin.CD↗

arXiv2023

Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning

Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on next-generation reservoir computing to extrapolate the bifurcation behavior of nonlinear dynamical systems using stationary training data samples. We show that this method can extrapolate tipping point transitions. Furthermore, it is demonstrated that the trained next-generation reservoir computing architecture can be used to predict non-stationary dynamics with time-varying bifurcation parameters. In doing so, post-tipping point dynamics of unseen parameter regions can be simulated.

cs.LG↗

arXiv2023

Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing

Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be trained to reproduce the target dynamics sufficiently well. On the example of forcing a chaotic parametrization of the Lorenz system into intermittent dynamics, we show first that classical reservoir computing excels at this task. In a next step, we compare those results based on different amounts of training data to an alternative setup, where next-generation reservoir computing is used instead. It turns out that while delivering comparable performance for usual amounts of training data, next-generation RC significantly outperforms in situations where only very limited data is available. This opens even further practical control applications in real world problems where data is restricted.

cs.LG↗

arXiv2022

Exploring the limits of multifunctionality across different reservoir computers

Multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we explore the performance of a continuous-time, leaky-integrator, and next-generation `reservoir computer' (RC), when trained on tasks which test the limits of multifunctionality. In the first task we train each RC to reconstruct a coexistence of chaotic attractors from different dynamical systems. By moving the data describing these attractors closer together, we find that the extent to which each RC can reconstruct both attractors diminishes as they begin to overlap in state space. In order to provide a greater understanding of this inhibiting effect, in the second task we train each RC to reconstruct a coexistence of two circular orbits which differ only in the direction of rotation. We examine the critical effects that certain parameters can have in each RC to achieve multifunctionality in this extreme case of completely overlapping training data.

cs.LG↗