ACDC at SIAM 2025 – May 6

Department of Mathematics, Vrije Universiteit Amsterdam

The Amsterdam Center for Dynamics and Computation (ACDC) is organizing a special event on May 6, 2025, one week before the SIAM Conference on Dynamical Systems and Applications. Since not everyone can attend SIAM, ACDC at SIAM offers a local platform for members to share and discuss their research.

This gathering will feature presentations from those attending SIAM, providing an opportunity to refine their talks while allowing the broader community to engage with the latest developments in dynamical systems.

The event is open to everyone: ACDC members, graduate and undergraduate students, and researchers in dynamical systems from outside the department. It offers a unique chance to explore a diverse range of topics, including:

• Network dynamical systems, Phase reductions

• Coupled oscillators, Reconstruction techniques

• Computer-assisted proofs, Navier-Stokes equations

• Spatially extended neural models

• Data assimilation, Uncertainty quantification

We invite all interested researchers to join us for a day of insightful discussions and knowledge sharing.

Participation is free, but registration is mandatory. Please complete the registration form by April 25 so we can arrange a suitable room and ensure a well-organized event.

Registration form 

Organizer: Fahimeh Mokhtari. Email: f.mokhtari@vu.nl

Participants

• Confirmed Speakers:

  • Bengi Dönmez (VU Amsterdam)

  • Christian Bick (VU Amsterdam)

  • Daniele Avitabile (VU Amsterdam)

  • Lindsey van der Aalst (VU Amsterdam)

Schedule: 

13:00 - 13:30 Bengi Dönmez - Reconstructing Networks and Hypernetworks of Coupled Oscillators from Time Series

13:30 - 14:30 Christian Bick- Hidden Networks: From Phase Reductions to Effective Network Interactions

14:30 - 15:00 Break

15:00 - 15:30 Daniele Avitabile- Data assimilation and Uncertainty Quantification in cortical models

16:00 - 16:30 Lindsey van der Aalst- Three-dimensional periodic solutions in the forced Navier-Stokes equations

16:30 - 16:50 Closing & Discussion

17:00 - 18:00 Drinks

Abstracts

Bengi Dönmez

Title: Reconstructing Networks and Hypernetworks of Coupled Oscillators from Time Series

Abstract: We are interested in weakly coupled Kuramoto oscillators and aim to determine their network structure from time series data. The main challenge here is that the problem is not well-posed: two different network models can produce identical time series if there’s noise. As a result, it is impossible to reconstruct the exact model or network structure. To overcome this issue, rather than reconstructing the complete model, we focus on identifying the simplest form of the model that can replicate the observed dynamics. This involves using the normal form, which captures the core features of the dynamics. Our method uses least-squares fitting to achieve this. Fitting the normal form, we also don't need many data points, making the method efficient and robust. By examining the data and fitted terms, we further establish an explicit bound on the error in the reconstructed coupling coefficients. We illustrate our results with numerical simulations.

Christian Bick

Title: Hidden Networks: From Phase Reductions to Effective Network Interactions

Abstract: From networks of interconnected neurons in the brain to coupled electrochemical reactions: The collective dynamics of interacting dynamical systems shape the function (or dysfunction) of many systems that are critical for our everyday lives. For coupled oscillatory processes, synchronization is a prime example of emergent collective dynamics. But how oscillators interact is not necessarily obvious from (physical) connections between the oscillators. Here we look at phase reductions as a way to uncover the hidden 'effective' network interactions for coupled oscillators dynamics. On the one hand, these give insight into when oscillators do and do not interact (despite a link). On the other hand, they elucidate when and how nonpairwise higher-order interactions shape synchronization phenomena in coupled oscillator networks.

Daniele Avitabile

Title: Data assimilation and Uncertainty Quantification in cortical models

Abstract: This talk presents a framework for forward uncertainty quantification and data assimilation problems in spatially-extended neurobiological networks, for which we take neural fields as a prototype. Large-scale brain simulations of such models are currently performed heuristically, and the numerical analysis of these problems is largely unexplored. In the first part of the talk I will summarise recent developments for the rigorous numerical analysis of projection schemes for deterministic neural fields, which sets the foundation for developing Finite-Element and Spectral schemes for large-scale problems. The second part of the talk will discuss the case of networks in the presence of uncertainties modelled with random data, in particular: random synaptic connections, external stimuli, neuronal firing rates, and initial conditions. Such problems give rise to random solutions, whose mean, variance, or other quantities of interest have to be estimated using numerical simulations. In addition to this forward Uncertainty Quantification problem, I will also present results of an inverse problem in which cortical data is used to infer parameter and states of the neural field model.

This talk presents joint work with Francesca Cavallini (VU Amsterdam), Svetlana Dubinkina (VU Amsterdam), Gabriel Lord (Radboud University), and Khadija Meddouni (Radboud University).

 
Lindsey van der Aalst 

Title: Three-dimensional periodic solutions in the forced Navier-Stokes equations

Abstract: In this work, we extend results from existing literature on periodic solutions in the forced Navier-Stokes equations from two to three dimensions. Our approach relies on computer-assisted proof methods, based on a Newton-Kantorovich type argument, ensuring rigorous control over computational errors. Challenges posed by the higher-dimensional nature of the problem are alleviated by employing symmetry arguments. In this study, we focus on traveling wave solutions and on validating solutions at and near the Hopf bifurcations.