Many seminars during the year will be delivered by the Purdue University Fort Wayne LDS Team on topics of interest to students, researchers, and local and global communities. The regular time of the seminars is Wednesday from 1:30pm to 2:30pm.

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The work involves the study of SINDy algorithm on compact Riemannian manifolds. The basic SINDy algorithm is demonstrated through examples. However, simple SINDy algorithm cannot identify dynamical systems where equations involve implicit ordinary differential equations. Consequently, SINDy-PI is explored. As a case study, an example of a particle moving on a torus is developed. It is observed that SINDy-PI can accurately identify the dynamical systems only up to a small noise. 

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Causal inference is fundamental across scientific disciplines, yet stateof-the-art methods often struggle to capture instantaneous and time-evolving causal relationships in complex, high-dimensional systems. This talk introduces assimilative causal inference (ACI), a paradigm-shifting framework that reframes causality as a Bayesian inverse problem using data assimilation. Rather than measuring forward influence from causes to effects, ACI instead traces causality backwards by quantifying how incorporating future information about observed effects reduces uncertainty in the estimated system state [1]. In this sense, effects are interpolated onto causes, contrasting classical predictive approaches that extrapolate causes to identify effects. ACI determines dynamic causal interactions without requiring observations of candidate causes, accommodates short and incomplete datasets, and scales efficiently to high dimensions. Crucially, it provides online tracking of causal roles, which may reverse intermittently, and facilitates the development of mathematically rigorous criteria for the causal influence range (CIR) of a relationship. The ACI-based CIR metric is objectively defined, without empirical thresholds, and admits both forward- and backward-in-time formulations. The forward CIR quantifies the temporal reach of a cause, while the backward CIR traces the onset of triggers for an observed effect, enabling causal predictability and attribution in transient regimes [2]. The effectiveness of ACI is demonstrated on nonlinear dynamical systems showcasing intermittency and extreme events.

[1] Andreou, M., Chen, N. & Bollt, E. Assimilative causal inference. Nat Commun (2026). https://doi.org/10.1038/s41467-026-68568-0 

[2] Andreou, M. & Chen, N.  Bridging Prediction and Attribution: Identifying Forward and Backward Causal Influence Ranges Using Assimilative Causal Inference. arXiv (2025). https://doi.org/10.48550/arXiv.2510.21889 (Under review in Physica D: Nonlinear Phenomena.)

A 7-minute short video about ACI: https://youtu.be/lrcPweSC7mQ || More information: https://mariosandreou.short.gy/ACI

Abstract

If we want to analyze chaotic dynamics in experimental data, we have to face some drawbacks, such as short and noisy recordings, which can lead to imprecise (or even incorrect) results when standard techniques are applied. In recent years, Deep Learning has been successfully used to perform dynamical systems analyses. In par- ticular, Deep Learning has been shown to be useful for detecting chaos in dynamical systems [1] and for approximating the full Lyapunov exponents spectrum using only partial information [2]. However, the amount of real-world data is sometimes limited, and there may not be enough samples to properly train a Deep Learning network. To address the aforementioned limitations, we propose a novel algorithm [3] that combines Deep Learning and mathematical strategies to analyze chaotic dynamics in experimental time series. In particular, we show the performance of the algorithm on frog heart signals.

The works presented in this talk are in collaboration with Roberto Barrio, Alvaro  ́ Lozano, Ana Mayora-Cebollero, Antonio Miguel, Alfonso Ortega, Sergio Serrano, Rub ́en Vigara (Universidad de Zaragoza, Spain), Flavio H. Fenton, Molly Halprin, Conner Herndon and Mikael J. Toye (Georgia Institute of Technology, USA).

References

[1] R. Barrio, A. Lozano, A. Mayora-Cebollero, C. Mayora-Cebollero, A. Miguel, A. Ortega, S. Serrano, R. Vigara. Deep Learning for chaos detection. Chaos: An Interdis- ciplinary Journal of Nonlinear Science 33(7): 073146 (2023) https://doi.org/10.1063/5.0143876

[2] C. Mayora-Cebollero, A. Mayora-Cebollero, A. Lozano, R. Barrio. Full Lyapunov exponents spectrum with Deep Learning from single-variable time series. Physica D: Nonlinear Phenomena 472: 134510 (2025) https://doi.org/10.1016/j.physd.2024.134510

[3] C. Mayora-Cebollero, F.H. Fenton, M. Halprin, C. Herndon, M.J. Toye, R. Barrio. Deep Learning for analyzing chaotic dynamics in biological time series: Insights from frog heart signals. Neurocomputing 660: 131820 (2026) https://doi.org/10.1016/j. neucom.2025.131820.

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Coming Soon!