Designing Complex Behaviour: Novel Pathways for Assisting Design Based on Dynamics-Informed Machine Learning in Structural Mechanics

Develop and experimentally validate novel forecasting methods using the Reservoir Computing (RC) framework to predict nonlinear structural dynamics that are parametrized in design variables. Overcome the cold start problem of ML, i.e. allow few-shot learning from small datasets.

Key Goals:

• Create fast, energy-efficient surrogates for forecasting nonlinear dynamics under external loads for early design phases.
• Develop generic dynamics-informed reservoir computing (RC) methods tailored for limited data
• Use RC for robust predictions of complex systems under unknown design parameters, external loads, and conditions.
• Build an open-source Python library for easy installation, use, and modification.

A short overview about goals achieved during the first phase:

• Implementation and benchmarking of RC methods as a design assistants for a nonlinear structural oscillator.
• Achievement of multiparametric generalization capabilities of RC trained on minimal data.
• Definition of the benchmark data set DORA [link: https://github.com/maneesh51/Benchmark-Tasks/tree/main ] for the design for structural dynamcis
• Publication of the Python library PyReCo [link: https://github.com/Cyber-Physical-Systems-in-Mech-Eng/pyReCo ]
• Collaborations within SPP:
  • Contribution of DORA dataset as an example from engineering design in Ebel, H et. al [3] 
  • RC framework’s usability in  in engineering design techniques in Payrebrune, K. de et. al [4]. 

• Task: Predict the response of a forced Duffing oscillator using minimal training data for varying system parameters (driving several bifurcations from period-1 to period-n and chaotic dynamics).
• Generalization Test: Evaluate the model's ability to extrapolate system responses in unseen parameter regimes: train on few samples of periodic dynamics, generalize to chaotic dynamics.
• Results [1]: RC accurately captures system behaviors like the exact number of cycles in limit-cycle regimes. Identifies chaotic trajectories when amplitude changes.

• Easy to install, use and modify
• Similar syntax as common ML packages
• Freedom to choose/modify RC architecture
• Publicly available on pypi.org [Link: https://pypi.org/project/pyreco/]

• Prof. Sudeshna Sinha (Deputy Director IISER Mohali, India) visited in Oct. 2023 for collaboration in optimization of RC structures with evolving networks [2].
• Rasha Shanaz (Physics Ph.D. student at Bharathidasan Uni., Tiruchirappalli, India) visited in March-May 2024 and contributed in building RC methodologies and PyReCo library.
• Several Bachelor and Master thesis for engineering students for building RC methodologies in engineering applications.
• 6 Talks in several national and international conferences including GAMM (Magdeburg 2024) and Dynamics Days Europe (Bremen 2024).

• Experimental data of complex dynamical system
• Optimization algorithms for evolution RC
• Design challenges: Design for dynamics in mechanical systems

• Experience with time-series predictions of dynamical sytems
• Generalization required to understand unknown parameters of complex dynamical system
• Theoretical and practical machine learning experience

1. Yadav, M.; Chauhan S.; Shrimali, M. D.; Stender, M. (2024). Predicting multi-parametric dynamics of externally forced oscillator using reservoir computing and minimal data. Nonlinear Dynamics. https://doi.org/10.1007/s11071-024-10720-w 
2. Yadav, M.; Sinha, S.; Stender, M. (2024) Evolution beats random chance: Performance-dependent network evolution for enhanced computational capacity, accepted at PRE. https://doi.org/10.48550/arXiv.2403.15869
3. Ebel, H.; Delden, J. van; Lüddecke, T.; Borse, A.; Gulakala, R.; Stoffel, M.; Yadav, M.; Stender, M.; Schindler, L.; Payrebrune, K. de; Raff, M.; Remy, C.D.; Röder, B.; Eberhard, P. (2024). Data Publishing in Mechanics and Dynamics: Challenges, Guidelines, and Examples from Engineering Design. URL: https://doi.org/10.48550/arXiv.2410.18358 submitted on 27.11.2024 to Data-Centric Engineering.
4. Payrebrune, K. de; Flasskamp, K.; Ströhla, T.; Sattel, T.; Bestle, D.; Röder, B.; Eberhard, P.; Peitz, S.; Stoffel, M.; Gulakala, R.; Borse, A.; Wohlleben, M.; Sextro, W.; Raff, M.; Remy, C. D.; Yadav, M.; Stender, M.; Delden, J. van; Lüddecke, T.; Langer, S. C.; Schultz, J.; Blech, C. (2024). The Impact of AI on Engineering Design Procedures for Dynamical Systems. URL: https://arxiv.org/abs/2412.12230, submitted on  20.11.2024 to Technische Mechanik.