Designing complex behaviour: novel pathways for assisting design based on dynamics-informed machine learning in structural mechanics

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Mechanical systems are central to many areas of pressing societal demand for progress, such as sustainability, decarbonization, transportation, medicine, and many more. The state-of-the-art system design paradigms are mostly based on a number of crucially simplifying and idealizing assumptions on load and system complexity, with nonstationarity forming perturbations to steady-state operations. In fact, static load cases actually occur only rarely in real-life systems: aircraft engines, wind turbines, and vehicle components consistently operate under non-stationary, non-periodic, multi-scale, and in total complex loads. Numerically, time-resolved simulations are prohibitively compute-intensive, and yet not particularly accurate owing to inherent modeling and parameterization inaccuracies. Experimentally, only small data can be acquired from prototypical systems. As a result, design engineers lack a toolset for subjecting early-stage designs to realistic loading scenarios and formalized criteria, and thereby tailoring designs towards the actual operation dynamics. This project aims at developing new machine learning approaches to derive design assistants for the nonlinear dynamical behavior of structures under complex transient loads from small data. To provide the engineer with a formalized objective for designing a structure’s dynamical behavior under hundreds of time-resolved scenarios, novel Dynamics-Informed Reservoir Computers (DIRCs) are proposed. This new systematic design strategy strives at adapting the prediction model structure and complexity to the individual system dynamics, thereby arriving at highly accurate surrogate models with small data requirements and real-time capabilities. Their modularity makes DIRCs are highly flexible and thus easy to integrate into existing toolsets, while having a minimal ecological footprint compared to data-hungry and compute-intense deep learning techniques. This visionary project aims at enhancing simulation-driven design studies in the field of dynamical behavior beyond numerical and experimental state-of-the-art techniques. Novel design assistants are developed by combining nonlinear vibrations, complex network theory, and cutting-edge machine learning approaches. Since dynamics are inherently related to sequential data, a novel class of dynamics-informed machine learning approaches is tailored towards the prediction task. The proposed methods will a) enable early-stage design towards transient and complex loading scenarios under operation with minimal computational cost, b) be flexible and modular for direct interfacing with established numerical and experimental tools, and c) be developed and validated for a series of benchmark cases in mechanical vibrations spanning the horizon of (quasi-) periodic, irregular, transient, multi-scale, and spatio-temporal dynamics both numerically and experimentally.