Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks
This work addresses the challenge of adaptive model identification for complex dynamic systems with variable input lengths, offering incremental improvements over existing data-driven techniques.
The paper tackles the problem of real-time parameter updating in dynamical system identification by proposing an innovative encoding approach using Set Encoding methods like Deep Set and Set Transformer, achieving superior performance compared to the OASIS framework on benchmarks such as Lotka Volterra and Lorenz systems.
The promising outcomes of dynamical system identification techniques, such as SINDy [Brunton et al. 2016], highlight their advantages in providing qualitative interpretability and extrapolation compared to non-interpretable deep neural networks [Rudin 2019]. These techniques suffer from parameter updating in real-time use cases, especially when the system parameters are likely to change during or between processes. Recently, the OASIS [Bhadriraju et al. 2020] framework introduced a data-driven technique to address the limitations of real-time dynamical system parameters updating, yielding interesting results. Nevertheless, we show in this work that superior performance can be achieved using more advanced model architectures. We present an innovative encoding approach, based mainly on the use of Set Encoding methods of sequence data, which give accurate adaptive model identification for complex dynamic systems, with variable input time series length. Two Set Encoding methods are used, the first is Deep Set [Zaheer et al. 2017], and the second is Set Transformer [Lee et al. 2019]. Comparing Set Transformer to OASIS framework on Lotka Volterra for real-time local dynamical system identification and time series forecasting, we find that the Set Transformer architecture is well adapted to learning relationships within data sets. We then compare the two Set Encoding methods based on the Lorenz system for online global dynamical system identification. Finally, we trained a Deep Set model to perform identification and characterization of abnormalities for 1D heat-transfer problem.