ECCOMAS 2024

Attention is all you need - an interpretable artificial neural network architecture

  • Novelli, Nico (Polytechnic University of Marche, Ancona, Ita)
  • Belardinelli, Pierpaolo (Polytechnic University of Marche, Ancona, Ita)
  • Lenci, Stefano (Polytechnic University of Marche, Ancona, Ita)
  • Hellmann, Frank (Potsdam Institute for Climate Impact Research)

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This paper presents an innovative data-driven model order reduction approach for complex dynamical system through a piecewise artificial neural network architecture, which incorporates a state space-based attention mechanism, designed to enhance both predictive performance and interpretability. The proposed framework combines multiple sub-networks, each characterized by distinct architecture (hyper-parameters), to capture diverse patterns and features within the data. The attention mechanism at the culmination of the architecture further enriches the model’s interpretability by dynamically indicating which sub-network is most representative for a given input, offering an insightful decomposition of the system’s phase space. Our framework can be seen as a generalization of the concepts presented by Rewienski et al. [1], evolving the idea to encompass a broader range of models and complex scenarios. The novelty of our approach lies in its ability to learn directly from data both the model order reduction and the phase space partition, rather than relying only on physics knowledge. To demonstrate the efficacy and interpretive capabilities of our framework, we apply it to a network system of 20 Kuramoto oscillators. The results showcase not only good performance in terms of efficiency but also an enhanced ability to glean meaningful insights from the model’s predictions. This balance of high performance and interpretability positions our piecewise approach as a promising tool for applications where understanding the “why” behind predictions is as crucial as the predictions themselves.