ECCOMAS 2024

Operator learning for systems with partially hidden physics

  • Kag, Vijay (Bosch Reaearch and Technology Center India)
  • Pal, Birupaksha (Bosch Reaearch and Technology Center India)
  • Goswami, Somdatta (Brown University)

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In the modern software driven world where virtualization holds the key, system modelling lies at the heart of most modern engineering and scientific research. Typically, one approaches modelling using the available physical knowledge of the system. Use of the first principles greatly aid in providing deep insights into the system and in model interpretability. But oftentimes either it's impossible to consider all the complex physics involved or simpler models are considered to keep within the limits of the available resources. This renders the considered model incomplete or deficient. For such scenarios if one would go for a pure ML model built only using measurement data then the valuable available physical information of the system would remain unutilized. This in turn influences the generalizability and interpretability of the model. Recent advances in SciML like the deep hidden physics models can address this space of deficient equations by combining the available physics and data. First introduced as a neural network based method, the core idea has been extended using Gaussian processes as well as sparse and symbolic regression. Further, as it might not always be possible to train the model for all possible inputs or loads, model generalizability poses an important challenge which has direct consequence in model deployment. Operator learning methods like DeepONets holds an answer for this, where the focus is on learning the system as an operator or functions of the inputs, so that once trained, the model is able to react adequately for a change in inputs. In this work we present a novel idea on how to use a DeepONet framework of operator learning with hidden physics to achieve input generalization for system models where the full governing equations are not known.