Physics-based methods have been widely used in industrial applications, where the behavior of a system is derived from the first principles of the underlying physics. As the system becomes more complicated, acquiring an accurate solution, in the engineering sense, to a set of governing equations subjected to the associated boundary conditions gets more challenging and computationally expensive. On the other hand, the behavior of a system can also be determined through sensory observations of the input to and output from the system. Nonetheless, the predictability of the data-driven approximate model heavily depends on the volume and quality of the data based on which the model has been constructed, and the generalizability of the model is limited. A natural way of improving the modeling efficacy and generalizability is to blend physics with data by utilizing the advantages of both, especially when sensors and computational resources are becoming increasingly available and affordable.

The objective of the proposed research topic is to address how to develop and apply hybrid models by blending physics-based methods with data-driven approaches. Physics-based models are built with a set of governing laws and boundary conditions for static or dynamic solid, fluid, or coupled systems. They can be solved analytically or numerically with a finite element method, a boundary element method, a finite volume method, or a meshfree method. A data-driven model can be constructed with artificial intelligence approaches such as regression, neural networks, neural operators, and stochastic inferences. Here, data could result from sensors mounted on physical systems or from numerical simulations thereof. One popular hybrid modeling approach is to model a physical system with governing equations and boundary conditions, represent the solution with a neural network or a neural operator, and learn the solution with available training data by optimizing the weights and biases of the network or operator. Physics could be used to select a network architecture, define a cost function, and initiate the weights and biases.

With the increasing availability and affordability of sensors and computational resources, a new field of hybrid modeling that blends physics-based methods with data-driven approaches is emerging. This special collection focuses on new developments of scientific work on, but not limited to, the following topics:

1. Use of Machine Learning in Applied Mechanics
2. Physics informed neural networks and neural operators
3. Stochastic inference of dynamic states
4. Digital Twin Applications
5. Advanced optimization algorithms for engineering applications

Full-length manuscripts that describe original research on analytical, numerical, and/or experimental work or a review of a special topic pertaining to hybrid modeling are welcome to be submitted.

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Frontiers in Mechanical Engineering

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