  The physics-based modeling has been the workhorse for many decades in many
scientific and engineering applications ranging from wind power, weather
forecasting, and aircraft design. Recently, data-driven models are increasingly
becoming popular in many branches of science and engineering due to their
non-intrusive nature and online learning capability. Despite the robust
performance of data-driven models, they are faced with challenges of poor
generalizability and difficulty in interpretation. These challenges have
encouraged the integration of physics-based models with data-driven models,
herein denoted hybrid analysis and modeling (HAM). We propose two different
frameworks under the HAM paradigm for applications relevant to wind energy in
order to bring the physical realism within emerging digital twin technologies.
The physics-guided machine learning (PGML) framework reduces the uncertainty of
neural network predictions by embedding physics-based features from a
simplified model at intermediate layers and its performance is demonstrated for
the aerodynamic force prediction task. Our results show that the proposed PGML
framework achieves approximately 75\% reduction in uncertainty for smaller
angle of attacks. The interface learning (IL) framework illustrates how
different solvers can be coupled to produce a multi-fidelity model and is
successfully applied for the Boussinesq equations that govern a broad class of
transport processes. The IL approach paves the way for seamless integration of
multi-scale, multi-physics and multi-fidelity models (M^3 models).

Computational Physics;Fluid Dynamics