The phrase "are approximated based on" is correct and usable in written English.
It can be used when discussing how certain values or results are estimated or calculated using specific criteria or data.
Example: "The results of the experiment are approximated based on the initial measurements taken during the trial."
Alternatives: "are estimated using" or "are calculated from".
To this end, several unknown functions are approximated based on the neural approximation, a novel recursive design method is used to remove the interconnection term, and Barrier Lyapunov function is introduced to avoid the violation of the output constraints.
The governing equations are approximated based on the first-order shear deformation shell theory (FSDT) and non-uniform rational B-Spline (NURBS) basis functions.
The activation stresses, 15 and 6 MPa, respectively, for the {10¯12}⟨10¯11⟩ extension twinning and detwinning, are approximated, based on the relaxation of the internal stresses in the matrix and twin grains.
Emphasis is put on the system being divisible into components, as this underlying assumption motivates the algorithm in its entirety in that rather simple relations between the system components are modeled as explicit structural constraints, while the significantly more complex relations within each component are approximated based on the underlying simulator data.
Therefore, (varvec{Gamma }^{(1)}) and (varvec{Gamma }^{(2)}), which are approximated based on Swarm Alpha and Charlie data, carry similar information content (regarding the estimation of the model parameters) to the (ideal) radial gradient ((varvec{Gamma }^{(0)})), which is not possible to be measured or estimated directly from the Swarm configuration.
Days After Flowering (DAF) are approximated based on pod length and seed size.
In this work, we extend our previous esophageal transport model using an immersed boundary (IB) method with discrete fiber-based structural model, to one using a continuum mechanics-based model that is approximated based on finite elements (IB-FE).
The scene at the Save the Children office in Sikasso was approximated, based on information told to the writer by the psychologist working there at the time about how such interviews often took place.
The inverse of the process transfer function matrix in the direct synthesis method is approximated based on the relative gain array concept.
The discussions are organized as follows: First, the governing concept that the elastic nonlinear behavior can be approximated based on an analogy to the axial-bending coupling of an Euler column, is presented.
