This document discusses different computational methodologies for solving problems, including hard computing and soft computing. Hard computing uses certain methods to solve problems, while soft computing uses approximate methods to find implicit solutions. Artificial intelligence (AI) derivatives are similar to soft computing methods. The document also describes white, black, and grey box models for mathematical modeling, where white box models are based on first principles, black box models explore input-output relationships without structure, and grey box models identify patterns and provide structure. Finally, it mentions AI learning methods and structural optimization techniques for finding optimal designs that meet criteria like strength, stiffness, weight, and cost.

1. Introduction
10/12/2023 4
Computational
Methodologies AI derivatives
The nature of computational methods that can be applied to solve a problem can be generally divided into two groups, often referred to
as Soft Computing and Hard Computing .Hard computing includes methods that integrate a high degree of certainty to solve problems. On
the contrary, soft computing covers approximate methods that can be used to solve problems via implicit/useable yet not exact solutions.
As one can see, there is a common ground between the definition of AI derivatives with of soft computing methods.

2. Introduction
10/12/2023 5
Classification of the modelling
techniques (Adapted from
Giustolisi et al. 2007)
Referring to this figure, white-, black-and grey-box
models are three main categories for mathematical
modelling. If the variables and parameters are known
and the model is based on first principles (e.g. laws of
physics), then it is possible to explain the underlying
physical relationships of the system. Such models are
classified as white-box models. Black-box methods
explore the relationships between the input and output
data without providing a feasible structure of the
model. Conceptual methods that do not only identify
the existing patterns between the data but also provide
a mathematical structure of the model belong to the
grey-box category.
AI derivatives

3. Introduction
10/12/2023 6
AI Learning Methods

4. 10/12/2023 7
Structural optimization is the process of finding the best design for a structure that satisfies
certain criteria, such as strength, stiffness, weight, cost, or aesthetics. It can be applied to
various types of structures, such as buildings, bridges, towers, shells, or trusses.
Optimization !
The three categories of structural optimization: (a) sizing optimization of a truss structure, (b) shape optimization,
and (c) topology optimization; the initial problems (left) and the optimal solutions (right). ( konstantinos et al 2015).