Artificial Intelligence #24 Surrogate models – understanding the algorithms behind digital twins

Hello all

Welcome to Artificial Intelligence #24

In the last edition, we discussed why digital twins matter

This was based on our course Digital Twins: Enhancing Model-based Design with AR, VR and MR (Online)

?After that post, one person asked me: Which algorithms do we use to implement digital twins ?

In our course, I refer to an excellent paper called Modelling for Digital Twins—Potential Role of Surrogate Models ?(link and details below) which I am using for this post also. In this post, I will cover the algorithms that are used to implement digital twins. Since I already covered an overview of digital twins in the last edition, I will not discuss the fundamentals again

What problem do digital twins solve?????????

To understand the algorithms behind digital twins, its important to understand the exact problem we are trying to solve via the digital twin. You can use the idea of digital twins to solve many existing problems in AI and Edge such as real time monitoring of complex systems, predictive maintenance etc. But if we consider problems that are uniquely solved using digital twins, then we have to consider the mathematical models underlying digital twins. Digital twins often use mathematical models that contain some unique characteristics. These include

• Models which do not lend themselves to traditional optimization techniques
• Models that need complex simulation of multiple entities that work together to deliver an outcome (a systems-based approach)
• Models that have multiple objectives
• Models that need complex scheduling or planning scenarios.
• Typically, these models need high computation to evaluate unknown model functions in noisy or discontinuous environments.

Here, we discuss one such approach called surrogate modelling.

A?surrogate model?is an engineering method used when an outcome of interest cannot be easily directly measured,?so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (length, curvature, material, ..). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and?what-if?analysis become impossible since they require thousands or even millions of simulation evaluations.(wikipedia)

One way of alleviating this burden is by constructing approximation models, known as?surrogate models,?metamodels?or?emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheap(er) to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), solely the input-output behavior is important. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as?curve fitting.

Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations.

?Essentially, the surrogate model has the following characteristics:

• The model can be extracted from the complex simulators of digital twins
• The model can handle the uncertainty and complex behaviour of the systems,
• The model can be utilised in optimisation and control algorithms.

Surrogate models - Applications in Engineering

Digital twins and the underlying surrogate models apply to a range of engineering problems as shown below including an example and the details of the algorithms used to implement the model (to understand the meaning of the algorithms themselves, you should refer to the paper below)

Direct and Global Optimization

Ex: Optimize operating conditions of a hydrocracking process

• Neural Network?????????
• Polynomial Function?
• Radial Basis Function
• Support Vector Machines,
• Kriging and Neural Network
• Kriging????????????

Multi-objective Optimization

Ex: Multi-objective optimisation of management options for agricultural landscapes

• Support Vector Machine???????
• Polynomial Function?
• Kriging
• Neural Network?????????

Synthesis and Design

Ex: Design of a reusable launch vehicle for multi-mission

• Piecewise Linear Regression?
• Linear Regression and Neural Network
• Polynomial Function?

Scheduling and Planning

Ex: Integrated optimisation of scheduling and dynamic optimisation problems for a sequential batch process

• Piecewise Linear Regression
• Linear Regression
• Neural Network
• Polynomial Function

?Design and Control

Ex: Integration of design and control under uncertainty is developed for multiple

steady-state processes

• Power Series Expansion????????
• Fuzzy Model??
• State Space Model????

These algorithms depend on industry For example, in the chemical industry as below

Source: Modelling for Digital Twins—Potential Role of Surrogate Models ?

Putting surrogate models in context

Surrogate models can be used to implement digital twins but we need to put this in the wider context

As depicted below, there are three main approaches for building digital twins

Source: Modelling for Digital Twins—Potential Role of Surrogate Models

Physics-based modelling is based on observing the behaviour of the physical entity and developing a partial understanding. A model is then developed based on the mathematical equations derived from the observations. This can be costly and also not all phenomenon can be observed (hence modelled). Examples Runge-Kutta solvers for ordinary differential equations, or Finite-Element methods for partial differential equations. Fidelity of the models can be improved with parameter-based estimation from hardware data. The models can also be used to support observers in a system, e.g. Kalman estimators.

?

Data-driven modelling is based on data from the process. The main disadvantages of this approach is the likelihood of uncertainties in the models. Examples include using regressions, look-up tables, or system identification techniques

Hybrid modelling combines physics-based modelling and data-driven modelling

with big data approaches and allows the inclusion of more physics by increasing model

complexity.

This post was based on our course Digital Twins: Enhancing Model-based Design with AR, VR and MR (Online)

?The blog is based on this excellent paper that you can download for free:

Modelling for Digital Twins—Potential Role of Surrogate Models