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
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:
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
Multi-objective Optimization
Ex: Multi-objective optimisation of management options for agricultural landscapes
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Synthesis and Design
Ex: Design of a reusable launch vehicle for multi-mission
Scheduling and Planning
Ex: Integrated optimisation of scheduling and dynamic optimisation problems for a sequential batch process
?Design and Control
Ex: Integration of design and control under uncertainty is developed for multiple
steady-state processes
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.
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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:
Demand Management - Airbus
3 年Dear Ajit Jaokar, Thank for your post, they are always highly instructifs even for someone not expert on the subject. I’m doing my thesis after a master on Supply Chain in order to answer the question what’s the relevance of AI (specially machine learning) as a resilience lever in Supply Chain Risk Management. What kind of algorithms do you think are the most adapted for risk management??Is ML the best way to improve it?
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Head of Apple Product Development & Management @ Boost Mobile | Dish Wireless, an EchoStar company | Fellow RSA | Fellow BCS | IEEE Senior Member
3 年Dear Ajit Jaokar This is an excellent article. I am working on 'Application of Digital Twins in Smart Cities,' Is there any book, paper, or other sources you recommend on this topic. Thank you again for sharing interesting articles.