Digital Twin

A digital twin is a collection of digital data representing a physical object. The concept of a digital twin is born within engineering disciplines. A digital twin is created to optimize and test designs even before they are manufactured. The relation between the digital twin and the actual one doesn’t end there. Once manufactured, data and measurements are fed back to make the digital model more accurate.

In some cases, digital twins can be used to predict the life, wear and fatigue of an object before it happens in the actual object.

The digital twin is extended outside of an object within the autonomous driving domain. A digital world is created to mimic the physics and randomness to train and improve models that drive autonomously.

As the cost of computation and the necessary hardware required for doing so comes down, there is a possibility that the digital twin of an object could be embedded within the object.

Decomposing a System

Systems can be decomposed in many ways. Depending on various aspects the resulting decomposition can look different. If they are divided in terms of technology, you could end up with different compartments or layers classified by the underlying technology. A system can be broken down by structure or function. Compartmental models are a good example. A system can be broken down based on the domain. That particularly helps when a group of people and roles are required to work around the system. Makes it easier for different groups of people to focus on different areas of the system. Hiring, research, experiments all become more manageable.

Another heuristic way of decomposing a system is by identifying the atomics parts of the system. What I mean by that is these sub-units cannot be broken down any further and the behaviour of these units are fundamentally fixed. Either by definition or by some kind of universal laws. By doing this we can then express the system as a combination of these units.

This opens up to thinking about 2 aspects. How can we put these units together in different ways to reach different outcomes. Secondly, how the inherent behaviour of these atomic units can be changed. Has anything changed (new invention, better technology etc.) that can modify the behavoiur of these atomic units. Sometimes it can be easier to solve the problem on the atomic level rather than on the system level.

Compartmental Models

Compartmental models is a type of mathematical model that tries to simulate events and systems by breaking them into compartments. An example of a compartmental model is the material flow in a production plant. A typical production plant would have stations that are sequentially arranged along which the product is built. Each station would have one or many feeder lines feeding different components and tools. Such a model could then be used to optimize the flow of material and effort along the production line.

A system needs to be broken down into various compartments first. The relations between these compartments have then to be realized. This is the tricky part. A system can be broken down in multiple ways. This has two implications down the line. Different decomposed versions of the same system can expose different parameters of interest. Since these compartments are dependent on each other, the same parameter can have different behaviour on the same system just because it was decomposed and modelled differently.

Compartmental models are used in the field of epidemiology, primarily to simplify the mathematical modelling of infectious disease. A simple model uses “susceptible”, “infectious” and “recovered” as the 3 compartments to label the population and study the behaviour. A more complex version of the model uses an additional compartment “carrier” as well to model the behaviour of a part of the population that are not suffering from symptoms but is a carrier.

Turing Complete

A system of data-manipulation rules is said to be Turing complete if it can be used to simulate any Turing Machine. A Turing Machine is a mathematical model of computation that defines an abstract machine which manipulates data based on a set of rules. The actual machine invented by Alan Turing in 1936 was based on a tape with symbols and a machine that scans it. The machine is also capable for writing symbols. This became an early version of a central processing unit. In simple words, a Turing complete system is one which you can write a program that can find an answer. A Turing Machine can solve any problem that can be coded. Most programming languages are Turing complete. Even software like Microsoft Excel and Powerpoint are Turing complete. A blockchain can be used to solve problems by embedding a scripting language that can utilize the distributed nature of a blockchain.

Monte Carlo Simulations

Monte Carlo simulations are used to determine the probability of an outcome from a model by using random variables. When the model contains a variable that is uncertain, Monte Carlo simulation takes that variable and assigns it a random value. Based on repeated runs of the simulation the end result is than averaged to provide an estimate. In many cases, this has proven to be more accurate than “gut feeling” and other soft methods. Since this model can output different outputs for the same input due to the random variable interference, it is a Stochastic Process. This method works when the model contains many coupled variables. The repeated simulation of the model can uncover patterns with varying inputs for the random variable.

Of course, a model can only predict and account for whatever is built into it. If there are inefficiencies and non-linearities that were approximated to simplify the model, that will be reflected in the outcome as well. Monte Carlo simulations have applications in a wide range of fields including finance, statistical physics, oil exploration etc.

What are Models?

A model is a representation of a real world system. In most cases, they are a simplification of this real world. Models are used extensively within all fields to better understand any system. Ranging from cosmic events to the model of an atom. Models also help us predict the behaviour and manipulate outcomes of systems. There are 2 components to the use of models, one is the academic aspect and the other is the application aspect.

Models can be mathematical. If the behaviour of a system can be represented by a set of parameters and the relation between these parameters can be deduced via experiments, natural observation, logical reasoning etc.
Models can be more abstract than a set of equations. Models can be in the form of data in tables, like financial models in a spreadsheet. A flow chart can be used to represent a process and interaction between stages in a process. Models can be a block diagram that breaks down a system into its constituents and shows the relation and interaction between them. These kind of models are widely used within the realms of systems engineering. Thought processes and intuitive perception can be expressed using mental models. Mental models are just explanations of thought processes.
In a nutshell, models can take a form of numbers, equations, diagrams or text.