DML stands for “Dynamical Machine Learning” (more in the book, “SYSTEMS Analytics for IoT Data Science”, 2017). This match is not surprising once you realize that DML & IoT are both based on the venerable Systems Theory. Let us dig deeper . . .

Consider IoT for industrial applications. A machine is instrumented with sensors, data are collected in real-time (or at intervals), communicated to the cloud where IoT Data Science techniques predict machine condition which results in an action, if necessary, such as repair action on the machine. This is a classic **“closed-loop” system**. The theory that abstracts and governs this closed-loop system is the subject matter of Systems Theory, an undergraduate engineering topic.

Systems Theory is broad and deep – in the past 70 or so years, a great body of work has been developed from deep theory to day-to-day applications such as GPS in your mobile phones, controlling massive chemical plants or Dreamliner airplanes. Systems Theory’s *state-space model based methods allow you to describe, estimate/predict and control all parts of a closed-loop system.*

DML is a topic in “Systems Analytics” (“SYSTEMS Analytics for IoT Data Science”, 2017). A key algorithm to implement DML is called “Rocket” Kalman algorithm developed in the book. As opposed to “static” ML (a more illuminating operational definition is “learn-once-and-use-for-ever” method!), “dynamical” ML permits continuous learning. For long term use of IoT for machinery monitoring and for rapidly changing systems, it is obvious that *dynamic* or *continuous* learning will be much more appropriate and hence more accurate, robust and reliable.

__State-space:__

In general terms, state space is the “space” in which the machine “exists”. Of course, quantitative aspects of the machine alone are captured in this “space”. It could be graphical (state-space trajectories, for example) or a list of the value of the “states” for each time interval.

Closed-loop system’s evolution over time is fully captured in these diagrams. While the visual representation by itself can be revealing (in some cases), we use the “state” equations in which these values are embedded as parameters for quantitative operations such as estimation and prediction. Since data associated with systems such as machine vibration or temperature are generally random, statistical methods are employed to obtain useful predictions such as, “Where is the State trajectory going next?”. *This is the right system-theoretic question to ask of your machine’s future condition!*

Here is a picture of “Rocket” Kalman for DML.

State Space Model:

** s[**n] =

__A__**[n-1] +**

__s__**[n-1]**

__q__y[n] = ** H**[n]

**[n] + r[n]**

__s__** s**[n] in the equations are the “States” that we have been discussing. As you can see, if we knew the States,

**[n], and a few other quantities, we can calculate the output, y[n]. In certain cases, this can be formulated as the ***

__s__**prediction of machine condition*** that we are interested in!

In summary, the “Rocket” Kalman block diagram is a general “**Digital Twin**” of our machine and the values of the States fully quantify a *specific* machine – ‘Digital Twin of Machine serial number: xxx’.

__DML for IoT Machine Learning:__

From the foregoing discussion, you got a glimpse of the basis for the assertion, “DML & IoT are based on Systems Theory”. A less technical discussion follows.

If we took a still picture of an athlete competing in a hurdles race, the picture of the runner will be fuzzy due to her movement. One the other hand, if we had a video camera, we can record the race faithfully. The current “static” machine learning (which I call “Loue” for Learn Once & Use for Ever!) is akin to the still camera picture and DML is like a video!

It is also notable that each video *frame* will have captured the runner in action at a particular instant faithfully (because of the frequent “updates” of the picture) without the fuzziness! This is a window into how to use DML for cases where “static” ML may suffice from an application/business value point of view. Observe that the video frame picture is NOT fuzzy but the still camera picture is; the “clarity” provided by the video frame will give us better results when DML is used for “LOUE” applications instead of Static ML.

*What does this mean in practice?*

In “ML speak”, DML is used for “learning” from the Training Set. *NOTE that DML is the canonical solution for CONTINUOUS machine learning; “Rocket” Kalman is an algorithm to realize DML*. What is learned is the State “evolution” – a “video” of States in the first picture – what we call a “Digital Twin Video”.

For each Feature Vector in the TEST Set, we find the corresponding “video frame” or the “vector of State values” (using some similarity measure) that will provide the best estimate of the ML output. The theory described in my book, “SYSTEMS Analytics for IoT Data Science”, shows that this **output is the OPTIMAL estimate in the Bayesian sense. This is the best we can do!**

*DML is a powerful framework based on Systems Theory which also underpins IoT closed-loop systems. “Rocket” Kalman is just one example of an algorithm, but optimal in the Bayesian sense. “Systems” thinking and new algorithms can be built up on this DML framework for diverse IoT applications.*

*PG Madhavan, Ph.D. – “LEADER . . . of a life in pursuit of excellence . . . in IoT Data Science”*