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Relevancy of Machine Learning to climatic models

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Re-starting a conversation which forked off-topic on the 2016/2017 freezing season thread,1611.msg96388/topicseen.html#msg96388

Let me sum up the question and elements of answers so-far.

Machine Learning has provided spectacular advances some call a paradigm shift in domains as various as image and speech recognition, automatic translation and help to decision to quote a few. Ongoing research is trying to apply Machine Learning approaches to weather forecast and climate models, see e.g.,

Arguments mostly against this approach so far (NeilT, Archimid, epiphyte)

- Not enough quality data to feed the learning, hence Garbage In, Garbage Out most likely.
- We are entering uncharted territories, data we have are irrelevant. The machine would learn about the past only.
- Inscrutability of Machine Learning algorithms, making them difficult to be adopted as scientific method.

The latter point is certainly the most fascinating one. Enthusiastic transhumanists are ready to bleep over that one and trust inscrutable algorithms provided they are efficient. Majority of scientists certainly less so, because science is about understanding how it works, not only making "correct" decisions.

I wrote a small post a while ago which can be relevant although not specific to climate science.

Machine learningas it is practiced so far is used to develop patterns and trends from past data. For example if given celestial mass and trajectory data they can "discover" the laws of gravity.  However they are useless when there multiple physical involved and noisy measurements. They can discover physical correlations but cannot predict the existence of clifs. As such machine learning cannot see the future if data used cannot capture those patterns or behaviors. In a similar situation a genetic algorithm can find the global.optimum in a non-convex multidimensional function, but given a small set of data it cannot see through the cliffs and product the existence of valleys in the function's value. 

Isn't the problem here the limits of models, rather than the deficiencies of algorithms?

Machine learning could produce better algorithms, and thus provide better results, but state change behaviours in complex systems, although deterministic, can be difficult to predict with any accuracy, due to limitations in mathematics.

Without a state change in mathematics itself (and who could predict that?) I don't think we'll ever get to the point of being able to know in advance how a complex system will evolve far from equilibrium at the edge of chaos, or back again.

Murray Gell-Mann famously called such systems "an accumulation of frozen accidents."

Successful climate modeling needs to include a correct interpretation of likely anthropogenic input and correct interpretation of output to consider the role of Lorenz attractors (chaos theory) w.r.t. climate sensitivity.

In this regards, machine learn and AI are just sub-sets of systems theory (see the discuss of complex adaptive systems (CAS) in the first linked Wikipedia article and the associated second attached image).  Furthermore, I note that "systems theory" is synonymous with "cybernetics", and there are many lessons that can be used from such research that can be applied towards the goal of achieving a sustainable global socio-economic system :

Extract: "Cybernetics is the study of the communication and control of regulatory feedback both in living and lifeless systems (organisms, organizations, machines), and in combinations of those. Its focus is how anything (digital, mechanical or biological) controls its behavior, processes information, reacts to information, and changes or can be changed to better accomplish those three primary tasks.

The terms "systems theory" and "cybernetics" have been widely used as synonyms.

Complex adaptive systems (CAS) are special cases of complex systems. They are complex in that they are diverse and composed of multiple, interconnected elements; they are adaptive in that they have the capacity to change and learn from experience. In contrast to control systems in which negative feedback dampens and reverses disequilibria, CAS are often subject to positive feedback, which magnifies and perpetuates changes, converting local irregularities into global features. Another mechanism, Dual-phase evolution arises when connections between elements repeatedly change, shifting the system between phases of variation and selection that reshape the system.

The term complex adaptive system was coined at the interdisciplinary Santa Fe Institute (SFI), by John H. Holland, Murray Gell-Mann and others. An alternative conception of complex adaptive (and learning) systems, methodologically at the interface between natural and social science, has been presented by Kristo Ivanov in terms of hypersystems. This concept intends to offer a theoretical basis for understanding and implementing participation of "users", decisions makers, designers and affected actors, in the development or maintenance of self-learning systems."

Also, I provide the following second link to a Wikipedia article on complex systems research where models of such complex systems uses formulae from chaos theory, statistical physics, information theory and non-linear dynamics.  Per the following extract: "Many real complex systems are, in practice and over long but finite time periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations."  Such insights are useful when considering the transformation of our current BAU based global socio-economic system, into what we will collectively become:

Extract: "Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment.
The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex. The physical manifestations of such systems are difficult to define, so a common choice is to identify "the system" with the mathematical information model rather than referring to the undefined physical subject the model represents.

Complexity and modeling

One of Hayek's main contributions to early complexity theory is his distinction between the human capacity to predict the behaviour of simple systems and its capacity to predict the behaviour of complex systems through modeling. He believed that economics and the sciences of complex phenomena in general, which in his view included biology, psychology, and so on, could not be modeled after the sciences that deal with essentially simple phenomena like physics. Hayek would notably explain that complex phenomena, through modeling, can only allow pattern predictions, compared with the precise predictions that can be made out of non-complex phenomena.

Complexity and chaos theory

Complexity theory is rooted in chaos theory, which in turn has its origins more than a century ago in the work of the French mathematician Henri Poincaré. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order. Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and of the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions about the future of the system, though in practice this is impossible to do with arbitrary accuracy. Ilya Prigogine argued that complexity is non-deterministic, and gives no way whatsoever to precisely predict the future.

The emergence of complexity theory shows a domain between deterministic order and randomness which is complex. This is referred as the "edge of chaos".

When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as within the chaos theory in which it prevails. As stated by Colander, the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.

Therefore, the main difference between chaotic systems and complex systems is their history. Chaotic systems do not rely on their history as complex ones do. Chaotic behaviour pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'. On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist Murray Gell-Mann called "an accumulation of frozen accidents." In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite time periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations."

As a follow-on to my last post on "Systems Theory" and "Complex Systems" modeling, I provide the open access linked reference that uses technology substitution dynamic modeling within an Integrated Assessment Model, IAM, of the electricity sector.  This somewhat limited application of dynamic modeling indicates both the high likelihood that we will exceed the 2C limit this century, and that consideration of regional impacts of climate change is critical when assessing likely damage assessments:

A. M. Foley, P. B. Holden, N. R. Edwards, J.-F. Mercure, P. Salas, H. Pollitt, and U. Chewpreecha (2016), "Climate model emulation in an integrated assessment framework: a case study for mitigation policies in the electricity sector", Earth Syst. Dynam., 7, 119–132, doi:10.5194/esd-7-119-2016

Abstract. We present a carbon-cycle–climate modelling framework using model emulation, designed for integrated assessment modelling, which introduces a new emulator of the carbon cycle (GENIEem).We demonstrate that GENIEem successfully reproduces the CO2 concentrations of the Representative Concentration Pathways when forced with the corresponding CO2 emissions and non-CO2 forcing. To demonstrate its application as part of the integrated assessment framework, we use GENIEem along with an emulator of the climate (PLASIMENTSem) to evaluate global CO2 concentration levels and spatial temperature and precipitation response patterns resulting from CO2 emission scenarios. These scenarios are modelled using a macroeconometric model (E3MG) coupled to a model of technology substitution dynamics (FTT), and represent different emissions reduction policies applied solely in the electricity sector, without mitigation in the rest of the economy. The effect of cascading uncertainty is apparent, but despite uncertainties, it is clear that in all scenarios, global mean temperatures in excess of 2 oC above pre-industrial levels are projected by the end of the century. Our approach also highlights the regional temperature and precipitation patterns associated with the global mean temperature change occurring in these scenarios, enabling more robust impacts modelling and emphasizing the necessity of focusing on spatial patterns in addition to global mean temperature change.

Finally, while "Systems Theory" and "Complex Systems" modeling is only beginning to be applied to climate change modeling, I note that even more dynamic progress is being made in the area of the regulation of DNA gene expression (a complex system critical to life):


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