Robustness and validity of dynamic global systemic risk models

Description of the project

The question of the limits to growth of our modern societies was first raised on a large scale both in scientific circles and by the general public with the publication of the "Meadows Report" (Limits to Growth, Universe Books, 1972) more than forty years ago. This question concerns in particular the generalized interconnection of all areas of human activity on a global scale. This interconnection has been accelerating since the turn of the 1950s and raises questions about the availability of resources, the increase in diffuse pollution, and more generally the risks associated with this interconnection for modern societies. These questions are the subject of increasing attention in various disciplines, both in the environmental sciences and in the human and social sciences.
In this multidisciplinary landscape, the World3 model, on which Limits to Growth is based, retains particular importance despite the emergence of a few other dynamic global models over time. This importance is linked in particular to the balance it strikes between the sophistication and genericity of modeling choices. In fact, the renewed interest in this model has increased since the turn of the 2000s, particularly following a more objective re-reading of its content by various researchers in the humanities and hard sciences; from this point of view, Turner's study (Global Environmental Change, 2008, 18, 397-411) marked an important turning point in the evaluation of this model.
Nevertheless, and in spite of this recent work, global dynamic models still suffer from a lack of analysis of their reliability and the robustness of their conclusions, both epistemologically and in terms of their mathematisation. This deficit is all the more critical in the light of the interest that they arouse and the sometimes polemical discussions to which they are subjected. This is the case for World3, and the purpose of this thesis is to remedy this state of affairs through a rigorous analysis of the weaknesses and robustness of the model and its qualitative and quantitative conclusions.
In this thesis, we intend to analyze the question of the reliability and robustness of the World3 model along two complementary axes :

1. Qualitative and semi-quantitative study.
   a. First of all, a numerical analysis of the dynamics of the output variables of the model as a function of the dynamics of the input variables (exogenous and endogenous) will be carried out. It will make it possible to qualify the robustness of the model in the presence of uncertainty, and to reduce the uncertainty by classifying the input variables as a function of the uncertainty they inject into the model. To do this, unsupervised classification approaches can be quickly envisaged.
   b. However, it has recently been shown that such an analysis is highly combinatorial (NP-Complete in the general case of probabilistic logic networks 2 ), and classical brute force analysis methods such as Morris or Sobol indices require large computation times and quickly show their limitations. A possible direction of this thesis is to explore the extent to which constraint programming could reduce the computation time of sensitivity indices. This could be done by getting closer to the problem of deterministic optimal control under constraints, and by exploring in particular what necessary and sufficient second order conditions could exist, and allow to strongly reduce the state space to be explored.
   This point will also include a detailed study of the different time scales present in the model, and their endogenous/exogenous character, and the sensitivity of these time scales with respect to the choice of parameters. The objective will be to confront the popularized discourse held on this model with objective elements of analysis, and to estimate the extent to which these discourses are validated or invalidated by this analysis.

2. Quantitative dynamic validation of the different sub-elements of the model.
On this second point, the parameterization of the different scenarios of the model will be more generally evaluated in the light of the most recent information available on the global systems represented, and the different sectors of the model and the feedback loops that link them will be analyzed. The most delicate point is the second one (feedback), since it is linked to modeling choices a priori of the original team. These could be tested by disaggregating the model in a limited way on two levels: on the one hand at the level of finesse of certain sectors, and on the other hand geographically. This work will therefore require modelling work that is indispensable in the realization of the disaggregations. On the other hand, it will not be a question here of reproducing other models developed in the meantime, but on the contrary of studying the influence of these disaggregations on the qualitative and quantitative conclusions of the model. Several avenues are currently being considered for this second axis, including an automated analysis of the topology of the network of variables in the model and the study of the link between distance-to-positive-feedback and the dynamics of the model in phase space.

Finally, the scope of this analysis for other models of the same type can also be examined in the course of the thesis.

Theme

The generalized interconnection of all areas of human activity, on a global scale, has been accelerating since the turn of the 1950s and raises questions of systemic risks for modern societies. These questions are the subject of increasing attention in various academic disciplines, both in environmental sciences and in human and social sciences.
In this multidisciplinary landscape, global dynamic models are of particular importance. Nevertheless, and despite recent work, these models still suffer from a lack of analysis of their reliability and the robustness of their conclusions, both epistemologically and in terms of their mathematisation. This deficit is all the more critical in the light of the interest that they generate and the sometimes polemical discussions to which they are subjected. This is the case for World3, and the purpose of this thesis is to remedy this state of affairs through a rigorous analysis of the weaknesses and robustness of this model and its qualitative and semi-quantitative conclusions.

Background

Since the turn of the 2000s, global systemic models, and in particular the World3 model, have been the subject of more sustained attention from both the general public and the academic community, due to the emergence of environmental issues. In the academic community, the initial (essentially economic) criticism, which was, moreover, scientifically rather unfounded, gave way to a more informed and also more demanding criticism of the validity of this type of modeling, and, on another front, simpler models have emerged on more specific issues.
The questions raised in recent years, particularly in terms of validation and advanced sensitivity analysis (i.e. more complex and complete than those currently available in the literature) are still unanswered.

Method

Concerning the first line of work, it is in particular a question of qualifying the robustness of the model in the presence of uncertainty, by classifying the input variables according to the uncertainty they inject into the model. To do this, unsupervised classification approaches are rapidly being considered; another possible approach is to explore to what extent the
Constraint programming could reduce the calculation time of Sobol-type sensitivity indices.
Several avenues are currently being considered for the second line of work, including an automated analysis of the topology of the network of variables in the model and the study of the link between the distance-to-positive-feedback and the dynamics of the model in the phase space.

Expected results

Ideally, the sensitivity analysis should allow the characterization of the different dynamic regimes of the model. The main question is whether it is possible to identify the links between parameter domains and dominant feedback loops, and to cross-reference these regimes with the knowledge of the realistic ranges of variation of the input parameters. Failing this, it will at least be possible to characterize the limits of validity of different broad categories of scenarios in terms of input parameters.
The second part of the work should refine the understanding of the structure of the feedback loops, and identify more precisely which ones are the most critical with respect to the qualitative conclusions of the different scenarios.

References

• Bardi, U. The Limits to Growth revisited. Springer, 2011.
• Castro, R. Arguments on the imminence of global collapse are premature when based on simulation models. GAiA, 21, 271. 2012
• Meadows, D, Randers, J, Meadows, D. Limits to Growth, the 30-year update. Chelsea Green, 2004.
• Meadows, D, Behrens III, W, Meadows, D, Naill, R, Randers, J, Zahn, E. Dynamics of Growth in a Finite World, Wright-Allen Press, 1974.
• Turner, G. A comparison of The Limits to Growth with 30 years of reality, Global Environmental Change, 18, 397. 2008