Pro­fes­sor Sal­im Bouzeb­da has been Direc­tor of the Com­piègne Applied Math­e­mat­ics Lab­o­ra­to­ry (UTC-LMAC) since 2021. He explains how math­e­mat­ics can help find solu­tions to envi­ron­men­tal, eco­nom­ic and social challenges.

More con­crete­ly? “Math­e­mat­ics plays a cru­cial role in under­stand­ing, mod­el­ling, mea­sur­ing and opti­mis­ing com­plex envi­ron­men­tal, eco­nom­ic and social sys­tems. Devel­op­ing and mod­el­ling sim­ple mod­els from com­plex sys­tems is a real chal­lenge”, explains Sal­im Bouzebda.

In par­tic­u­lar, how do you mod­el envi­ron­men­tal sys­tems that are inher­ent­ly com­plex? “We use a num­ber of math­e­mat­i­cal tech­niques, in par­tic­u­lar sim­u­la­tion mod­els that reflect real­i­ty as close­ly as pos­si­ble. These sim­u­la­tion, regres­sion and dif­fer­en­tial equa­tion mod­els have a huge advan­tage over real exper­i­ments in terms of cost”, he explains.

Exam­ples of the appli­ca­tion of these meth­ods? which a large num­ber of uni­ver­si­ties are tack­ling. How can it be cal­cu­lat­ed? We can; to illus­trate, mod­el the green­house gas emis­sions asso­ci­at­ed with agri­cul­tur­al pro­duc­tion, using para­me­ters such as water and ener­gy con­sump­tion and waste pro­duc­tion. This can also be applied to dif­fer­ent modes of trans­port. In this case, we will use data such as the dis­tances trav­elled, the amount of fuel con­sumed and the num­ber of pas­sen­gers car­ried. The aim of math­e­mat­i­cal mod­els is to enable a more detailed analy­sis to be made based on glob­al data. An analy­sis that can be passed on to an ecol­o­gist, for exam­ple, to find an opti­mal solu­tion to a par­tic­u­lar envi­ron­men­tal aspect. In short, these are deci­sion-mak­ing tools”, he stresses.

But when we talk about eco­log­i­cal tran­si­tion, we are also invok­ing invest­ment in the green econ­o­my. “The cost aspect of the tran­si­tion is impor­tant. In this case, the maths can be used to define the opti­mum solu­tion for green invest­ment. In renew­able ener­gies, for exam­ple, math­e­mat­i­cal mod­els seek to com­bine max­i­mum yield and min­i­mum cost. These mod­els also involve analysing the risks, par­tic­u­lar­ly the finan­cial risks, asso­ci­at­ed with these invest­ments”, he concludes.