Research database

Industry 4.0 is the ongoing automation of traditional manufacturing and industrial practices, using modern smart technology. This contemporary industrial revolution asks for new mathematics as a catalyst for ground-breaking ideas. The project "Mathematics for Industry 4.0" (MATH4I4) aims at developing the required innovative mathematical physics methods and theories to solve partial differential models of timely interest related to industrial applications of soft and complex matter at different length-scales. MATH4I4 proposes a ground-breaking scientific approach in applied mathematics pushing innovation in industry 4.0, aiming to deliver: -new theories, methods of nonlinear analysis and of effective computation to explore and to characterize selected classes of partial differential systems; -knowledge of unexplored marginally stable states in nonlinear elasticity, new instabilities in evolutionary nonlinear PDEs, proving rigorous results on their existence, regularity, long-time behaviors; -optimal control of patterning and topological transitions in industrial processes concerning complex materials at different length-scales; -mathematical insights pushing innovative paradigms of material design in digital factories. The high risks are related to the difficulty in fully characterizing the interwoven effects of this unprecedented mix of nonlinearities, non-convexity and nonlocality of such partial differential problems beyond standard physical mathematical theories. The high gain is to provide a fundamental mathematical understanding on selected partial differential systems of timely interest, enabling innovation in engineering. The research is structured into five work packages, each addressing an urgent, unanswered problem concerning a novel application, including morphable devices, 3D and 4D printing, additive manufacturing, micro-swimmers, poroelastic composite materials, liquid crystals, NEMS/MEMS. The work program of MATH4I4 promotes interdisciplinary interactions between these research centers over a wide range of applications and mathematical theories and methods, such as morphoelasticity, phase separation, optimal transport, shape optimization and machine learning. A valuable part of the financial support will be devoted to postdoc positions. The major impact of MATH4I4 consists in delivering the key mathematics for dominating complexity in industry 4.0, in order to push this on-going societal trend by proving the basic science understanding required to enable the next technological progress.