Adapted Numerical Methods And Pinns-Based Approaches For Reaction-Diffusion Problems
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Real applications usually lead to mathematical models based on reaction-diffusion Partial Differential Equations (PDEs). Among these, we mention for example: models for the description of the evolution of vegetation in arid environments, such as the African Savannah; models for the description of the corrosive state of materials, useful e.g. for the predictive maintenance of architectural works and more; models relating to the design and production of solar cells for renewable energy. Models of PDEs from applications are generally characterized by high stiffness and a-priori known inherent properties that would be appropriate to preserve when computing a related numerical solution. This forces the usage of specific non-trivial numerical techniques. However, recent developments regard the employment of numerical approaches based on Physics-Informed Neural Networks (PINNs) for solving PDEs, able to integrate the physics of the problem. This talk focuses on appropriately modified (adapted to the problem) finite difference discretizations and PINNs-based approaches for reaction-diffusion PDEs mentioned above.
