Modeling and Simulation to understand the physical world => Mathematics: from Fundamentals to Applications

Today, the most pressing technological, environmental, and health care problems call for predictive numerical models that can describe systems of increasing complexity and enable real-time simulations. Real-time computations are a prerequisite for controlling and acting on systems. The complexity may arise from the nonlinear coupling of several physical phenomena, interacting on several spatial and time scales, from high-dimensionality and from noisy data sets. The goal of this action is to propose new numerical models and simulation methods for complex physical systems. Four dimensions of complexity are considered:

• Multi-scale, multi-physics modeling

• Uncertainties in modeling

• Numerical methods and High-performance computing

• Optimization and inverse problems