The Role of the Mathematical Sciences in Science Based Simulations

The mathematical and computational sciences are increasingly important in scientific and policy decisions on energy, water, health, climate, and the economy. Mathematical models, based on the underlying physical models, can help the scientific and political communities understand and evaluate the potential effectiveness of different approaches in these complex problems.

Today's scientific world is experiencing a paradigm shift where the sophistication of mathematical models, the accuracy and efficiency of numerical algorithms, the robustness of computer software, and the power of computation have become so great that numerical simulations are now considered a third pillar, along with theory and experiment, in the triad of tools used for scientific discovery. The rate of advances in these fields, and our ability to simulate complex physical systems, will increasingly be the limiting factors in our ability to solve many of our most pressing scientific challenges. I will describe recent advances in mathematical models, numerical algorithms, software, and hardware that have allowed computer simulations of complex multidisciplinary problems to have unprecedented impact in guiding scientific discoveries.