# Mathematical Methods and Tools

Understanding Waves and Making Use of Big Data

Digitalization causes data volumes to grow significantly. Mathematical methods and tools to evaluate them reliably in climate research or when planning future energy systems are developed by scientists of the KIT MathSEE Center (Mathematics in Sciences, Engineering, and Economics). This Center pools interdisciplinary mathematical research at KIT. Researchers work on interdisciplinary research projects in four areas of methods. Mathematical structures: Shapes, geometry, number theory, and algebra. Mathematical modeling: Differential equations, numerics, simulation. Inverse problems: Optimization. And stochastic modeling: Statistical data analysis and forecasting. The MathSEED graduate school offers doctoral and master’s students a comprehensive interdisciplinary training program.

## Research Highlights

Waves are everywhere: Seeing and listening are based on the propagation of light waves or acoustic waves, human heartbeat is driven by depolarization waves, and modern communication technology is largely based on electromagnetic waves. Waves even play a role in weather forecasts when undulatory air movements are captured mathematically in various situations. Propagation of waves can be described mathematically by so-called differential equations relating the value of a function to the variation of this value.

Research is aimed at understanding analytically the propagation of waves under close-to-reality conditions, simulating it numerically, and controlling the waves, i.e. their reflection, refraction, and scattering as well as characteristic wave phenomena, such as standing waves and resonances.

Work of the Center also focuses on data and data analysis from the mathematical perspective. Rapidly growing data volumes open up opportunities to solve problems facing society, science, and industry, including the planning and operation of future energy systems and investigation of renewable energy sources and their fluctuating energy supply. Climate projections are also based on complex simulation models and measurement data of variable quality. Data and analysis are always subject to uncertainties in practice. Appropriate probability theory methods, however, may turn uncertainties into a source of information. Work is aimed at gaining reliable knowledge from data by means of applicable mathematical tools and methods.