Mattias Sandberg

Research interests

My research is in numerical analysis. I focus on the mathematical foundations of computational methods: I derive error estimates and convergence rates that explain when and why a method works, and how accurate it is.

A long-standing theme in my work is the numerical analysis of optimal control. I study how to approximate optimally controlled ordinary and partial differential equations, including how to regularize these often ill-posed problems well, how discretization errors affect the computed optimal solutions and their values, and how to design methods with optimal complexity, for example through adaptivity.

I also study molecular dynamics derived from quantum mechanics. I analyze how classical, mean-field and path integral molecular dynamics approximate quantum observables for molecular systems, and I quantify the error these approximations introduce.

Another line of work is the mathematical analysis of machine learning, particularly random Fourier feature neural networks. Topics include adaptive training based on frequency resampling or Metropolis sampling, convergence rates for neural network approximation in molecular dynamics, and generalization error for deep compared to shallow residual networks.

I have also worked on error estimates for finite element methods for PDEs with rough stochastic data.

Other role

I am the director of the master's programme in Applied and Computational Mathematics at KTH.