Stellarator Optimization
Stellarators are a class of devices to generate fusion energy. The standard optimization of stellarator design includes two steps: first, one aims to find the optimal plasma shape w.r.t. physical performance criteria; in the second step one tries to find a coil configuration that reproduces the desired target magnetic field confining the plasma. Two projects I am currently working on (besides others) are model reduction methods for turbulent transport (related to the first optimization step) and the design of robust coil configurations (related to the second optimization step).
Model Reduction Methods for Turbulent Transport
Turbulent transport is a crucial mechanism behind energy loss in fusion plasmas. Unfortunately, turbulent transport models via the electro-magnetic Vlasov-Maxwell equations require fine discretizations leading to high-dimensional models, thus taking long computing times. Therefore, optimization routines for the design of fusion devices usually rely on less expensive proxies for turbulent transport. We need to build a reduced model to accurately compute turbulent transport fast enough to use the computation in an optimization loop. Even more importantly, this reduced model should share the same physical structure/conservations laws; otherwise, the reduced model could be unphysical and yield poor approximation quality. To this end, we work on preliminary steps towards model reduction methods for transport equations (like Vlasov-Maxwell) that preserve the Hamiltonian structure of the underlying equations and assess and control the error in the reduced model (w.r.t. the high-dimensional model) via an error estimator.
Efficient Stochastic Optimization of Stellarator Coil Configurations
Construction and placement of the coils of a stellarator are difficult tasks since minor errors in the fabrication or alignment can lead to major modifications of the magnetic field. To this end, we consider the efficient stochastic optimization of stellarator coil configurations in high dimensions. Our goal is to increase coil construction tolerances without compromising the performance of the magnetic field. We employ surrogate optimization to drastically lower the number of function evaluations needed to arrive at a risk minimum. In particular, we design a two-step method. First, we perform an approximate global search to find feasible regions via a sample efficient risk-neutral trust-region Bayesian optimization. We conduct a local risk-neutral optimization using these feasible regions previously discovered to arrive at a well-refined minimum in the second step.