After numerical experiments with the implementations in #60 and #103, which requires tuning of the method parameters that might be case-dependent, we are motivated to find a way to learn the adaptivity parameters or the parameters in these methods on the fly with sequential optimization approaches.
Speaking of the adaptivity parameters, we would want to find the optimal coarsening_const $C_c$ - refining_const $r_c$-historical_parameter $h$ to minimize the runtime under simulation error constraints. According to Felix, it would benefit the prediction a lot if we have a priori knowledge(global model) about the relationship between error/runtime and the three parameters. And this knowledge also gives info on if we need to scale the parameters or the runtime/error, which might range across multiple orders, to a logarithmic space.
For the optimization we could start with classic Gaussian process. For the global model we could use paper data and do experiments with heat-conduction tutorial.
After numerical experiments with the implementations in #60 and #103, which requires tuning of the method parameters that might be case-dependent, we are motivated to find a way to learn the adaptivity parameters or the parameters in these methods on the fly with sequential optimization approaches.
Speaking of the adaptivity parameters, we would want to find the optimal
coarsening_const$C_c$ -refining_const$r_c$-historical_parameter$h$ to minimize the runtime under simulation error constraints. According to Felix, it would benefit the prediction a lot if we have a priori knowledge(global model) about the relationship between error/runtime and the three parameters. And this knowledge also gives info on if we need to scale the parameters or the runtime/error, which might range across multiple orders, to a logarithmic space.For the optimization we could start with classic Gaussian process. For the global model we could use paper data and do experiments with heat-conduction tutorial.