Commit a040d4b1 by Tim Keil

### [docs/tutorials] last comments from stephan

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 ... ... @@ -183,7 +183,7 @@ to resolve the data structure in the diffusion. This suggests to use an even finer mesh. However, for enabling a faster runtime for this tutorial, we stick with this mesh and remark that refining the mesh does not change the interpretation of the methods that are discussed below. It rather furhter improves the speedups achieved by model reduction. It rather further improves the speedups achieved by model reduction. Before we discuss the first optimization method, we define helpful functions for visualizations. ... ... @@ -360,7 +360,7 @@ a perfect surrogate model in the sense that a low error tolerance for the :func:~pymor.algorithms.greedy.rb_greedy already suffices to converge to the same minimum. In our case we choose atol=1e-2 and yield a very low dimensional space. In general, however, it is not a priorily clear how to choose atol In general, however, it is not a priori clear how to choose atol in order to arrive at a minimum which is close enough to the true optimum. ... ... @@ -484,7 +484,7 @@ equation, i.e. .. math:: r_\mu^{\text{pr}(u)[v] := l_\mu(v) - a_\mu(u, v) &&\text{for all }v \in V r_\mu^{\text{pr}}(u)[v] := l_\mu(v) - a_\mu(u, v) &&\text{for all }v \in V A major issue of this approach is that the computation of the full gradient requires :math:P solutions of :math:\eqref{sens}. ... ... @@ -603,7 +603,7 @@ output functional. report(opt_rom_result, opt_rom_minimization_data, reference_mu) The online phase is even slightly faster than before but the offline phase is obviously still the same as before. We also conclude that the phase is still the same as before. We also conclude that the ROM model eventually gives less speedup by using a better optimization method for the FOM and ROM. ... ... @@ -697,8 +697,9 @@ for the gradients since we compute the dual solutions with the ROM. Adaptively enriching along the path ----------------------------------- This gives rise to another idea where we only enrich if it is necessary. For example it could be the case that the model is already good at In order to further speedup the above algorithm, we enhance it by only adaptive enrichments of the model. For instance it may happen that the model is already good at the next iteration, which we can easily check by evaluating the standard error estimator which is also used in the greedy algorithm. In the next example we will implement this adaptive way of enriching and set a ... ... @@ -821,21 +822,17 @@ the traditional offline/online splitting by only enriching the model along the path of optimization or (even better) only enrich the model if the standard error estimator goes above a certain tolerance. A main drawback of the content in this tutorial was that the choice of the tolerance atol that has been used to build the RB spaces cannot be known a priorily. This shows the need for certified and robust reduced methods. For some standard literature for faster and robust optimization tools we refer to CGT00 __ and In this tutorial we have only covered a few basic approaches to combine model reduction with optimization. For faster and more robust optimization algorithms we refer to the textbooks CGT00 __ and NW06 __. For recent research on using trust-region methods for MOR of PDE-constrained optimization problems, we refer to For recent research on combining trust-region methods with model reduction for PDE-constrained optimization problems we refer to YM13 __, QGVW17 __ and KMSOV __ where for the latter, pyMOR has been used for the numerical experiments. KMSOV20 __ where for the latter a pyMOR implementation is available as supplementary material. Download the code: :jupyter-download:script:tutorial_optimization ... ...
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