On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling

A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full order model. Therefore, a reduced order model (ROM) is generated. Using a hybrid ROM-preconditioned FE solver, additional effective stress-strain data is simulated while the number of samples is kept to a moderate level by using a dedicated and physics-guided sampling technique. Machine learning (ML) is subsequently used to build the second surrogate by means of artificial neural networks (ANN). Different ANN architectures are explored and the features used as inputs of the ANN are fine tuned in order to improve the overall quality of the ML model. Additional ANN surrogates for the stress errors are generated. Therefore, conservative design guidelines for error surrogates are presented by adapting the loss functions of the ANN training in pure regression or pure classification settings. The error surrogates can be used as quality indicators in order to adaptively select the appropriate -- i.e. efficient yet accurate -- surrogate. Two strategies for the on-the-fly switching are investigated and a practicable and robust algorithm is proposed that eliminates relevant technical difficulties attributed to model switching. The provided algorithms and ANN design guidelines can easily be adopted for different problem settings and, thereby, they enable generalization of the used machine learning techniques for a wide range of applications. The resulting hybrid surrogate is employed in challenging multilevel FE simulations for a three-phase composite with pseudo-plastic micro-constituents. Numerical examples highlight the performance of the proposed approach

Remedy for Now but Prohibit for Tomorrow: The Deterrence Effects of Merger Policy Tools

Antitrust policy involves not just the regulation of anti-competitive behavior, but also an important deterrence effect. Neither scholars nor policymakers have fully researched the deterrence effects of merger policy tools, as they have been unable to empirically measure these effects. We consider the ability of different antitrust actions – Prohibitions, Remedies, and Monitorings – to deter firms from engaging in mergers. We employ cross-jurisdiction/pan-time data on merger policy to empirically estimate the impact of antitrust actions on future merger frequencies. We find merger prohibitions to lead to decreased merger notifications in subsequent periods, and remedies to weakly increase future merger notifications: in other words, prohibitions involve a deterrence effect but remedies do not