Optimizing artificial neural networks for mechanical problems by physics-based Rao-Blackwellization: example of a hyperelastic microsphere model

The Rao-Blackwell scheme provides an algorithm on how to implement sufficient information into statistical models and is adopted here to deterministic material modeling. Even crude initial predictions are improved significantly by Rao-Blackwellization, which is proven by an error inequality. This is first illustrated by an analytical example of hyperelasticity utilizing knowledge on principal stretches. Rao-Blackwellization improves a 1-d uniaxial strain-energy relation into a 3-d relation that resembles the classical micro-sphere approach. The presented scheme is moreover ideal for data-based approaches, because it supplements existing predictions with additional physical information. A second example hence illustrates the application of Rao-Blackwellization to an artificial neural network to improve its prediction on load paths, which were absent in the original training process

Incorporating sufficient physical information into artificial neural networks: a guaranteed improvement via physics-based Rao-Blackwellization

The concept of Rao-Blackwellization is employed to improve predictions of artificial neural networks by physical information. The error norm and the proof of improvement are transferred from the original statistical concept to a deterministic one, using sufficient information on physics-based conditions. The proposed strategy is applied to material modeling and illustrated by examples of the identification of a yield function, elasto-plastic steel simulations, the identification of driving forces for quasi-brittle damage and rubber experiments. Sufficient physical information is employed, e.g., in the form of invariants, parameters of a minimization problem, dimensional analysis, isotropy and differentiability. It is proven how intuitive accretion of information can yield improvement if it is physically sufficient, but also how insufficient or superfluous information can cause impairment. Opportunities for the improvement of artificial neural networks are explored in terms of the training data set, the networks' structure and output filters. Even crude initial predictions are remarkably improved by reducing noise, overfitting and data requirements

Ritz‐type surface homogenization

Surfaces possess mechanical features on smaller scales that stand out against bulk phases, e.g., scaling of stiffness, curvature‐dependence, surfactant control and anchoring‐induced anisotropy. Continuum properties for the respective scales are often derived from ab initio simulations. This scale‐bridging however bears conceptual challenges and we highlight three aspects for the example of pure copper. First, free surface atoms relax and alter the boundary region in terms of interatomistic distances and resulting initital stresses. Second, eliminating the influence of finite thickness on the two‐dimensional continuum surface can be achieved by different averages or limit definitions, not all being physically consistent. Third, the continuum model of the surface is usually coupled to a continuum model of the bulk, which causes an approximation error itself. However, the bulk phase can not be eliminated direclty from the examination and simple averaging may even mask the aforementioned influences on the surface mechanics. A thermodynamically sound parameter identification across the scales is hence required. We present a Ritz‐type modeling approach for surfaces that ensures energy equivalence between atmostic and continuum simulations. The influences of relaxation, finite thickness and bulk approximation are identified by a mismatch in the energy contributions and accounted for by using appropriate homogenization limits

Efficiency review of Austria’s social insurance and healthcare system: volume 1 – international comparisons and policy options

In 2016, the London School of Economics and Political Science (LSE Health) was engaged by the Austrian Ministry of Labour, Social Affairs and Consumer Protection to undertake an efficiency review of the country’s social insurance system (see Appendix A for the original Concept Note). The review was specifically targeted at health competencies within the social insurance system; for this reason, consideration of accident and pension insurance, as well as other forms of care covered by Federal and Länder governments, were only examined where directly applicable