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We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP)-based method to approximate the joint distribution of the unknown parameters and the data, built on recent work (Kandasamy, Schneider, & Póczos, 2015). In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.

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Selective laser melting (SLM), due to its unique additive manufacturing processing philosophy, demonstrates a high potential in producing bulk-form nanocomposites with novel nanostructures and enhanced properties. In this study, the nanoscale TiC particle reinforced AlSi10Mg nanocomposite parts were produced by SLM process. The influence of “laser energy per unit length” (LEPUL) on densification behavior, microstructural evolution, and wear property of SLM-processed nanocomposites was studied. It showed that using an insufficient LEPUL of 250 J/m lowered the SLM densification due to the balling effect and the formation of residual pores. The highest densification level (>98% theoretical density) was achieved for SLM-processed parts processed at the LEPUL of 700 J/m. The TiC reinforcement in SLM-processed parts experienced a structural change from the standard nanoscale particle morphology (the average size 75–92 nm) to the relatively coarsened submicron structure (the mean particle size 161 nm) as the applied LEPUL increased. The nanostructured TiC reinforcement was generally maintained within a wide range of LEPUL from 250 to 700 J/m and the dispersion state of nanoscale TiC reinforcement was homogenized with increasing LEPUL. The sufficiently high densification rate combined with the uniform distribution of nanoscale TiC reinforcement throughout the matrix led to the considerably low coefficient of friction of 0.38 and wear rate of 2.76 × 10−5 mm3 N−1 m−1 for SLM-processed nanocomposites at 700 J/m. Both the insufficient SLM densification response at a relatively low LEPUL of 250 J/m and the disappearance of nanoscale reinforcement at a high LEPUL of 1000 J/m lowered the wear performance of SLM-processed nanocomposite parts.