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Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been explored and what has not. In this context, we utilize the geometric learning of explored data space using modern machine learning methods to keep track of already explored regions and samples from the regions that are unexplored. For this purpose, we use a modified version of a robust random-cut forest along with other heuristic-based approaches. We demonstrate our method and its progression in two-dimensional Euclidean space but it can be extended to any dimension since the underlying method is generic.

The precipitation behavior in Nimonic‐263 has been studied using ultrasonic velocity and hardness measurements. The study clearly revealed that ultrasonic velocity measurements are more sensitive to the initiation of the precipitation, whereas the influence of precipitation on hardness can be felt only after the precipitates attain a minimum size to influence the movement of dislocations. These observations are corroborated with the electron microscopy studies. Further, ultrasonic shear wave velocity is found to be more sensitive than longitudinal wave velocity in assessment of precipitation of intermetallic phases. Ultrasonic velocity measurements could also reveal faster kinetics and lesser amount of precipitation at 1073 K as compared to 923 K due to higher solubility of precipitate forming elements at 1073 K.

The cost and marketing of groundwater have been assessed in the Nalanda district, which is one of the most agriculturally advanced districts of the Bihar state. For the study, 60 farmers have been randomly selected from the district. It has been found that small and marginal farms use their tubewells mainly for hiring, whereas, large and medium farms use them mainly for their own purposes during the main crop seasons, i.e. kharif and rabi. The average installation cost on a tubewell has been found highest on large size of holdings (Rs 33,130), followed by medium (Rs 27,240), small (Rs 23,850), and marginal (Rs 19,610) holdings. The capital budgeting techniques, viz. net present value (NPV), benefit-cost ratio (B:C ratio) and internal rate of return (IRR) have been used for evaluating the investment on tubewells. The NPV has been found positive (Rs 1440) and B:C ratio more than one (1.05:1). The IRR has been estimated to be more than the capital cost (10.95%). But, the tubewells have failed to generate income flow equal to the investment by marginal farms. Farm size-wise analysis has revealed that the owner-seller farms category predominates in the water market in the study area. The participation in water market has been found to decline with increase in the size of farms. Financial analysis has revealed that the installation of tubewells is financially viable on large and medium farms but not on small and marginal farms. However, with the development of water market in the area, adoption of modern technologies in crop production and cultivation of cash crops would make the installation of tubewells on marginal and small size of farms financially viable.