Computational methods robustness

In any docking scheme, two conflicting requirements must be balanced (i) the desire for a robust and accurate procedure and (ii) reasonable run time of the laboratory workstation for the computational method chosen. 

The use of computational methods for the calculation of molecular properties has been a perennial goal of chemists. In recent years, the field of computational chemistry has become a firmly established discipline. Computational chemists have made impressive contributions to almost every aspect of chemistry, ranging from structural organic and inorganic chemistry to the prediction of polymer properties and the design of medicinally important therapeutic agents. While many computer-based methods are robust and widely utilized, the continued development and refinement of software and the underlying theory remains an active area of research.1,2... 

Step 5 in Table 8-6 involves the computation of the optimum point. Quite a few techniques exist to obtain the optimal solution for a problem. We describe several classes of methods below. In general, the solution of most optimization problems involves the use of a digital computer to obtain numerical answers. Over the past 15 years, substantial progress has been made in developing efficient and robust computational methods for optimization. Much is known about which methods are most successful. Virtually all numerical optimization methods involve iteration, and the effectiveness of a given technique can depend on a good first guess for the values of the variables at the optimal solution. After the optimum is computed, a sensitivity analysis for the objective function value should be performed to determine the effects of errors or uncertainty in the objective function, mathematical model, or other constraints. 

The review is largely of rather traditional techniques — fragment methods and correlation between properties. More modem techniques based on wholly a priori computational approaches have not yet yielded methods that are robust in fact, much published material in this area is singularly unconvincing. Why should that be It is because physiochemical properties involve such matters as solvation and intermolecular forces that computational methods frequently fail the energy differences that need to be understood are small and not easily predicted computationally. 

The R-RMSECV values are rather time consuming because, for every choice of k, they require the whole RPCR procedure to be performed n times. Faster algorithms for cross validation are described [80], They avoid the complete recomputation of resampling methods, such as the MCD, when one observation is removed from the data set. Alternatively, one could also compute a robust R2-value [61], For q= 1 it equals ... 

When investigating mechanistic proposals, one has to perform a large number of calculations to find different transition states and intermediates to test the various scenarios. Consequently, the computational scheme used has to be fast and robust enough to allow this. At the same time, the accuracy of the approximations made in the models has to be higher than or comparable to the accuracy of the underlying computational method. One very fruitful approach has been to cut out a relatively small model of enzyme around the active site and treat it at a quite high level of theory. The effects of the parts of the enzyme that are not included in the quantum model are modeled using different approximations. 

The breadth and depth of the contributions not only demonstrate the crucial role that computational methods play in the study of a wide range of organometallic reactions, but also attest to the robust health of the field that continues to benefit from, as well as inspire, novel experimental studies. 

Beyer, H.G. Sendhoff, B. 2007. Robust Optimization. A comprehensive survey. Computer Methods in Applied Mechanics and Engineering doi 10.1016/j.cma.2007.03.003. 

Doltsinis, I., Kang, A. Cheng, G. 2005. Robust design of non-linear structures using optimization methods. Computer Methods in Applied Mechanics and Engineering 194, 1779-1795. 

Doltsinis, L, Kang, Z. Robust design of structures using optimization methods. Comput Methods Appl Mech Eng 2004 193 2221-2237. 

Membrane filtration is an important technology for ensuring the purity, safety and/or efiticiency of the treatment of water or effluents. In this study, various types of membranes are reviewed, first. After that, the states of the computational methods are applied to membranes processes. Many studies have foeused on the best ways of using a particular membrane process. But, the design of new membrane systems requires a considerable amoimt of proeess development as well as robust methods. Monte Carlo and molecular dynamics methods ean specially provide a lot of interesting information for the development of polymer/carbon nanotube membrane processes. 

So far we have performed detailed studies for flow over isolated bodies, for example, curved fractures, shale arrays, and fractured boreholes. Here we will focus on steady and transient-compressible reservoir-scale flows produced by multilateral well systems. Because their topologies are not simple, we turn to computational methods. We will highlight problems that arise in reservoir simulator development, and importantly, we will describe a recently developed, three-dimensional algorithm that is very robust, numerically stable, exceptionally fast, and extremely accurate, and now available to the user community. Engineering implementation is an objective of the work oil companies want practical solutions that optimize operations, profits, and time value of money. The model provides tools that evaluate what if production scenarios, infill drilling strategies, and waterflood sweep efficiencies. In addition to being accurate, the solutions require minimal hardware, software, and costly human resources. 

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