Biased sampling algorithms for scientific and engineering applications

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This proposal seeks to extend our recent progress in enhancing the applicability, numerical accuracy and computational efficiency of biased sampling methods. These techniques efficiently determine the likelihood that macroscopic variables, such as the energy or error rate, of a system comprised of many subsystems with randomly fluctuating states adopt rarely occurring but physically significant values. This is achieved numerically by discarding a certain fraction of simulated fluctuations that displace the system away from the low probability region of interest. When the calculation is complete, the actual macroscopic state probabilities are extracted from the biased result. To classify the properties of rare events and further estimate if a given configuration of input variables will produce an unusual system response, we will integrate biased sampling with appropriate machine learning and related methods. While the resulting algorithms will be benchmarked against idealized models of magnetic spin systems, we will simultaneously insure that our research continues to be directly relevant to applied physics and engineering by examining the statistics and behavior of extreme events in fluids, nonlinearity compensation in multichannel coherent optical systems and networks. Explicitly, in solid-state physics we have previously developed a method for investigating critical behavior in the Ising model that combined the Wolff cluster reversal algorithm with a transition matrix reformulation of biased sampling. In future work, we will however replace the Ising-specific Wolff algorithm by an analogous but more general construct containing a significantly smaller number of component variables than the system of interest. This will enable the prediction and classification of phase transitions and extreme statistics over a wide range of complex linear and nonlinear systems and networks. In fluid mechanics, we will apply machine-learning techniques in combination with biased sampling to estimate e.g. the drag coefficient of a perturbed structure without solving the underlying equations of motion. Finally, we will optimize methods for compensating nonlinear effects in multi-wavelength optical communication systems by preprocessing the transmitted or post processing the detected signals according to a prescription determined by a combined biased sampling / machine-learning algorithm. Here we will as well devise novel physical and computational refinements that incorporate qualitative physical models of the nonlinearities.