Free energy computations by minimization of Kullback–Leibler divergence: An efficient adaptive biasing potential method for sparse representations

The present paper proposes an adaptive biasing potential technique for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective of minimizing the Kullback–Leibler divergence between appropriately selected densities. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.     

Multi-output local Gaussian process regression: Applications to uncertainty quantification

We develop an efficient, Bayesian Uncertainty Quantification framework using a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Experimental Design techniques in order to learn a multi-output Gaussian process. The constructed surrogate can provide analytical point estimates, as well as error bars, for the statistics of interest. We numerically demonstrate the effectiveness of the suggested framework in identifying discontinuities, local features and unimportant dimensions in the solution of stochastic differential equations.     

Global sensitivity analysis for the design of nonlinear identification experiments

Nonlinear Dynamics - Bayesian inference techniques have been used extensively in recent years for parameter estimation in nonlinear systems. Despite the many advances made in the field, highly...