Related papers: Augmented Harmonic Linear Discriminant Analysis

This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…

Model precision in a classification task is highly dependent on the feature space that is used to train the model. Moreover, whether the features are sequential or static will dictate which classification method can be applied as most of…

The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…

Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…

Ensemble modeling has been widely used to solve complex problems as it helps to improve overall performance and generalization. In this paper, we propose a novel TemporalAugmenter approach based on ensemble modeling for augmenting the…

Contemporary tasks of complex system simulation are often related to the issue of uncertainty management. It comes from the lack of information or knowledge about the simulated system as well as from restrictions of the model set being…

Identifying a reduced set of collective variables is critical for understanding atomistic simulations and accelerating them through enhanced sampling techniques. Recently, several methods have been proposed to learn these variables directly…

In the absence of impurities and boundary effects, first order phase transitions are initiated by the nucleation of critical bubbles. In thermally driven transitions many systems can remain metastable for an extended time, possibly tens of…

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical…

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…

The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes enhanced sampling methods are used. While many such methods…

Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…

Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that…

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…

In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly-valid asymptotic solutions to autonomous and non-autonomous difference equations in the neighbourhood of a…

Engineers and computational scientists often study the behavior of their simulations by repeated solutions with variations in their parameters, which can be for instance boundary values or initial conditions. Through such simulation…

Many experimentally-accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled…

How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…