Related papers: Robustly simulating biochemical reaction kinetics …
Understanding interaction effects among variables is important for regression modeling in various applications. The conventional approach of quantifying interactions as the product of variables often lacks clear interpretability, especially…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…
Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…
While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
Tailoring the performance of next-generation high entropy materials requires a deep understanding of the competition between entropy-driven random solid solution and enthalpy-driven chemical ordering. Investigating such order and disorder…
While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…
Normal molecular dynamics simulations are usually unable to simulate chemical reactions due to the low probability of forming the transition state. Therefore, enhanced sampling methods are implemented to accelerate the occurrence of…
We propose a control variate multilevel Monte Carlo method for the kinetic BGK model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carlo technique with the computation of the optimal control…
In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e.,…
Ab initio quantum chemical methods for accurately computing interactions between molecules have a wide range of applications but are often computationally expensive. Hence, selecting an appropriate method based on accuracy and computational…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address…
We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students…
We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…