26 papers · ranked by Valyu relevance
Yang Liu, Robert J. B. Goudie
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model and prevent feedback from suspect modules, using a cut model. After observing data, this…
Shuze Liu, Shuhang Chen, Shangtong Zhang
Stochastic approximation is a class of algorithms that update a vector iteratively, incrementally, and stochastically, including, e.g., stochastic gradient descent and temporal difference learning. One fundamental challenge in analyzing a stochastic approximation algorithm is to establish its stability, i.e., to show…
Sebastian Allmeier, Nicolas Gast
We study stochastic approximation algorithms with Markovian noise and constant step-size α. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between θn —the value at iteration n— and θ ˚ —the unique equilibrium of the corresponding…
Pier Paolo Poir, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Xiaochi Qian, Zixuan Xie, Xinyu Liu, Shangtong Zhang
Approximation and Reinforcement Learning with Markovian Noise Authors: ['Xiaochi Qian' 'Zixuan Xie' 'Xinyu Liu' 'Shangtong Zhang'] This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms…
Pier Paolo Poier, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Tom Van Wouwe, Lena H. Ting, Friedl De Groote, Adrian M. Haith
Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while…
Ignacio A. Rodriguez-Brenes, Dominik Wodarz, Natalia L. Komarova
Spatial stochastic simulations of evolutionary processes are computationally expensive. Here, based on spatially explicit decoupling approximations (SEDA) introduced in [1], we derive a deterministic approximation to a spatial stochastic birth-death process in the presence of two types: the less advantageous resident…
Faezeh Nassajian Mojarrad
We present a novel solution method for Itˆo stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main properties of the stochastic numerical methods, e.g. convergence, consistency…
Matthew J. Simpson, Ruth E. Baker, Pascal R. Buenzli, Ruanui Nicholson + 1 more
Stochastic individual-based mathematical models are attractive for modelling biological phenomena because they naturally capture the stochasticity and variability that is often evident in biological data. Such models also allow us to track the motion of individuals within the population of interest. Unfortunately…
Lucy Ham, Megan A. Coomer, Michael P. H. Stumpf
Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly…
Masaya Kannari, Riu Naito, Toshihiro Yamada, Sergio Curilef + 1 more
'Francisco Calderón'] The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based…
José Augusto Fontenele Magalhães, Muhammad Fuady Emzir, Francesco Corona
In order to characterise the dynamics of a biochemical system such as the chemostat, we consider a differential description of the evolution of its state under environmental fluctuations. We present solutions to the filtering problem for a chemostat subjected to geometric Brownian motion. Under this modelling…
Davoud Mirzaei
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Yuan Yu, Philip Broadbridge
For a family of stochastic differential equations driven by additive Gaussian noise, we study the asymptotic behaviors of its corresponding Euler-Maruyama scheme by deriving its convergence rate in terms of relative entropy. Our results for the convergence rate in terms of relative entropy complement the conventional…
Alex N Popinga, Jack Forman, Dmitri Svetlov, Huy Vo + 1 more
Biological data is prone to both intrinsic and extrinsic noise and variability between experimental replicas. That same stochasticity and heterogeneity can carry information about underlying biochemical mechanisms but, if not incorporated in modeling and probabilistic inference, can also bias parameter estimates and…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Authors not listed
Molecular Polariton is becoming one of the leading directions to control a multitude of chemical and physical processes, such as charge transfer, selective bond breaking, and excited state dynamics. Accurately and efficiently simulating polariton properties under the collective coupling regimes (between $N$ molecules…
Dylan Morris, John Maclean, Andrew J. Black
Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be accurately approximated by including an additional random time-shift to the…
Riccardo Mannella, Aneta Stefanovska, Philip C.E. Stamp, Mark Dykman + 2 more
The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun scheme is constructed from a low-order integrator. The convergence, stability, and…
Matías Mantiñan, Francisco D. Mazzitelli, Leonardo G. Trombetta, Viktor Dodonov
'Viktor Dodonov'] We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic particle creation with the deterministic…
Akshay Thakur, Souvik Chakraborty
We propose a deep learning-based surrogate model for stochastic simulators. The basic idea is to use generative neural network to approximate the stochastic response. The challenge with such a framework resides in designing the network architecture and selecting loss-function suitable for stochastic response. While we…
Eric Koessler, Arkajit Mandal, Pengfei Huo
We derive the L-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the L-MFE method that satisfies this exact…
Julien Genovese, Francesco Ballarin, Gianluigi Rozza, Claudio Canuto
AbstractIn this manuscript we propose and analyze weighted reduced order methods for stochastic Stokes and Navier-Stokes problems depending on random input data (such as forcing terms, physical or geometrical coefficients, boundary conditions). We will compare weighted methods such as weighted greedy and weighted POD…
Authors not listed
Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to molecular dynamics…
Authors not listed
Optimizing the synthesis conditions of advanced materials is challenging, especially when outcomes are subject to inherent experimental uncertainties. Bayesian optimization is a popular tool for accelerating materials discovery, but its standard risk-neutral framework overlooks the variability of outcomes under…