Related papers: A low-rank complexity reduction algorithm for the …

There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…

In this paper we present a new method for deriving It\^{o} stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME,…

Stochastic Computing (SC) is a computing paradigm that allows for the low-cost and low-power computation of various arithmetic operations using stochastic bit streams and digital logic. In contrast to conventional representation schemes…

We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large…

Stochastic models for chemical reaction networks have become very popular in recent years. For such models, the estimation of parameter sensitivities is an important and challenging problem. Sensitivity values help in analyzing the network,…

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…

While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current KMC algorithms. The origins of…

In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stochastic differential equations (SDEs) coming from classical…

Motivation: Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

The chemical master equation (CME) is a fundamental description of interacting molecules commonly used to model chemical kinetics and noisy gene regulatory networks. Exact time-dependent solutions of the CME -- which typically consists of…

With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…

Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…

Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme…

We introduce a mini-batch stochastic variance-reduced algorithm to solve finite-sum scale invariant problems which cover several examples in machine learning and statistics such as principal component analysis (PCA) and estimation of…

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…

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…

Simulating chemical systems is highly sought after and computationally challenging, as the number of degrees of freedom increases exponentially with the size of the system. Quantum computers have been proposed as a computational means to…

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information spreading. While devising stochastic models of such processes is relatively easy, analyzing them is very…

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…