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Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of…
Identification and verification of molecular properties such as side effects is one of the most important and time-consuming steps in the process of molecule synthesis. For example, failure to identify side effects before submission to…
To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand,…
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…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
How smart can a micron-sized bag of chemicals be? How can an artificial or real cell make inferences about its environment? From which kinds of probability distributions can chemical reaction networks sample? We begin tackling these…
Model reduction methods are relevant when the computation time of a full convection-diffusion-reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we review a model reduction approach based on…
We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…
Molecular circuits capable of autonomous learning could unlock novel applications in fields such as bioengineering and synthetic biology. To this end, existing chemical implementations of neural computing have mainly relied on emulating…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…