Related papers: Efficient implementation of the hybrid method for …
This paper presents a hybrid optimization methodology for parameter estimation of reactive transport systems. Using reduced-order advection-diffusion-reaction (ADR) models, the computational requirements of global optimization with dynamic…
In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities…
An improved version of a recently developed stochastic cluster dynamics (SCD) method {[}Marian, J. and Bulatov, V. V., {\it J. Nucl. Mater.} \textbf{415} (2014) 84-95{]} is introduced as an alternative to rate theory (RT) methods for…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
The presented previously indirect optimization method (IOM) developed within biochemical systems theory (BST) provides a versatile and mathematically tractable optimization strategy for biochemical systems. However, due to the local…
The M{\O}D computational framework implements rule-based generative chemistries as explicit transformations of graphs representing chemical structural formulae. Here, we expand M{\O}D by a stochastic simulation module that simulates the…
This paper considers the problem of real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of hybrid control algorithms is often prohibitive for real-time applications…
Diffusion-based generative processes, formulated as differential equation solving, frequently balance computational speed with sample quality. Our theoretical investigation of ODE- and SDE-based solvers reveals complementary weaknesses: ODE…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process, computational cost can be prohibitive for networks of…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…
Motivated by an ongoing collaboration with clinical oncologists and pathologists, we develop a hybrid partial differential equation--ordinary differential equation (PDE--ODE) framework that captures (i) competition between susceptible and…
Ordinary differential equations (ODE) are widely used for modeling in Systems Biology. As most commonly only some of the kinetic parameters are measurable or precisely known, parameter estimation techniques are applied to parametrize the…
Simulation-based inference (SBI) methods tackle complex scientific models with challenging inverse problems. However, SBI models often face a significant hurdle due to their non-differentiable nature, which hampers the use of gradient-based…
We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…