Related papers: Model selection focusing on longtime behavior of d…
In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that…
One of the important challenges facing high resolution molecular dynamics calculations is to reproduce biological functions that occur in the macroscopic world and involve macroscopic variables. Some of these functions can be well described…
Discrete Choice Modelling serves as a robust framework for modelling human choice behaviour across various disciplines. Building a choice model is a semi structured research process that involves a combination of a priori assumptions,…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
Online parameter identification is of importance, e.g., for model predictive control. Since the parameters have to be identified simultaneously to the process of the modeled system, dynamical update laws are used for state and parameter…
Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the mechanisms that govern these systems. It is proposed in this…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
Understanding kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to…
Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing…
Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process,…
Mechanistic mathematical models of biological systems usually contain a number of unknown parameters whose values need to be estimated from available experimental data in order for the models to be validated and used to make quantitative…
In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Approximate Bayesian Computation is widely used to infer the parameters of discrete-state continuous-time Markov networks. In this work, we focus on models that are governed by the Chemical Master Equation (the CME). Whilst originally…
Constraining the parameters of physical models with $>5-10$ parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
When mathematical biology models are used to make quantitative predictions for clinical or industrial use, it is important that these predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models…