Related papers: Uncertainty Quantification in Classical Molecular …

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of…

In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only…

In a data-scarce field such as healthcare, where models often deliver predictions on patients with rare conditions, the ability to measure the uncertainty of a model's prediction could potentially lead to improved effectiveness of decision…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…

Introduction: Computational modeling has rapidly advanced over the last decades, especially to predict molecular properties for chemistry, material science and drug design. Recently, machine learning techniques have emerged as a powerful…

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

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…

Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex…

An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is…

Along with recent progress in structural biology and genome biology, structural dynamics of molecular systems including nucleic acids has attracted attention in the context of gene regulation. Structure-function relationship is an important…

In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or…

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…

The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…

Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…