I will provide a brief introduction to molecular dynamics (the computational implementation of the theory of statistical physics) and relate it to Bayesian inference, as these are two situations where sampling a high dimensional probability measure is required. Average properties for these two applications are typically obtained through ergodic averages of discretizations of certain stochastic...
An important aspect in the interpretation of a molecular simulation model is to quantify which parameter uncertainties have the most influence on the simulation results. We present an approach to such Global Sensitivity Analysis (GSA) on basis of the Cramers-von Mises distance. Unlike revalent approaches to GSA it combines the following properties: i) it is equally suited for deterministic as...
Collective variables (CVs) play an important role in understanding the
dynamics of high-dimensional metastable molecular dynamics. Given a set of
CVs, effective dynamics of diffusion processes have been constructed using
conditional expectations and their properties have been studied in previous works. In this talk, we extend the definition of effective dynamics to discrete-in-time Markov...
First, we will briefly introduce the basics of statistical inversion, where, in its most basic form, the goal is to study how to estimate model parameters from data. We will introduce mathematical concepts and computational tools for systematically treating these inverse problems in a Bayesian framework, including assessing how uncertainties affect the solution. In the second part, we will...
Machine learning interatomic potentials (MLIPs) are machine learning (ML) models that map molecular configurations to corresponding energies and potentially forces, replacing highly accurate but expensive quantum chemical calculations. Quantum chemical calculations are carried out to calculate reference energies for only a few molecular configurations. When the ML model predicts an unseen...
The global shift towards carbon-neutral energy systems has heightened the need for efficient and secure storage solutions for renewable energies, with hydrogen (H₂) storage in deep saline aquifers emerging as a viable option for large-scale storage with high flexibility in terms of the number of annual storage cycles and the stored gas volume. This study aims to advance our understanding of...
Surrogate models approximate the action of expensive scientific calculations, saving time, energy and cost. Surrogate model parameters are typically determined by minimising the negative log likelihood, or empirical loss. However, as the loss ignores model misspecification, Bayesian parameter uncertainties are largely epistemic and thus severe underestimates, vanishing in the large-data...
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Parameter dependence is typically explored through repeating simulations with resampled parameters, a forward-only approach that becomes prohibitively expensive for the high parameter dimension of modern machine learning potentials.
In this talk,...
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the experimental or theoretical setup. Uncertainty estimation is essential to quantify this error, and make application of data-centric approaches more...
Predicting reaction barriers for arbitrary atomic configurations based on only a limited set of density functional theory (DFT) calculations would render the simulation of reactions within complex materials highly efficient. We propose Gaussian process regression (GPR) as a method of choice if DFT calculations are limited to hundreds or thousands of barrier calculations. For the case of...
