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Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in…
We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
In this paper, we apply multi-task Gaussian Process (MT-GP) to show that the adsorption energy of small adsorbates on transition metal surfaces can be modeled to a high level of fidelity using data from multiple sources, taking advantage of…
Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
A mapping of the process on a continuous configuration space to the symbolic representation of the motion on a discrete state space will be combined with an iterative aggregation and disaggregation (IAD) procedure to obtain steady state…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
In molecular dynamics (MD) simulations, accessing transition probabilities between states is crucial for understanding kinetic information, such as reaction paths and rates. However, standard MD simulations are hindered by the capacity to…
Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
Stochastic model-predictive control (SMPC) has evolved to a powerful framework for the control of stochastic dynamical systems. SMPC utilizes a probabilistic uncertainty description to provide a systematic trade-off between the control…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…