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High-dimensional high-frequency time series prediction with a mixed integer optimisation method
No full textWe study a functional autoregressive model for high-frequency time series. We approach the estimation of the proposed model using a Mixed Integer Optimisation method. The proposed model captures serial dependence in the functional time series by including high-dimensional curves. We illustrate our methodology on large-scale natural gas network data. Our model provides more accurate day-ahead hourly out-of-sample forecast of the gas in and out-flows compared to alternative prediction models
Hydrogen diffusion in garnet: insights from atomistic simulations
No full textGarnet has been widely used to decipher the pressure-temperature-time history of rocks, but its physical properties such as elasticity and diffusion are strongly affected by trace amounts of hydrogen. Experimental measurements of H diffusion in garnet are limited to room pressure. We use atomistic simulations to study H diffusion in perfect and defective garnet lattices, focusing on protonation defects at the Si and Mg sites, which are shown to be energetically favored. Transient trapping of H renders ab-initio simulations of H diffusion computationally challenging, which is overcome with machine learning techniques by training a deep neural network that encodes the interatomic potential. Our results from such deep potential molecular dynamics (DeePMD) simulations show high mobility of hydrogen in defect-free garnet lattices, whereas H diffusivity is significantly diminished in defective lattices. Tracer simulations focusing on H alone highlight the vital role of atomic vibrations of heavier atoms like Mg on the release of H atoms. Two regimes of H diffusion are identified: a diffuser-dominated regime at high hydrogen content with low activation energies due to saturation of vacancies by hydrogen, and a vacancy-dominated regime at low hydrogen content with high activation energies due to trapping of H atoms at vacancy sites. These regimes account for experimental observations, such as a H-concentration dependent diffusivity and the discrepancy in activation energy between deprotonation and D-H exchange experiments. This study underpins the crucial role of vacancies in H diffusion and demonstrates the utility of machine-learned interatomic potentials in studying kinetic processes in the Earth's interior
Random walk based snapshot clustering for detecting community dynamics in temporal networks
No full textThe evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper, we introduce a novel random walk based approach that can identify clusters of time-snapshots in which network community structures are stable. This allows to detect significant structural shifts over time, such as the splitting, merging, birth, or death of communities. We also provide a low-dimensional representation of entire snapshots, placing those with similar community structure close to each other in the feature space. To validate our approach, we develop an agent-based algorithm that generates synthetic datasets with the desired characteristic properties, enabling thorough testing and benchmarking. We further demonstrate the effectiveness and broad applicability of our technique by testing it on various social dynamics models and real-world datasets and comparing its performance to several state-of-the-art algorithms. Our findings highlight the strength of our approach to correctly capture and analyze the dynamics of complex systems
Large-scale functional network time series model solved with mathematical programming approach
No full textA functional network autoregressive model is proposed for studying large-scale network time series observed at high temporal resolution. The model incorporates high-dimensional curves to capture both serial and cross-sectional dependence in large-scale network functional time series. Estimation of the model is approached using a Mixed Integer Optimization method. Simulation studies confirm the consistency of parameter and adjacency matrix estimation. The method is applied to data from a real-life natural gas supply network. Compared to alternative prediction models, the proposed model delivers more accurate day-ahead hourly out-of-sample forecasts of the gas inflows and outflows at most gas nodes
Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity
No full textEuclidean diffusion models have achieved remarkable success in generative modeling across diverse domains, and they have been extended to manifold case in recent advances. Instead of explicitly utilizing the structure of special manifolds as studied in previous works, we investigate direct sampling of the Euclidean diffusion models for general manifold-constrained data in this paper. We reveal the multiscale singularity of the score function in the embedded space of manifold, which hinders the accuracy of diffusion-generated samples. We then present an elaborate theoretical analysis of the singularity structure of the score function by separating it along the tangential and normal directions of the manifold. To mitigate the singularity and improve the sampling accuracy, we propose two novel methods: (1) Niso-DM, which introduces non-isotropic noise along the normal direction to reduce scale discrepancies, and (2) Tango-DM, which trains only the tangential component of the score function using a tangential-only loss function. Numerical experiments demonstrate that our methods achieve superior performance on distributions over various manifolds with complex geometries
Generative modeling of conditional probability distributions on the level-sets of collective variables
No full textGiven a probability distribution in represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable , where . We propose a general and efficient learning approach that is able to learn generative models on different level-sets of simultaneously. To improve the learning quality on level-sets in low-probability regions, we also propose a strategy for data enrichment by utilizing data from enhanced sampling techniques. We demonstrate the effectiveness of our proposed learning approach through concrete numerical examples. The proposed approach is potentially useful for the generative modeling of molecular systems in biophysics, for instance
Topological analysis reveals multiple pathways in molecular dynamics
No full textMolecular Dynamics simulations are indispensable tools for comprehending the dynamic behavior of biomolecules, yet extracting meaningful molecular pathways from these simulations remains challenging due to the vast amount of high dimensional data. In this work, we present Molecular Kinetics via Topology (MoKiTo), a novel approach that combines the ISOKANN algorithm to determine the membership function of a molecular system with a topological analysis tool inspired by the Mapper algorithm. Our strategy efficiently identifies and characterizes distinct molecular pathways, enabling the detection and visualization of critical conformational transitions and rare events. This method offers deeper insights into molecular mechanisms, facilitating the design of targeted interventions in drug discovery and protein engineering
