[01/04/24] Forecasting with an N-dimensional Langevin equation and a neural-ordinary differential equation. Accurate prediction of electricity day-ahead prices is essential in competitive electricity markets. Although stationary electricity-price forecasting techniques have received considerable attention, research on non-stationary methods is comparatively scarce, despite the common prevalence of non-stationary features in electricity markets. Specifically, existing non-stationary techniques will often aim to address individual non-stationary features in isolation, leaving aside the exploration of concurrent multiple non-stationary effects. Our overarching objective here is the formulation of a framework to systematically model and forecast non-stationary electricity-price time series, encompassing the broader scope of non-stationary behavior. For this purpose, we develop a data-driven model that combines an N-dimensional Langevin equation (LE) with a neural-ordinary differential equation (NODE). The LE captures fine-grained details of the electricity-price behavior in stationary regimes but is inadequate for non-stationary conditions. To overcome this inherent limitation, we adopt a NODE approach to learn, and at the same time predict, the difference between the actual electricity-price time series and the simulated price trajectories generated by the LE. By learning this difference, the NODE reconstructs the non-stationary components of the time series that the LE is not able to capture. We exemplify the effectiveness of our framework using the Spanish electricity day-ahead market as a prototypical case study. Our findings reveal that the NODE nicely complements the LE, providing a comprehensive strategy to tackle both stationary and non-stationary electricity-price behavior. The framework’s dependability and robustness is demonstrated through different non-stationary scenarios by comparing it against a range of basic naïve methods.

Our study has been published in Chaos journal, focus issue on Data-Driven Models and Analysis of Complex Systems.


[20/03/24] We are excited to announce that Dr. Dimitrios Gourzoulidis has joined us from École Polytechnique Fédérale de Lausanne in Switzerland to work as Postdoctoral Research Associate in Machine Learning of Nonequilibrium Processes. The position is part of the ERC Advanced Grand/UKRI Frontier Research “Machine-Aided General Framework for Fluctuating Dynamic Density Functional Theory (MAGFFDDFT)”.

Dimitrios' research background and expertise are in the areas of applied and computational mathematics, numerical analysis and scientific computing.

Dimitrios, welcome to Imperial and to our group.


[08/03/24] Dr. Peter Yatsyshin and Mr. Antonio Malpica-Morales, gave contributed talks at the APS March Meeting, Minneapolis, Minnesota, March 3-8, 2024. Their talks were entitled,

"Data-driven solution of the inverse problem in classical statistical mechanics"

and

"A data-driven framework for non-stationary complex systems: Blending generalized Langevin and neural ordinary differential equations",

respectively.


[21/02/24] Prof. Serafim Kalliadasis gave an invited talk entitled "Classical density-functional theory: from formulation to nanofluidics to machine learning" at the newly established annual Solid Mechanics and Mathematics Seminar Series, University of Oxford.  This was the 2024--inaugural talk of the Seminar Series.

https://www.maths.ox.ac.uk/node/66070


[16/02/24] A falling fluid droplet in an oscillating flow field. We examine the flow in and around a falling fluid droplet in a vertically oscillating flow. We assume axisymmetric Stokes flow, and for small deformations to the droplet, the governing equations can be linearized leading to an infinite system of linear ordinary differential equations. In this study, we have analytically solved the problem in the small-capillary limit. We note that the solution locally breaks down at the poles of the droplet. The drag and center of the mass were also obtained. In the case when only odd modes are present, the droplet shows three-dimensional axisymmetric heart-shaped solutions oscillating vertically in time. When only even modes are present, the droplet exhibits axisymmetric stretching and squeezing.

Our study has been published in Physics of Fluids journal.