[24/11/23] Research Highlight -- Thomas Young Centre. Our recent work on density-functional theory and machine learning:
- Physics-informed Bayesian inference of external potentials in classical density-functional theory.
- Physics-constrained Bayesian inference of state functions in classical density-functional theory.
featured as a Research Highlight on the website of the Thomas Young Centre -- The London Centre for the Theory & Simulation of Materials & Molecules
and was included in the Thomas Young Centre News and Updates.
[22/09/23] Data-driven modelling and prediction of complex systems.
From the departmental research project poster presentation on Friday September 22. Our MSc student Tushar Verma presented a poster for his project "Data-driven modelling and prediction of complex systems by neural ODEs." From left to right: Antonio Malpica-Morales, Serafim Kalliadasis, Tushar Verma.
[13/09/23] Physics-informed Bayesian inference of external potentials in classical density-functional theory. The swift progression and expansion of machine learning (ML) have not gone unnoticed within the realm of statistical mechanics. In particular, ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable automatic discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within classical DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a classical many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external-potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional classical particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to characterize the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption, wetting, and capillarity, to name a few.
Our study has been published in The Journal of Chemical Physics, special issue on Chemical Physics of Controlled Wettability and Super Surfaces.
This work featured as Research Highlight on the website of the Thomas Young Centre -- The London Centre for the Theory & Simulation of Materials & Molecules, and was included in the Thomas Young Centre News and Updates.
[08/07/23] The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics. We study a prototypical example in nonlinear dynamics where transition to self-similarity in a singular limit is fundamentally changed as a parameter is varied. Here, we focus on the complicated dynamics that occur in a generalised unstable thin-film equation that yields finite-time rupture. A parameter, n, is introduced to model more general disjoining pressures. For the standard case of van der Waals intermolecular forces, n = 3, it was previously established that a countably infinite number of self-similar solutions exist leading to rupture. Each solution can be indexed by a parameter, ϵ = ϵ1 < ϵ2 < . . . < 0, and the prediction of the discrete set of solutions requires examination of terms beyond-all-orders in ϵ. However, recent numerical results have demonstrated the surprising complexity that exists for general values of n. In particular, the bifurcation structure of self-similar solutions now exhibits branch merging as n is varied. In this work, we shall present key ideas of how branch merging can be interpreted via exponential asymptotics.
Our study has been published in the Physica D: Nonlinear Phenomena journal, special issue on Applied and Computational Complex Analysis in the Study of Nonlinear Phenomena.
[04/07/23] Prof. Serafim Kalliadasis together with Prof. Pierre Degond from Institut de Mathématiques de Toulouse, CNRS & Université Paul Sabatier, Toulouse, France and Prof. Grigorios Pavliotis from the Department of Mathematics, Imperial College London, UK co-organised the CNRS-ICL workshop "Mean field limits for interacting particle systems: uniform propagation of chaos, phase transitions and applications" July 4, 2023 - July 6, 2023. Details are given here.
[23/06/23] Antonio Malpica-Morales gave a talk and presented a poster about our latest research work on "Physics-informed Bayesian inference of external potentials in classical density-functional theory" at the Imperial President's PhD Scholars Research Symposium 2023. You can check the details of this research work in the Projects section.
[10/03/23] Prof. Serafim Kalliadasis together with Jim Lutsko from Université Libre de Bruxelles and Erik Santiso from North Carolina State University co-organised the CECAM flagship workshop "Metastability and multiscale effects in interfacial phenomena" March 13, 2023 - March 15, 2023. Details are given here.
[07/02/23] Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation. We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of free-energy potentials, including Ginzburg-Landau and Flory-Huggins, to general wetting boundary conditions, and to degenerate mobilities. Its central thrust is the upwind methodology, which we combine with a semi-implicit formulation for the free-energy terms based on the classical convex-splitting approach. The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature, which allows to efficiently solve higher-dimensional problems with a simple parallelization. The numerical schemes are validated and tested through a variety of examples, in different dimensions, and with various contact angles between droplets and substrates.