[14/11/22] Machine learning memory kernels as closure for non-Markovian stochastic processes. From classical mechanics, we know that any function on the microscopic state of a Hamiltonian system evolves according to Liouville's equation. To obtain an evolution law just in terms of observables, i.e. as a closed equation, we need to remove information that is "uninteresting" (unobservable) to us. This can be done systematically via the so-called "projection-operation formalism". Its application gives rise to a formally exact equation of evolution for the observables, known as the "Mori- Zwanzig identity". 

This law of evolution can be cast as a generalized Langevin equation (GLE) with the left-hand-side simply the dynamic variation of the observables, the most general model for the evolution of observables in complex multiscale systems (CMS). But whereas the GLE structure is formally exact, the GLE itself is not particularly useful for applications as the specific analytic expressions of its components, such as the memory kernel, are not known in general. Indeed, its terms still depend on all the microscopic degrees of freedom (DoF) via convoluted integrals with integrands requiring knowledge of the explicit functional dependency of the observables with the DoF. This information is unknown in most cases of practical interest.

Our recently published article in IEEE Transactions on Neural Networks and Learning Systems puts forward a novel approach by which we adopt elements from machine learning, and in particular neural networks, to determine the unknowns in the GLE, thus circumventing its limitations. This results in an efficient and systematic data-driven computational framework that allows us to model CMS. Our framework is exemplified with several prototypical examples, from a single colloidal particle and particle chains immersed in a thermal bath to climatology and finance, showing in all cases excellent agreement with the actual observable dynamics.

 [31/10/22] Prof. Serafim Kalliadasis has won his second ERC Advanced Grant, check out the story here. ERC Advanced Grants are the most prestigious European grants available, judged by a panel of international peers. "ERC Advanced Grants allow exceptional established research leaders in any field of science, engineering and scholarship to pursue frontier research of their choice." Professor Serafim Kalliadasis is one of the few researchers in Europe to win two ERC Advanced Grants. We all know how tough it is to win one of these. To win two is incredible! The latest project aims to better understand complex and many body systems using data-driven techniques and machine learning.

[15/08/22] A positivity-preserving scheme for fluctuating hydrodynamics. We propose a finite-difference hybrid numerical method for the solution of the isothermal fluctuating hydrodynamic equations. The primary focus is to ensure the positivity-preserving property of the numerical scheme, which is critical for its functionality and reliability especially when simulating fluctuating vapour systems. The accuracy and robustness of the proposed scheme is verified against several benchmark theoretical predictions for the statistical properties of density, velocity fluctuations and liquid-vapour interface, including the static structure factor of the density field and the spectrum of the capillary waves excited by thermal fluctuations at interface. Our study has been published in the Journal of Computational Physics.

[16/02/22] A data-driven approach to the inverse problem of classical statistical mechanics. Given the experimental data on the collective motion of a classical many-body system, how does one characterize the free energy landscape of that system? We approached this inverse problem question by combining non-parametric Bayesian inference with physically motivated constraints. Our efforts led to develop an efficient learning algorithm that automates the construction of approximate free-energy functionals. The learning algorithm and our findings have been published in an article in The Journal of Chemical Physics.