Strojové učení kontinuální teorie interakce rozhraní

• Název práce v češtině: Strojové učení kontinuální teorie interakce rozhraní
• Název v anglickém jazyce: Machine Learning a Continuum Theory of Interfacial Interactions
• Klíčová slova: elektrostatika|kontinuální modelování|strojové učení|víceškálové modelování
• Klíčová slova anglicky: electrostatics|machine learning|multiscale modeling|continuum models
• Akademický rok vypsání: 2024/2025
• Typ práce: disertační práce
• Ústav: Matematický ústav UK (32-MUUK)
• Vedoucí / školitel: Christoph Allolio, Ph.D.

Zásady pro vypracování

The applicant will
- derive an extended statistical field theory, incorporating energy terms from machine learning and electrostatics.
- find a saddle point and random phase approximation of the theory
- implement a solver for the theory using,e.g. finite elements.
- perform molecular dynamics simulations of a set of representative biomolecular interfaces
- extract continuum properties, such as charge densities and stress profiles.
- validate the model using this data.

Seznam odborné literatury

[1] Blossey, R.; Podgornik, R. Phys. Rev. Res. 2022, 4, 023033.
[2] Kjellander, R. in Electrostatics of Soft and Disordered Matter 2014, 51. 13754–13769.
[3] Grisafi, A.; Nigam, J.; Ceriotti, M. Chem. Sci. 2021, 12, 2078–2090.
[4] Allolio, C.; Harries, D. ACS Nano 2021, 15,12880–12887.

Předběžná náplň práce

The elementary theory of interfacial interactions is the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Its main component, the Poisson-Boltzmann (PB) equation, is widely used to describe interfacial interactions in presence of electrolytes. However, this traditional mean-field theory does not include molecular structure on any level and is, therefore, unable to compute solvation mediated interactions, such as hydration forces or solvent-mediated aggregation phenomena of membranes and proteins.
The fundamental issue is that the presence of molecular structure contributes ``nonelectrostatic'' short-range forces, which affect permittivity.
In recent years, molecular environment based machine learning has been very successful in the prediction of short-range interactions. Symmetry invariant descriptors, can also be used to explicitly formulate nontrivial model potentials. The so-called SOAP kernel can be as simple as a dot product of SOAP descriptors on atomic centers. The recent LODE generalization to long-range interactions exploits the close similarity to electrostatics showing how a Coulomb-type SOAP-kernel is easily obtained. This suggests, the possibility to create a self-consistent mean field theory of the energy. If a sufficient number of local environments is sampled, the mean-field theory will describe both nonlocal electrostatic interactions and local interactions. The subject of the thesis is develop such a theory and collect the necessary data from atomistic simulations.

Předběžná náplň práce v anglickém jazyce

The elementary theory of interfacial interactions is the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Its main component, the Poisson-Boltzmann (PB) equation, is widely used to describe interfacial interactions in presence of electrolytes. However, this traditional mean-field theory does not include molecular structure on any level and is, therefore, unable to compute solvation mediated interactions, such as hydration forces or solvent-mediated aggregation phenomena of membranes and proteins.
The fundamental issue is that the presence of molecular structure contributes ``nonelectrostatic'' short-range forces, which affect permittivity.
In recent years, molecular environment based machine learning has been very successful in the prediction of short-range interactions. Symmetry invariant descriptors, can also be used to explicitly formulate nontrivial model potentials. The so-called SOAP kernel can be as simple as a dot product of SOAP descriptors on atomic centers. The recent LODE generalization to long-range interactions exploits the close similarity to electrostatics showing how a Coulomb-type SOAP-kernel is easily obtained. This suggests, the possibility to create a self-consistent mean field theory of the energy. If a sufficient number of local environments is sampled, the mean-field theory will describe both nonlocal electrostatic interactions and local interactions. The subject of the thesis is develop such a theory and collect the necessary data from atomistic simulations.