Strojové učení kontinuální teorie interakce rozhraní
Název práce v češtině: | Strojové učení kontinuální teorie interakce rozhraní |
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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 |
Jazyk práce: | |
Ústav: | Matematický ústav UK (32-MUUK) |
Vedoucí / školitel: | Christoph Allolio, Ph.D. |
Řešitel: |
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. |