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A temperature (T)-dependent coarse-grained (CG) Hamiltonian of polyethylene glycol/oxide (PEG/PEO) in aqueous solution is reported to be used in implicit-solvent material models in a wide temperature (i.e., solvent quality) range. The…
We extend classical coarse-grained entropy, commonly used in many branches of physics, to the quantum realm. We find two coarse-grainings, one using measurements of local particle numbers and then total energy, and the second using local…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
This paper investigates the uncertainty of Generative Pre-trained Transformer (GPT) models in extracting mathematical equations from images of varying resolutions and converting them into LaTeX code. We employ concepts of entropy and mutual…
Brute-force simulations for dynamics on very large networks are quite expensive. While phenomenological treatments may capture some macroscopic properties, they often ignore important microscopic details. Fortunately, one may be only…
In this paper we analyze a PDE system modelling (non-isothermal) phase transitions and damage phenomena in thermoviscoelastic materials. The model is thermodynamically consistent: in particular, no {\em small perturbation assumption} is…
Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
Based on the earlier obtained equations of state for the ternary systems H2O-CO2-CaCl2 and H2O-CO2-NaCl, an equation of state for the four-component fluid system H2O-CO2-NaCl-CaCl2 is derived in terms of the Gibbs excess free energy. A…
This paper addresses the design of linear and nonlinear stabilization procedures for high-order continuous Galerkin (CG) finite element discretizations of scalar conservation laws. We prove that the standard CG method is entropy…
Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it…
A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different…
The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
In this work we describe a set of Coarse-grained (CG) tools that allow to simulate the uptake of the nanoparticles (NPs) coated with proteins by a lipid bilayer. We describe a CG model to calculate the adsorption energies and the most…
This work introduces a stochastic hierarchical optimization framework inspired by Sloppy Model theory for the efficient calibration of physical models. Central to this method is the use of a reduced Hessian approximation, which identifies…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
This thesis investigates the interactions of different degrees of freedom of one joint system within the theory of stochastic thermodynamics. First, a comprehensive introduction to the subjects of stochastic processes, information theory…
Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…
In this work, we present a high-fidelity and efficient point-particle direct numerical simulation framework based on a multi-block overset curvilinear grid system, enabling large-scale Lagrangian particle tracking in complex geometries with…