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We develop a comprehensive method to construct analytical continuum models for moir\'e systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum…
We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems.…
Simulating large scale lattice dynamics directly is computationally demanding due to the high complexity involved, yet such simulations are crucial for understanding the mechanical and thermal properties of many physical systems. In this…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
The paper contains an application of the generalized lattice model to multicomponent systems with internal degrees of freedom. The short-range inter-atomic repulsions and smooth long-range parts of the inter-atomic potentials are considered…
The phase-transition sequence of a ferroelectric perovskite such as BaTiO_3 can be simulated by computing the statistical mechanics of a first-principles derived effective Hamiltonian [Zhong, Vanderbilt and Rabe, Phys. Rev. Lett. 73, 1861…
We present a modified bond-valence model of PbTiO$_3$ based on the principles of bond-valence and bond-valence vector conservation. The relationship between the bond-valence model and the bond-order potential is derived analytically in the…
Accurate modelling of electrostatic interactions and charge transfer is fundamental to computational chemistry, yet most machine learning interatomic potentials (MLIPs) rely on local atomic descriptors that cannot capture long-range…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…
Large-scale first principles molecular dynamics are crucial for simulating complex processes in chemical, biomedical, and materials sciences. However, the unfavorable time complexity with respect to system sizes leads to prohibitive…
Particle-based modeling of materials at atomic scale plays an important role in the development of new materials and understanding of their properties. The accuracy of particle simulations is determined by interatomic potentials, which…
The study of real time dynamics of nuclear systems is of great importance to provide theoretical predictions of cross sections relevant for both terrestrial experiments as well as applications in astrophysics. First principles simulations…
Symbolic regression identifies key physical parameters describing materials properties by uncovering correlations as nonlinear analytical expressions. However, the pool of expressions grows rapidly with complexity, compromising its…
Accurate models of precipitation kinetics are essential to control and design structural materials. These models are highly sensitive to the thermodynamic description of precipitates. We use atomistic simulations of a model Fe-Cr system to…
We extend our previous first-principles theory for perovskite ferroelectric phase transitions to treat also antiferrodistortive phase transitions. Our approach involves construction of a model Hamiltonian from a Taylor expansion,…
Atomic-scale simulations have progressed tremendously over the past decade, largely due to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the…
In this paper, we study the mechanics of statistically non-uniform two-phase elastic discrete structures. In particular, following the methodology proposed in (Luciano and Willis, Journal of the Mechanics and Physics of Solids 53,…
An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation the flow potential near a small…
We develop a two-dimensional Lattice Boltzmann model for liquid-vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. In order to…