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Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…
This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order. We propose to truncate and properly dither the data prior…
We describe an energy-enstrophy conserving discretisation for the rotating shallow water equations with slip boundary conditions. This relaxes the assumption of boundary-free domains (periodic solutions or the surface of a sphere, for…
In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-related quadratic tracer variances. Our approach relies on…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of…
Port-Hamiltonian systems provide a highly-structured framework for modeling of physical systems. By definition, they encode a balance equation relating energy changes to supplied and dissipated energy. Capturing this energy balance in…
The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the…
We propose a variational quantum algorithm for estimating microcanonical expectation values in models obeying the eigenstate thermalization hypothesis. Using a relaxed criterion for convergence of the variational optimization loop, the…
Simplifying the geometry of a CAD model using defeaturing techniques enables more efficient discretisation and subsequent simulation for engineering analysis problems. Understanding the effect this simplification has on the solution helps…
In this paper, we build on recent work using a mathematical programming approach for incremental state update in analysis of non-linear mechanics models. In particular, we consider quasi-static analysis of continuum problems in the…
Path integral calculations of equilibrium isotope effects and isotopic fractionation are expensive due to the presence of path integral discretization errors, statistical errors, and thermodynamic integration errors. Whereas the…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…
We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…
In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the…
High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…
We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the…
Deep ensembles are a powerful tool in machine learning, improving both model performance and uncertainty calibration. While ensembles are typically formed by training and tuning models individually, evidence suggests that jointly tuning the…
In two recent publications [Kov{\'a}cs, Larsson, and Mesforush, SIAM J. Numer. Anal. 49(6), 2407-2429, 2011] and [Furihata, et al., SIAM J. Numer. Anal. 56(2), 708-731, 2018], strong convergence of the semi-discrete and fully discrete…