arXiv subjects

Sebastian Matera

Publications and source records attributed to Sebastian Matera.

16 recordsLinked to original sources

arXiv2026

On low-rank tensor train approximability for linear nearest neighbor systems

Low-rank tensor methods are an important tool in the numerical treatment of equations with a high-dimensional state space. Nearest neighbor interaction systems like the Ising model or more general Markov jump processes, as well as 1D finite-state quantum systems are examples of such problems. While low-rank tensor train/matrix product state models have been shown to be highly efficient for the simulation of such systems, providing theoretical justification for this remains a challenging task. One approach for obtaining estimates on required ranks for certain accuracies is to investigate the rank increase in Krylov subspace methods for solving the problem at hand. In the context of area laws for ground states of 1D spin systems, nontrivial results on rank-increasing properties of nearest neighbor operator polynomials have been obtained in work of Arad et al. [arXiv:1301.1162] by studying the partial commutativity of local operators. In the present work, this technique is applied to polynomial methods for definite linear equations and dissipative linear ODEs with nearest neighbor structure. This allows to derive corresponding low-rank approximability statements for solutions of such problems which are independent of the system size. Numerical simulations of high-dimensional nearest neighbor systems illustrate the theoretical findings.

math.NA↗

arXiv2026

Noise-balanced multilevel on-the-fly sparse grid surrogates for coupling Monte Carlo models into continuum models with application to heterogeneous catalysis

Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models can overcome this but come with some challenges. One such challenges arise by the sampling noise in the underlying Monte Carlo data, which leads to uncontrolled errors possibly corrupting the surrogate even though it would be highly accurate in the case of noise-free data. Another challenge arises by the 'curse of dimensionality' when the response depends on many macro-variables. These points are addressed by a novel noise-balanced sparse grids interpolation approach which, in a quasi-optimal fashion, controls the amount of Monte Carlo sampling for each data point. The approach is complemented by a multilevel on-the-fly construction during the multiscale simulation. Besides its efficiency, a particularly appealing feature is the ease of use of the approach with only a single hyperparameter controlling the whole surrogate construction - from the surrogate's accuracy with guaranteed convergence to which data needs to be created with which accuracy. The approach is demonstrated on challenging examples from heterogeneous catalysis, coupling microscopic kinetic Monte Carlo models into macroscopic reactor simulations.

physics.comp-ph↗

arXiv2025

Reduced Basis Approach for Convection-Diffusion Equations with Non-Linear Boundary Reaction Conditions

This paper aims at an efficient strategy to solve drift-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous catalysis. Since the non-linearity only involves the degrees of freedom along (a part of) the boundary, a reduced basis ansatz is suggested that computes discrete Green's-like functions for the present drift-diffusion operator such that the global non-linear problem reduces to a smaller non-linear problem for a boundary method. The computed basis functions are completely independent of the non-linearities. Thus, they can be reused for problems with the same differential operator and geometry. Corresponding scenarios might be inverse problems in heterogeneous catalysis but also modeling the effect of different catalysts in the same reaction chamber. The strategy is explained for a mass-conservative finite volume method and demonstrated on a simple numerical example for catalytic CO oxidation.

math.NA↗

arXiv2023

Kinetic trapping of charge-transfer molecules at metal interfaces

Despite the common expectation that conjugated organic molecules on metals tend to adsorb in a flat-lying wetting layer, several recent studies have found strong indications for coverage-dependent transitions to upright-standing phases, which exhibit notably different physical properties. In this work, we argue that from an energetic perspective, thermodynamically stable upright-standing phases may be more common than hitherto thought. However, for kinetic reasons this phase may often not be observed experimentally. Indeed, using first principles kinetic Monte Carlo simulations, we find that the structure with lower molecular density is (almost) always formed first, reminiscent of Ostwalds rule of stages. The phase transitions to the thermodynamically stable upright-standing phase are likely to be kinetically hindered under conditions typically used in surface science (gas phase adsorption at low flux). This provides a possible explanation why they are commonly not observed. Investigating both the role of the growth conditions and the energetics of the interface, we find that the time for the phase transition is determined mostly by the deposition rate and, thus, mostly independent of the nature of the molecule.

cond-mat.mtrl-sci↗

arXiv2023

A Fuzzy Classification Framework to Identify Equivalent Atoms in Complex Materials and Molecules

The nature of an atom in a bonded structure -- such as in molecules, in nanoparticles or solids, at surfaces or interfaces -- depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with equivalent environments is a frequent task, to gain an understanding of the material function, to interpret experimental results or to simply restrict demanding first-principles calculations. While routine, this task can often be challenging for complex molecules or non-ideal materials with breaks of symmetries or long-range order. To automatize this task, we here present a general machine-learning framework to identify groups of (nearly) equivalent atoms. The initial classification rests on the representation of the local atomic environment through a high-dimensional smooth overlap of atomic positions (SOAP) vector. Recognizing that not least thermal vibrations may lead to deviations from ideal positions, we then achieve a fuzzy classification by mean-shift clustering within a low-dimensional embedded representation of the SOAP points as obtained through multidimensional scaling. The performance of this classification framework is demonstrated for simple aromatic molecules and crystalline Pd surface examples.

physics.chem-ph↗

arXiv2023

Quantum dynamics of coupled excitons and phonons in chain-like systems: tensor train approaches and higher-order propagators

We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations, we aim at reducing memory consumption and computational costs. As an example, coupled excitons and phonons modeled in terms of Fr\"{o}hlich-Holstein type Hamiltonians are studied here. By comparing our tensor-train based results with semi-analytical results, we demonstrate the key role of the ranks of the quantum state vectors. Typically, an excellent quality of the solutions is found only when the maximum number of ranks exceeds a certain value. One class of propagation schemes builds on splitting the Hamiltonian into two groups of interleaved nearest-neighbor interactions commutating within each of the groups. In particular, the 4-th order Yoshida-Neri and the 8-th order Kahan-Li symplectic composition yield results close to machine precision. Similar results are found for 4-th and 8-th order global Krylov scheme. However, the computational effort currently restricts the use of these four propagators to rather short chains which also applies to propagators based on the time-dependent variational principle, typically used for matrix product states. Yet another class of propagators involves explicit, time-symmetrized Euler integrators. Especially the 4-th order variant is recommended for quantum simulations of longer chains, even though the high precision of the splitting schemes cannot be reached. Moreover, the scaling of the computational effort with the dimensions of the local Hilbert spaces is much more favorable for the differencing than for splitting or variational schemes.

quant-ph↗

arXiv2021

Solving the time-independent Schr\"odinger equation for chains of coupled excitons and phonons using tensor trains

We demonstrate how to apply the tensor-train format to solve the time-independent Schr\"{o}dinger equation for quasi one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Frenkel-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach which directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in case of homogeneous systems the tensor-train ranks of state vectors only marginally depend on the chain length which results in a linear growth of the storage consumption. However, the CPU time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wavepacket width and the corresponding stabilization energy on the exciton-phonon coupling strength, though only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the restrictions of the Frenkel-Holstein type Hamiltonians.

physics.comp-ph↗

arXiv2021

Revisiting the storage capacity limit of graphite battery anodes: spontaneous lithium overintercalation at ambient pressure

The market quest for fast-charging, safe, long-lasting and performant batteries drives the exploration of new energy storage materials, but also promotes fundamental investigations of materials already widely used. Presently, revamped interest in anode materials is observed -- primarily graphite electrodes for lithium-ion batteries. Here, we focus on the upper limit of lithium intercalation in the morphologically quasi-ideal highly oriented pyrolytic graphite (HOPG), with a LiC$_6$ stoichiometry corresponding to 100\% state of charge (SOC). We prepared a sample by immersion in liquid lithium at ambient pressure and investigated it by static $^7$Li nuclear magnetic resonance (NMR). We resolved unexpected signatures of superdense intercalation compounds, LiC$_{6-x}$. These have been ruled out for decades, since the highest geometrically accessible composition, LiC$_2$, can only be prepared under high pressure. We thus challenge the widespread notion that any additional intercalation beyond LiC$_6$ is not possible under ambient conditions. We monitored the sample upon calendaric aging and employed ab initio calculations to rationalise the NMR results. The computed relative stabilities of different superdense configurations reveal that non-negligible overintercalation does proceed spontaneously beyond the currently accepted capacity limit.

cond-mat.mtrl-sci↗

arXiv2018

Multilevel Adaptive Sparse Grid Quadrature for Monte Carlo models

Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore interested in some integral of the MC model's output over the input parameters. We present a Multilevel Adaptive Sparse Grid strategy for the numerical integration of such problems where the integrand is implicitly defined by a Monte Carlo model. In this approach, we exploit different levels of sampling accuracy in the Monte Carlo model to reduce the overall computational costs compared to a single level approach. Unlike existing approaches for Multilevel Numerical Quadrature, our approach is not based on a telescoping sum, but we rather utilize the intrinsic multilevel structure of the sparse grids and the employed locally supported, piecewise linear basis functions. Besides illustrative toy models, we demonstrate the methodology on a realistic kMC model for CO oxidation. We find significant savings compared to the single level approach - often orders of magnitude.

math.NA↗

arXiv2016

A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis

Lattice kinetic Monte Carlo simulations have become a vital tool for predictive quality atomistic understanding of complex surface chemical reaction kinetics over a wide range of reaction conditions. In order to expand their practical value in terms of giving guidelines for atomic level design of catalytic systems, it is very desirable to readily evaluate a sensitivity analysis for a given model. The result of such a sensitivity analysis quantitatively expresses the dependency of the turnover frequency, being the main output variable, on the rate constants entering the model. In the past the application of sensitivity analysis, such as Degree of Rate Control, has been hampered by its exuberant computational effort required to accurately sample numerical derivatives of a property that is obtained from a stochastic simulation method. In this study we present an efficient and robust three stage approach that is capable of reliably evaluating the sensitivity measures for stiff microkinetic models as we demonstrate using CO oxidation on RuO2(110) as a prototypical reaction. In a first step, we utilize the Fisher Information Matrix for filtering out elementary processes which only yield negligible sensitivity. Then we employ an estimator based on linear response theory for calculating the sensitivity measure for non-critical conditions which covers the majority of cases. Finally we adopt a method for sampling coupled finite differences for evaluating the sensitivity measure of lattice based models. This allows efficient evaluation even in critical regions near a second order phase transition that are hitherto difficult to control. The combined approach leads to significant computational savings over straightforward numerical derivatives and should aid in accelerating the nano scale design of heterogeneous catalysts.

physics.comp-ph↗

arXiv2016

Nearest-Neighbor Interaction Systems in the Tensor-Train Format

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to the so-called curse of dimensionality. This requires techniques to handle linear operators defined on extremely large state spaces and to solve the resulting systems of linear equations or eigenvalue problems. In this paper, we present a systematic tensor-train decomposition for nearest-neighbor interaction systems which is applicable to a host of different problems. With the aid of this decomposition, it is possible to reduce the memory consumption as well as the computational costs significantly. Furthermore, it can be shown that in some cases the rank of the tensor decomposition does not depend on the network size. The format is thus feasible even for high-dimensional systems. We will illustrate the results with several guiding examples such as the Ising model, a system of coupled oscillators, and a CO oxidation model.

math.NA↗

arXiv2016

Function-Space Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multi-grid solvers this approach allows to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

cond-mat.mtrl-sci↗

arXiv2012

When atomic-scale resolution is not enough: Spatial effects in in situ model catalyst studies

We investigate transport effects in in situ studies of defined model catalysts using a multi-scale modeling approach integrating first-principles kinetic Monte Carlo simulations into a fluid dynamical treatment. We specifically address two isothermal flow setups: i) a channel flow with the gas-stream approaching the single crystal from the side, as is representative for reactor scanning tunneling microscopy experiments; and ii) a stagnation flow with perpendicular impingement. Using the CO oxidation at RuO2 (110) as showcase we obtain substantial variations in the gas-phase pressures between the inlet and the catalyst surface. In the channel geometry the mass transfer limitations lead furthermore to pronounced lateral changes in surface composition across the catalyst surface. This prevents the aspired direct relation between activity and catalyst structure. For the stagnation flow the lateral variations are restricted to the edges of the catalyst. This allows to access the desired structure-activity relation using a simple model.

cond-mat.mtrl-sci↗

arXiv2010

Towards a first-principles chemical engineering: Transport limitations and bistability in in situ CO oxidation at RuO2(110)

We present a first-principles based multiscale modeling approach to heterogeneous catalysis that integrates first-principles kinetic Monte Carlo simulations of the surface reaction chemistry into a fluid dynamical treatment of the macro-scale flow structures in the reactor. The approach is applied to a stagnation flow field in front of a single-crystal model catalyst, using the CO oxidation at RuO2(110) as representative example. Our simulations show how heat and mass transfer effects can readily mask the intrinsic reactivity at gas-phase conditions typical for modern in situ experiments. For a range of gas-phase conditions we furthermore obtain multiple steady-states that arise solely from the coupling of gas-phase transport and surface kinetics. This additional complexity needs to be accounted for when aiming to use dedicated in situ experiments to establish an atomic-scale understanding of the function of heterogeneous catalysts at technologically relevant gas-phase conditions.

cond-mat.mtrl-sci↗

arXiv2009

First-Principles Approach to Heat and Mass Transfer Effects in Model Catalyst Studies

We assess heat and mass transfer limitations in in situ studies of model catalysts with a first-principles based multiscale modeling approach that integrates a detailed description of the surface reaction chemistry and the macro-scale flow structures. Using the CO oxidation at RuO2(110) as a prototypical example we demonstrate that factors like a suppressed heat conduction at the backside of the thin single-crystal, and the build-up of a product boundary layer above the flat-faced surface play a significant role.

cond-mat.mtrl-sci↗

arXiv2008

Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations

The conceptual idea of degree of rate control (DRC) approaches is to identify the "rate limiting step" in a complex reaction network by evaluating how the overall rate of product formation changes when a small change is made in one of the kinetic parameters. We examine two definitions of this concept by applying it to first-principles kinetic Monte Carlo simulations of the CO oxidation at RuO2(110). Instead of studying experimental data we examine simulations, because in them we know the surface structure, reaction mechanism, the rate constants, the coverage of the surface and the turn-over frequency at steady state. We can test whether the insights provided by the DRC are in agreement with the results of the simulations thus avoiding the uncertainties inherent in a comparison with experiment. We find that the information provided by using the DRC is non-trivial: It could not have been obtained from the knowledge of the reaction mechanism and of the magnitude of the rate constants alone. For the simulations the DRC provides furthermore guidance as to which aspects of the reaction mechanism should be treated accurately and which can be studied by less accurate and more efficient methods. We therefore conclude that a sensitivity analysis based on the DRC is a useful tool for understanding the propagation of errors from the electronic structure calculations to the statistical simulations in first-principles kinetic Monte Carlo simulations.

cond-mat.mtrl-sci↗