arXiv subjects

Elena Akhmatskaya

Publications and source records attributed to Elena Akhmatskaya.

12 recordsLinked to original sources

arXiv2026

Complexity reduction of physical models: An equation-free approach by means of scaling

The description of complex physical phenomena often involves sophisticated models that rely on a large number of parameters, with many dimensions and scales. One practical way to simplify those kinds of models is to discard some of the parameters, or terms of underlying equations, thus giving rise to reduced models. Here, we propose a general approach to obtaining such reduced models. The method is independent of the model in use, i.e., equation-free, depends only on the interplay between the scales and dimensions involved in the description of the phenomena, and controls over-parametrization. It also quantifies conditions for asymptotic models by providing explicitly computable thresholds on values of parameters that allow for reducing complexity of a model, while preserving essential predictive properties. Although our focus is on complexity reduction, this approach may also help with calibration by mitigating the risks of over-parameterization and instability in parameter estimation. The benefits of this approach are discussed in the context of the classical projectile model.

cond-mat.soft↗

arXiv2026

Compartmental Disease Models with Time-Varying Transmission Rates: A Bayesian Generalized Hamiltonian Monte Carlo framework with Applications to COVID-19

Epidemic transmission is shaped by changing behaviour, interventions, and unobserved factors, while incidence data are noisy and incomplete. We develop a Bayesian statistical-mechanistic framework that combines staged SIR/SEIR-like compartmental models with a time-varying transmission rate represented by Bayesian P-splines. A Negative Binomial observation model links the latent epidemic dynamics to incidence data, and posterior inference is performed using Generalised Hamiltonian Monte Carlo with gradients obtained from ODE sensitivity equations. Synthetic experiments and an application to COVID-19 incidence in the Basque Country show that the framework can recover temporal variation in transmission and quantify uncertainty. However, different compartmental structures may fit the observed incidence similarly while producing distinct transmission-rate and reproduction-number estimates. These findings highlight the importance of convergence diagnostics, sensitivity analyses, and epidemiological knowledge when selecting and interpreting flexible compartmental models.

stat.ME↗

arXiv2026

Adaptive tuning of Hamiltonian Monte Carlo methods

With the recently increased interest in probabilistic models, the efficiency of an underlying sampler becomes a crucial consideration. Hamiltonian Monte Carlo (HMC) is one popular option for models of this kind. Performance of the method, however, strongly relies on a choice of parameters associated with an integration for Hamiltonian equations. Up to date, such a choice remains mainly heuristic or introduces time complexity. We propose a novel computationally inexpensive and flexible approach (we call it Adaptive Tuning or ATune) that, by combining a theoretical analysis of the multivariate Gaussian model with simulation data generated during a burn-in stage of a HMC simulation, detects a system specific splitting integrator with a set of reliable sampler's hyperparameters, including their credible randomization intervals, to be readily used in a production simulation. The method automatically eliminates those values of simulation parameters which could cause undesired extreme scenarios, such as resonance artifacts, low accuracy or poor sampling. The new approach is implemented in the in-house software package HaiCS, with no computational overheads introduced in a production simulation, and can be easily incorporated in any package for Bayesian inference with HMC. The tests on popular statistical models reveal the superiority of adaptively tuned standard and generalized HMC methods in terms of stability, performance and accuracy over conventional HMC tuned heuristically and coupled with the well-established integrators. We also claim that the generalized HMC is preferable for achieving high sampling performance. The efficiency of the new methodology is assessed in comparison with state-of-the-art samplers, e.g. NUTS, in real-world applications, such as endocrine therapy resistance in cancer, modeling of cell-cell adhesion dynamics and influenza A epidemic outbreak.

stat.CO↗

arXiv2024

A transition state resonance radically reshapes angular distributions of the F + H2 -> F H(vf = 3) + H reaction in the 62-101 meV energy range

Reactive angular distributions of the benchmark F + H2(vi = 0) -> F H(vf = 3) + H reaction show unusual propensity towards small scattering angles, a subject of a long debate in the literature. We use Regge trajectories to quantify the resonance contributions to state-to-state differential cross sections. Conversion to complex energy poles allows us to attribute the effect almost exclusively to a transition state resonance, long known to exist in the F +H2 system and its isotopic variant F +HD. For our detailed analysis of angular scattering we employ the package DCS Regge, recently developed for the purpose [Comp. Phys. Comm., 2022, 277, 108370.]

quant-ph↗

arXiv2024

Imaginary past of a quantum particle moving on imaginary time

The analytical continuation of classical equations of motion to complex times suggests that a tunnelling particle spends in the barrier an imaginary duration $i|\mathcal T|$. Does this mean that it takes a finite time to tunnel, or should tunnelling be seen as an instantaneous process? It is well known that examination of the adiabatic limit in a small additional AC field points towards $|\mathcal T|$ being the time it takes to traverse the barrier. However, this is only half the story. We probe the transmitted particle's history, and find that it "remembers" very little of the field's past behaviour, as if the transit time were close to zero. The ensuing contradiction suggests that the question is ill-posed, and we explain why.

quant-ph↗

arXiv2024

Reducing model complexity by means of the Optimal Scaling: Population Balance Model for latex particles morphology formation

Rational computer-aided design of multiphase polymer materials is vital for rapid progress in many important applications, such as: diagnostic tests, drug delivery, coatings, additives for constructing materials, cosmetics, etc. Several property predictive models, including the prospective Population Balance Model for Latex Particles Morphology Formation (LPMF PBM), have already been developed for such materials. However, they lack computational efficiency, and the accurate prediction of materials' properties still remains a great challenge. To enhance performance of the LPMF PBM, we explore the feasibility of reducing its complexity through disregard of the aggregation terms of the model. The introduced nondimensionalization approach, which we call Optimal Scaling with Constraints, suggests a quantitative criterion for locating regions of slow and fast aggregation and helps to derive a family of dimensionless LPMF PBM of reduced complexity. The mathematical analysis of this new family is also provided. When compared with the original LPMF PBM, the resulting models demonstrate several orders of magnitude better computational efficiency.

cond-mat.soft↗

arXiv2024

Adaptive multi-stage integration schemes for Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers. The proper choice of the integrator of the Hamiltonian dynamics is key to the efficiency of HMC. It is becoming increasingly clear that multi-stage splitting integrators are a good alternative to the Verlet method, traditionally used in HMC. Here we propose a principled way of finding optimal, problem-specific integration schemes (in terms of the best conservation of energy for harmonic forces/Gaussian targets) within the families of 2- and 3-stage splitting integrators. The method, which we call Adaptive Integration Approach for statistics, or s-AIA, uses a multivariate Gaussian model and simulation data obtained at the HMC burn-in stage to identify a system-specific dimensional stability interval and assigns the most appropriate 2-/3-stage integrator for any user-chosen simulation step size within that interval. s-AIA has been implemented in the in-house software package HaiCS without introducing computational overheads in the simulations. The efficiency of the s-AIA integrators and their impact on the HMC accuracy, sampling performance and convergence are discussed in comparison with known fixed-parameter multi-stage splitting integrators (including Verlet). Numerical experiments on well-known statistical models show that the adaptive schemes reach the best possible performance within the family of 2-, 3-stage splitting schemes.

stat.CO↗

arXiv2020

An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation

In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance, the case of the Population Balance Equations (PBE) proposed to model the Latex Particles Morphology formation. The obvious way out of this difficulty is the use of dimensionless scaled quantities, although often the scaling procedure is not unique. In this paper, we introduce a conceptually new general approach, called Optimal Scaling (OS). The method is tested on the known examples from classical and quantum mechanics, and applied to the Latex Particles Morphology model, where it allows us to reduce the variation of the relevant coefficients from 49 to just 4 orders of magnitudes. The PBE are then solved by a novel Generalised Method Of Characteristics, and the OS is shown to help reduce numerical error, and avoid unphysical behaviour of the solution. Although inspired by a particular application, the proposed scaling algorithm is expected find application in a wide range of chemical, physical and biological problems.

cs.CE↗

arXiv2019

Modified Hamiltonian Monte Carlo for Bayesian inference

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. We call the resulting generalized HMC importance sampler---Mix & Match Hamiltonian Monte Carlo (MMHMC). The method is irreversible by construction and further benefits from (i) the efficient algorithms for computation of modified Hamiltonians; (ii) the implicit momentum update procedure and (iii) the multi-stage splitting integrators specially derived for the methods sampling with modified Hamiltonians. MMHMC has been implemented, tested on the popular statistical models and compared in sampling efficiency with HMC, Riemann Manifold Hamiltonian Monte Carlo, Generalized Hybrid Monte Carlo, Generalized Shadow Hybrid Monte Carlo, Metropolis Adjusted Langevin Algorithm and Random Walk Metropolis-Hastings. To make a fair comparison, we propose a metric that accounts for correlations among samples and weights, and can be readily used for all methods which generate such samples. The experiments reveal the superiority of MMHMC over popular sampling techniques, especially in solving high dimensional problems.

stat.CO↗

arXiv2018

Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods

Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of differential equations. We suggest novel integrators designed to enhance accuracy and sampling performance of MHMC methods. The novel integrators belong to families of splitting algorithms and are therefore easily implemented. We identify optimal integrators within the families by minimizing the energy error or the average energy error. We derive and discuss in detail the modified Hamiltonians of the new integrators, as the evaluation of those Hamiltonians is key to the efficiency of the overall algorithms. Numerical experiments show that the use of the new integrators may improve very significantly the sampling performance of MHMC methods, in both statistical and molecular dynamics problems.

physics.comp-ph↗

arXiv2016

Enhancing sampling in atomistic simulations of solid state materials for batteries: a focus on olivine NaFePO4

The study of ion transport in electrochemically active materials for energy storage systems requires simulations on quantum- atomistic- and mesoscales. The methods accessing these scales not only have to be effective but also well compatible to provide a full description of the underlying processes. We propose to adapt the Generalized Shadow Hybrid Monte Carlo (GSHMC) method to atomistic simulation of ion intercalation electrode materials for batteries. The method has never been applied to simulations in solid state chemistry but it has been successfully used for simulation of biological macromolecules, demonstrating better performance and accuracy than can be achieved with the popular molecular dynamics (MD) method. It has been also extended to simulations on meso-scales, making it even more attractive for simulation of battery materials. We combine GSHMC with the dynamical Core-Shell model to incorporate polarizability into the simulation and apply the new Modified Adaptive Integration Approach, MAIA, which allows for a larger time step due to its excellent conservation properties. Also, we modify the GSHMC method, without losing its performance and accuracy, to reduce the negative effect of introducing a shell mass within a dynamical shell model. The proposed approach has been tested on olivine NaFePO4, which is a promising cathode material for Na-ion batteries. The calculated Na-ion diffusion and structural properties have been compared with the available experimental data and with the results obtained using MD and the original GSHMC method. Based on these tests, we claim that the new technique is advantageous over MD and the conventional GSHMC and can be recommended for studies of other solid-state electrode and electrolyte materials whenever high accuracy and efficient sampling are critical for obtaining tractable simulation results.

cond-mat.mtrl-sci↗

arXiv2016

Adaptive multi-stage integrators for optimal energy conservation in molecular simulations

We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The AIA method has been implemented in the BCAM-modified GROMACS software package. Numerical tests in molecular dynamics and hybrid Monte Carlo simulations of constrained and unconstrained physical systems show that the method successfully realises the fail-safe strategy. In all experiments, and for each of the criteria employed, the AIA is at least as good as, and often significantly outperforms the standard Verlet scheme, as well as fixed parameter, optimized two-stage integrators. In particular, the sampling efficiency found in simulations using the AIA is up to 5 times better than the one achieved with other tested schemes.

math.NA↗