arXiv subjects

Martin Robinson

Publications and source records attributed to Martin Robinson.

16 recordsLinked to original sources

arXiv2024

PyBOP: A Python package for battery model optimisation and parameterisation

The Python Battery Optimisation and Parameterisation (PyBOP) package provides methods for estimating and optimising battery model parameters, offering both deterministic and stochastic approaches with example workflows to assist users. PyBOP enables parameter identification from data for various battery models, including the electrochemical and equivalent circuit models provided by the popular open-source PyBaMM package. Using the same approaches, PyBOP can also be used for design optimisation under user-defined operating conditions across a variety of model structures and design goals. PyBOP facilitates optimisation with a range of methods, with diagnostics for examining optimiser performance and convergence of the cost and corresponding parameters. Identified parameters can be used for prediction, on-line estimation and control, and design optimisation, accelerating battery research and development.

eess.SY↗

arXiv2024

Ten simple rules for training scientists to make better software

Computational methods and associated software implementations are central to every field of scientific investigation. Modern biological research, particularly within systems biology, has relied heavily on the development of software tools to process and organize increasingly large datasets, simulate complex mechanistic models, provide tools for the analysis and management of data, and visualize and organize outputs. However, developing high-quality research software requires scientists to develop a host of software development skills, and teaching these skills to students is challenging. There has been a growing importance placed on ensuring reproducibility and good development practices in computational research. However, less attention has been devoted to informing the specific teaching strategies which are effective at nurturing in researchers the complex skillset required to produce high-quality software that, increasingly, is required to underpin both academic and industrial biomedical research. Recent articles in the Ten Simple Rules collection have discussed the teaching of foundational computer science and coding techniques to biology students. We advance this discussion by describing the specific steps for effectively teaching the necessary skills scientists need to develop sustainable software packages which are fit for (re-)use in academic research or more widely. Although our advice is likely to be applicable to all students and researchers hoping to improve their software development skills, our guidelines are directed towards an audience of students that have some programming literacy but little formal training in software development or engineering, typical of early doctoral students. These practices are also applicable outside of doctoral training environments, and we believe they should form a key part of postgraduate training schemes more generally in the life sciences.

cs.CY↗

arXiv2023

Understanding the impact of numerical solvers on inference for differential equation models

Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers which seem sufficiently accurate for the forward problem, i.e., for obtaining an accurate simulation, may not be sufficiently accurate for the inverse problem, i.e., for inferring the model parameters from data. We show that for both fixed step and adaptive step ODE solvers, solving the forward problem with insufficient accuracy can distort likelihood surfaces, which may become jagged, causing inference algorithms to get stuck in local "phantom" optima. We demonstrate that biases in inference arising from numerical approximation of ODEs are potentially most severe in systems involving low noise and rapid nonlinear dynamics. We reanalyze an ODE changepoint model previously fit to the COVID-19 outbreak in Germany and show the effect of the step size on simulation and inference results. We then fit a more complicated rainfall-runoff model to hydrological data and illustrate the importance of tuning solver tolerances to avoid distorted likelihood surfaces. Our results indicate that when performing inference for ODE model parameters, adaptive step size solver tolerances must be set cautiously and likelihood surfaces should be inspected for characteristic signs of numerical issues.

math.ST↗

arXiv2022

Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes `random' latent factors affect the system in ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises due only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.

stat.ME↗

arXiv2022

Zigzag persistence for coral reef resilience using a stochastic spatial model

A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterising spatio-temporal data and understanding how changes at the local scale affect global dynamics/behaviour. Here, we extend a well-studied temporal mathematical model of coral reef dynamics to include stochastic and spatial interactions and generate data to study different ecological scenarios. We present descriptors to characterise patterns in heterogeneous spatio-temporal data surpassing spatially averaged measures. We apply these descriptors to simulated coral data and demonstrate the utility of two topological data analysis techniques--persistent homology and zigzag persistence--for characterising mechanisms of reef resilience. We show that the introduction of local competition between species leads to the appearance of coral clusters in the reef. We use our analyses to distinguish temporal dynamics stemming from different initial configurations of coral, showing that the neighbourhood composition of coral sites determines their long-term survival. Using zigzag persistence, we determine which spatial configurations protect coral from extinction in different environments. Finally, we apply this toolkit of multi-scale methods to empirical coral reef data, which distinguish spatio-temporal reef dynamics in different locations, and demonstrate the applicability to a range of datasets.

q-bio.QM↗

arXiv2020

Using flexible noise models to avoid noise model misspecification in inference of differential equation time series models

When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must be made about both parts of the system. If the signal process is incorrectly specified, our predictions using this model may generalise poorly; similarly, if the noise process is incorrectly specified, we can attribute too much or too little observed variation to the signal. With little justification, independent Gaussian noise is typically chosen, which defines a statistical model that is simple to implement but often misstates system uncertainty and may underestimate error autocorrelation. There are a range of alternative noise processes available but, in practice, none of these may be entirely appropriate, as actual noise may be better characterised as a time-varying mixture of these various types. Here, we consider systems where the signal is modelled with ordinary differential equations and present classes of flexible noise processes that adapt to a system's characteristics. Our noise models include a multivariate normal kernel where Gaussian processes allow for non-stationary persistence and variance, and nonparametric Bayesian models that partition time series into distinct blocks of separate noise structures. Across the scenarios we consider, these noise processes faithfully reproduce true system uncertainty: that is, parameter estimate uncertainty when doing inference using the correct noise model. The models themselves and the methods for fitting them are scalable to large datasets and could help to ensure more appropriate quantification of uncertainty in a host of time series models.

stat.ME↗

arXiv2020

Model Evidence with Fast Tree Based Quadrature

High dimensional integration is essential to many areas of science, ranging from particle physics to Bayesian inference. Approximating these integrals is hard, due in part to the difficulty of locating and sampling from regions of the integration domain that make significant contributions to the overall integral. Here, we present a new algorithm called Tree Quadrature (TQ) that separates this sampling problem from the problem of using those samples to produce an approximation of the integral. TQ places no qualifications on how the samples provided to it are obtained, allowing it to use state-of-the-art sampling algorithms that are largely ignored by existing integration algorithms. Given a set of samples, TQ constructs a surrogate model of the integrand in the form of a regression tree, with a structure optimised to maximise integral precision. The tree divides the integration domain into smaller containers, which are individually integrated and aggregated to estimate the overall integral. Any method can be used to integrate each individual container, so existing integration methods, like Bayesian Monte Carlo, can be combined with TQ to boost their performance. On a set of benchmark problems, we show that TQ provides accurate approximations to integrals in up to 15 dimensions; and in dimensions 4 and above, it outperforms simple Monte Carlo and the popular Vegas method.

stat.ML↗

arXiv2018

Probabilistic Inference on Noisy Time Series (PINTS)

Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of the underlying system based on observed time series. For both statistical and mechanistic models, inference involves finding parameter values, or distributions of parameters values, for which model outputs are consistent with observations. A wide variety of inference techniques are available and different approaches are suitable for different classes of problems. This variety presents a challenge for researchers, who may not have the resources or expertise to implement and experiment with these methods. PINTS (Probabilistic Inference on Noisy Time Series - https://github.com/pints-team/pints is an open-source (BSD 3-clause license) Python library that provides researchers with a broad suite of non-linear optimisation and sampling methods. It allows users to wrap a model and data in a transparent and straightforward interface, which can then be used with custom or pre-defined error measures for optimisation, or with likelihood functions for Bayesian inference or maximum-likelihood estimation. Derivative-free optimisation algorithms - which work without harder-to-obtain gradient information - are included, as well as inference algorithms such as adaptive Markov chain Monte Carlo and nested sampling which estimate distributions over parameter values. By making these statistical techniques available in an open and easy-to-use framework, PINTS brings the power of modern statistical techniques to a wider scientific audience.

cs.MS↗

arXiv2018

Separating the effects of experimental noise from inherent system variability in voltammetry: the $[$Fe(CN)$_6]^{3-/ 4-}$ process

Recently, we have introduced the use of techniques drawn from Bayesian statistics to recover kinetic and thermodynamic parameters from voltammetric data, and were able to show that the technique of large amplitude ac voltammetry yielded significantly more accurate parameter values than the equivalent dc approach. In this paper we build on this work to show that this approach allows us, for the first time, to separate the effects of random experimental noise and inherent system variability in voltammetric experiments. We analyse ten repeated experimental data sets for the $[$Fe(CN)$_6]^{3-/ 4-}$ process, again using large-amplitude ac cyclic voltammetry. In each of the ten cases we are able to obtain an extremely good fit to the experimental data and obtain very narrow distributions of the recovered parameters governing both the faradaic (the reversible formal faradaic potential, $E_0$, the standard heterogeneous charge transfer rate constant $k_0$, and the charge transfer coefficient $\alpha$) and non-faradaic terms (uncompensated resistance, $R_u$, and double layer capacitance, $C_{dl}$). We then employ hierarchical Bayesian methods to recover the underlying "hyperdistribution" of the faradaic and non-faradaic parameters, showing that in general the variation between the experimental data sets is significantly greater than suggested by individual experiments, except for $\alpha$ where the inter-experiment variation was relatively minor. Correlations between pairs of parameters are provided, and for example, reveal a weak link between $k_0$ and $C_{dl}$ (surface activity of a glassy carbon electrode surface). Finally, we discuss the implications of our findings for voltammetric experiments more generally.

eess.SP↗

arXiv2018

Particle-based simulations of reaction-diffusion processes with Aboria

Mathematical models of transport and reactions in biological systems have been traditionally written in terms of partial differential equations (PDEs) that describe the time evolution of population-level variables. In recent years, the use of stochastic particle-based models, which keep track of the evolution of each organism in the system, has become widespread. These models provide a lot more detail than the population-based PDE models, for example by explicitly modelling particle-particle interactions, but bring with them many computational challenges. In this paper we overview Aboria, a powerful and flexible C++ library for the implementation of numerical methods for particle-based models. We demonstrate the use of Aboria with a commonly used model in mathematical biology, namely cell chemotaxis. Cells interact with each other and diffuse, biased by extracellular chemicals, that can be altered by the cells themselves. We use a hybrid approach where particle-based models of cells are coupled with a PDE for the concentration of the extracellular chemical.

cs.CE↗

arXiv2017

Particle-based and Meshless Methods with Aboria

Aboria is a powerful and flexible C++ library for the implementation of particle-based numerical methods. The particles in such methods can represent actual particles (e.g. Molecular Dynamics) or abstract particles used to discretise a continuous function over a domain (e.g. Radial Basis Functions). Aboria provides a particle container, compatible with the Standard Template Library, spatial search data structures, and a Domain Specific Language to specify non-linear operators on the particle set. This paper gives an overview of Aboria's design, an example of use, and a performance benchmark.

cs.MS↗

arXiv2017

Diffusion of particles with short-range interactions

A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of matched asymptotic expansions. Numerical simulations are performed to compare the results of the model with those of the commonly used mean-field and Kirkwood-superposition approximations, as well as with Monte Carlo simulation of the stochastic particle system, for various interaction potentials. Our approach works best for very repulsive short-range potentials, while the mean-field approximation is suitable for long-range interactions. The Kirkwood superposition approximation provides an accurate description for both short- and long-range potentials, but is considerably more computationally intensive.

cond-mat.stat-mech↗

arXiv2014

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.

cond-mat.soft↗

arXiv2013

Adaptive two-regime method: application to front propagation

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al, Journal of the Royal Society Interface, 2012] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in terms of the Fisher equation [Fisher, Annals of Eugenics, 1937]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.

physics.comp-ph↗

arXiv2013

Fluid-particle flow and validation using two-way-coupled mesoscale SPH-DEM

First, a meshless simulation method is presented for multiphase fluid-particle flows with a two-way coupled Smoothed Particle Hydrodynamics (SPH) for the fluid and the Discrete Element Method (DEM) for the solid phase. The unresolved fluid model, based on the locally averaged Navier Stokes equations, is expected to be considerably faster than fully resolved models. Furthermore, in contrast to similar mesh-based Discrete Particle Methods (DPMs), our purely particle-based method enjoys the flexibility that comes from the lack of a prescribed mesh. It is suitable for problems such as free surface flow or flow around complex, moving and/or intermeshed geometries and is applicable to both dilute and dense particle flows. Second, a comprehensive validation procedure for fluid-particle simulations is presented and applied here to the SPH-DEM method, using simulations of single and multiple particle sedimentation in a 3D fluid column and comparison with analytical models. Millimetre-sized particles are used along with three different test fluids: air, water and a water-glycerol solution. The velocity evolution for a single particle compares well (less than 1% error) with the analytical solution as long as the fluid resolution is coarser than two times the particle diameter. Two more complex multiple particle sedimentation problems (sedimentation of a homogeneous porous block and an inhomogeneous Rayleigh Taylor instability) are also reproduced well for porosities 0.6 <= ε<= 1.0, although care should be taken in the presence of high porosity gradients. Overall the SPH-DEM method successfully reproduces quantitatively the expected behaviour in the test cases, and promises to be a flexible and accurate tool for other, realistic fluid-particle system simulations.

physics.flu-dyn↗

arXiv2011

Direct Numerical Simulation of decaying two-dimensional turbulence in a no-slip square box using Smoothed Particle Hydrodynamics

This paper explores the application of SPH to a Direct Numerical Simulation (DNS) of decaying turbulence in a two-dimensional no-slip wall-bounded domain. In this bounded domain, the inverse energy cascade, and a net torque exerted by the boundary, result in a spontaneous spin up of the fluid, leading to a typical end state of a large monopole vortex that fills the domain. The SPH simulations were compared against published results using a high accuracy pseudo-spectral code. Ensemble averages of the kinetic energy, enstrophy and average vortex wavenumber compared well against the pseudo-spectral results, as did the evolution of the total angular momentum of the fluid. However, while the pseudo-spectral results emphasised the importance of the no-slip boundaries as generators of long lived coherent vortices in the flow, no such generation was seen in the SPH results. Vorticity filaments produced at the boundary were always dissipated by the flow shortly after separating from the boundary layer. The kinetic energy spectrum of the SPH results was calculated using a SPH Fourier transform that operates directly on the disordered particles. The ensemble kinetic energy spectrum showed the expected k-3 scaling over most of the inertial range. However, the spectrum flattened at smaller length scales (initially less than 7.5 particle spacings and growing in size over time), indicating an excess of small-scale kinetic energy.

physics.flu-dyn↗