Seminar archive

Abstract

In this talk, I will give an overview of my research. Agent-based model is widely used in mathematical biology, in which every single cell is treated separately as an individual to track the precise location and cellular activities. In my research, I use centre-based model to describe the wound contraction in burn injuries and vertex-based model to study the cell shape evolution in cancer cell metastasis in a flexible micro-channel. Both models have been validated qualitatively. Meanwhile, a major portion of my research is regarding upscaling the agent-based model to continuum-based model utilizing Dirac delta distributions, particularly in linear elasticity model for cellular forces and in diffusion equation for compounds spreading over the domain. We did not only propose the approximated model but also studied the convergence between the models at different scales.

Abstract

We study the dynamics of quantum vortices in a spinning-down cylindrical container using a nonlinear Schrödinger model.We find convincing spatial-temporal evidence of avalanching behaviour resulting from vortex depinning and collective motion. During a typical avalanche, O(10) vortices exit the container in a short period, producing a glitch in the superfluid angular momentum and a localised void in the vorticity. After the glitch, vortices continue to depin and circulate around the vorticity void in a similar manner to that seen in previous point-vortex approaches. We present evidence of collective vortex motion throughout this avalanche process. We also show that the effective Magnus force can be used to predict when and where avalanches will occur. Finally, we comment on the challenge of extrapolating these results to conditions in real neutron stars, which contain many orders of magnitude more vortices.

Abstract

Many modern sampling methods can instead be viewed as optimisation procedures over a space of probability measures endowed with an appropriate geometry. In this talk I will begin by developing this lens via Wasserstein gradient flows: the Fokker–Planck dynamics for the overdamped Langevin diffusion which arises as the Wasserstein-2 gradient flow of the Kullback–Leibler functional, and the unadjusted Langevin algorithm (ULA) is precisely a forward-flow time-discretisation of that flow. In parallel, particle variational methods such as Stein variational gradient descent (SVGD) can be read as explicit-Euler updates for the gradient flow of KL under a kernelised (Stein) Wasserstein metric. This unifying viewpoint clarifies why these algorithms decrease appropriate objective functionals and what structural assumptions (e.g., geodesic convexity) ensure their convergence. The second part of the talk presents new work on how to practically implement these algorithms without the hassle of manually tuning the discretisation parameter. We introduce Fuse —a Functional Upper-bound Step-size Estimator —which yields adaptive, step-size-free discretisations of Wasserstein gradient flows. Fuse is a general approach which can be used practically to create tuning-free variants of algorithms such as ULA, SGLD, mean-field Langevin dynamics, SVGD, and variational gradient descent, to name a few. The resulting procedures retain the performance of optimally tuned baselines—provably up to logarithmic factors—under mild conditions such as geodesic convexity and locally bounded (stochastic) gradients. I will cover the derivation of Fuse from functional inequalities on the Wasserstein space, non-asymptotic guarantees for both forward-flow and forward-Euler discretisations, and empirical results spanning target sampling and mean-field neural network training that match (or surpass) the best tuned alternatives— without manual learning-rate selection.

Abstract

Auxin is an important plant hormone in the regulation of plant growth and evelopment, among others. It is transported from the top of the plant to the roots. Various proteins have been shown experimentally to be involved as local transporters over cell membranes inside the stem of the plant in this long-range transport. We shall discuss how multi-scale mathematical modelling and analysis was used in combination with well-tuned experimental workin the Plant BioDynamics Lab at the Leiden University to gain novel biological insights into the course that auxin takes inside the stem during this transport. Due to its small molecular size, auxin cannot be made visible by fluorescent protein tagging, for example. The model however enables to bridge the scales from macroscopic plant-level transport measurements to microscopic membrane-transport processes. We discuss and motivate how this was implemented, given a realistic setting with its particular experimental limitations. Screening of the long-range auxin transport data of various mutant plants in view of this model then suggested a different role for various transporter proteins than previously anticipated.

Abstract

Recent progress in the development of equivariant neural network architectures predominantly used for machine learning interatomic potentials (MLIPs) has opened new possibilities in the development of data-driven coarse-graining strategies. In this talk, I will first present our work on the development of learning potential energy surfaces and other physical quantities, namely the Hyperactive Learning framework [1], a Bayesian active learning strategy for automatic efficient assembly of training data in MLIP and ACEfriction [2], a framework for equivariant model construction based on the Atomic Cluster Expansion (ACE) for learning of configuration-dependent friction tensors in the dynamic equations of molecule surface interactions and Dissipative Particle Dynamics. In the second part of my talk, I will provide an overview of our work on the simulation and analysis of Generalized Langevin Equations [3,4] as obtained from systematic coarse-graining of Hamiltonian Systems via a Mori-Zwanzig projection and present an outlook on our ongoing work on developing data-driven approaches for the construction of dynamics-preserving coarse-grained representations.

1. van der Oord, C., Sachs, M., Kovács, D.P., Ortner, C. and Csányi, G. (2023). “Hyperactive learning for data-driven interatomic potentials.” npj Computational Materials.
2. Sachs, M., Stark, W.G., Maurer, R.J. and Ortner, C. (2024). “Equivariant Representation of Configuration-Dependent Friction Tensors in Langevin Heatbaths.” Machine Learning: Science & Technology.
3. Leimkuhler, B. and Sachs, M. (2022). “Efficient numerical algorithms for the generalized Langevin equation.” SIAM Journal on Scientific Computing.
4. Leimkuhler, B. and Sachs, M. (2019). “Ergodic properties of quasi-Markovian generalized Langevin equations with configuration-dependent noise and non-conservative force.” In Stochastic Dynamics Out of Equilibrium: Institut Henri Poincaré, 2017.

Abstract

Computational simulations are essential for scientific discovery. They enable experiments to be undertaken in silico that would be too costly, too risky, ethically questionable, or downright impossible to do in the real world. They can be used to increase understanding, validate hypotheses, or predict potential future developments. But computational simulations are complicated software systems requiring a very broad mix of skills to develop successfully: not only does one need subject-matter expertise, one also needs to be a programmer, a software engineer, and understand high-performance computing and data management. As a result, often simulation models are difficult to create, difficult to understand, and therefore difficult to reuse and validate. This can severely limit the value of computational simulation as a scientific instrument. In this presentation I will argue that software-engineering techniques for domain-specific modelling can be applied to address some of these challenges. I will illustrate this in the context of simulations developed in computational biology as well as healthcare settings and will suggest some potential applications in environmental modelling as a starting point for discussion with participants.

Abstract

Despite all recent in vivo , in vitro , and in silico advances, the understanding of the genuine biologically multiscale process of solid tumour invasion remains one of the greatest open questions for the scientific community. In this talk we present novel mathematical multiscale moving boundary modelling and structural analytical approaches for tumour invasion. Specifically, we focus on characterizing mathematically key aspects of the dynamic interactions that the migratory cancer cells population and the accompanying matrix degrading enzymes (MDEs) have with the extracellular matrix (ECM) components, and in particular with the ECM fibres. These are complex interactions enabled by a series of integrated multiscale systems, which are at least two-scale in nature and share (and contribute to) the same tumour macro-dynamics (i.e., tissue-scale dynamics) but have independent-in-nature micro-dynamics (i.e., cell-scale dynamics). For instance, on the bulk of the tumour, of major interest is the dynamics of fibres degradation and structural realignment occurring at micro-scale as well as the immediate impact that this continuously changing field of oriented ECM fibres has over the tumour macro-dynamics. On the other hand, the cell-scale proteolytic micro-dynamics occurring at the tumour invasive edge interacts with the peritumoural ECM fibres through the molecular fluxes of MDEs. This interfacial cell-scale interaction not only results in changes in the micro-scale structural distribution of peritumoural ECM fibres but also directly influences changes in the overall tumour morphology. The new mathematical multiscale modelling framework presented here aims to address the precise biological multiscale nature of these interactions between the cancer cells population and the surrounding fibrous environment during solid tumour invasion. This involves an appropriately derived novel 2D and 3D multiscale moving boundary modelling framework as well as state-of-the-art multiscale computational approaches. Furthermore, this research paves the way for new multiscale analysis research avenues that build on the novel concept of three-scale convergence that I established and introduced a while ago. Finally, we will conclude with very recent developments and extensions of this multiscale framework, outlined and discussed in the specific case of Glioblastoma progression and relapse.

Abstract

We give an overview of the recent results on the systematic studies of bifurcations of equilibria in small mass-action reaction networks, i.e., ones with a few species and a few reactions. Further, we provide a brief introduction to the inheritance theory of mass-action reaction networks, which allows us to infer dynamical properties of larger, more realistic reaction networks from their subnetworks. Joint work with Murad Banaji.

Abstract

Modeling discrete multicellular systems offers a range of approaches, from cellular Potts models to vertex models to center-based frameworks that explicitly capture cell-cell forces and interactions. Each option comes with its own trade-offs between computational cost, model detail, and biological interpretability. To this space, we introduce the Discrete Laplacian Cell Mechanics (DLCM) framework, developed for stochastic simulations of heterogeneous cell populations on a fixed grid and designed for an even balance between these three said aspects. Cell-cell communication cooperates with the population-level dynamics (e.g., migration or proliferation) through coupled Markov chains that define an event-based behaviour in continuous time. The cell population is embedded in continuous micro-environment fields, representing nutrients, mechanical pressure and diffusive chemical signals, all modeled by stationary reaction-diffusion equations. We will look at the framework capabilities in benchmark cases—including cell sorting, patterning through cell signalling, chemotaxis, tumor growth, and wound healing—and discuss future directions and improvements to its efficiency and expressiveness.

Abstract

Quantum fluids, such as those formed by ultra-cold atomic gases, have incredible properties such as the ability to flow without viscous effects and the quantisation of vorticity. These properties have led these gases to be dubbed “superfluids”. I will begin with a very general overview as to how these gases are formed, how they link to classical fluid dynamics, and why they are useful. I will then talk about recent advances in mixtures of two different quantum fluids, before mentioning recent work on a point-vortex model for quantum fluids with long-range interactions.

15:00 · PSC Lab 2

Abstract

Dynamical models of infectious disease processes are commonly used to unpick how pathogens spread through populations. At Lancaster, we are interested in how complex relationships between individuals, such as spatial proximity and networks, facilitate infection transmission, such that the inverse problem becomes the primary focus of interest. Yet detailed intervention-relevant questions often demand intricate, highly-detailed models. This is at odds with our capability to fit them quickly and efficiently to data. In this talk I will describe how we represent infectious disease transmission as a stochastic process, and outline some of the challenges in parameter estimation and hence prediction. I will also describe some current work trying to formalise model structure, and thereby automate the process of designing appropriate Bayesian Monte Carlo samplers for inference purposes.

Abstract

The Hypothalamic-Pituitary-Adrenal (HPA) axis is a major neuroendocrine system, and its dysregulation is implicated in various diseases. This system also presents interesting mathematical challenges for modeling. We consider a nonlinear delay differential equation model and calculate pseudospectra of three different linearizations: a time-dependent Jacobian, linearization around the limit cycle, and dynamic mode decomposition (DMD) analysis of Koopman operators (global linearization). The time-dependent Jacobian provided insight into experimental phenomena, explaining why rats respond differently to perturbations during corticosterone secretion’s upward versus downward slopes. We developed new mathematical techniques for the other two linearizations to calculate pseudospectra on Banach spaces and apply DMD to delay differential equations, respectively. These methods helped establish local and global limit cycle stability and study transients. Additionally, we discuss using pseudospectra to substantiate the model in experimental contexts and establish bio-variability via data-driven methods. This work is the first to utilize pseudospectra to explore the HPA axis.

Abstract

Understanding how infectious diseases spread through structured populations is essential for outbreak response and prediction. In this talk, I will present methods for inferring latent transmission dynamics from partially observed epidemic data, utilising state-transition models to capture individual-level heterogeneity and higher-order network structure. Infectious disease outbreaks in clinical settings are a key motivating example. Hospital surveillance typically records when a patient tests positive, but the key events that drive transmission - when infection likely occurred and when they ceased to be infectious - are unobserved. Without estimates of these hidden event times, it is difficult to identify the most likely sources of infection, distinguish competing transmission routes, and prioritise interventions. This incomplete observation process complicates parameter estimation and increases computational demands. I will illustrate these approaches through case studies with NHS and UKHSA collaborations, demonstrating how scalable inference can inform public health decision-making.

Abstract

A robust treatment of uncertainty is critical in structural dynamics and beyond. In this seminar, Dr Max Champneys will share a number of case-studies demonstrating practical Bayesian applications to problems in structural dynamics. These include: Nonlinear equation discovery with a Bayesian variant of SINDy; A Bayesian cointegration approach to removing variability in structural health monitoring features; and an uncertainty-aware approach to optimally route fibre-bragg strain gauges along an aircraft wing. Max will also share the details of an open-source dataset comprising comprehensive ground vibration testing of a BAE Hawk T1A aircraft with applications to structural health monitoring and system identification.

Abstract

Achieving internationally agreed energy and climate targets is now widely understood to be impossible without large‑scale removal of environmental contaminants, combined with substantial emission reductions across all sectors. Among the range of current technologies column adsorption is one of the most versatile and widely deployed methods for extracting contaminants from fluids. They are used in applications ranging from greenhouse‑gas capture and volatile‑organic‑compound removal to the treatment of emerging pollutants, PFA’s remediation, biogas purification, and biopharmaceutical processing. Their ease of integration into industrial systems and applicability to both gases and liquids make them a central tool in environmental remediation.

Abstract

Understanding the behaviour of dynamical systems arising from chemical reaction networks (CRNs) is crucial in several domains, including mathematical biology and chemical engineering. Studying CRNs raises interesting and challenging questions about how the combinatorial structure of a network determines its dynamical behaviours. We may want to know, for example, whether a given network permits certain kinds of limit sets or bifurcations for some choice of parameters. We may also hope to find out when allowed dynamical behaviours survive alterations in the network structure such as the addition of new species or reactions to the network, or the splitting of reactions. I will present an overview and discuss some recent work in CRN theory, illustrating how the structure-dynamics relationship in CRNs can be studied using approaches from analysis, algebra and geometry. In many cases, the solutions to CRN problems are naturally formulated as algorithms, and so theoretical work goes hand-in-hand with computational work.

Abstract

This talk will be a bit of a mix of a few projects I’ve been working on recently. I’ll share a bit about my experiences using renewal and Hawkes process models for infectious disease models and the problems I’ve encountered when trying to scale them up. I’ll also talk about machine learning methods I’ve used to predict childhood poverty from satellite images. Finally I’ll share a bit about the SPHERE-PPL community that I’m trying to build and the forecasting competitions that we are running that might be of interest.

Abstract

Background: Ultra-large-scale structures in cosmology are physically huge (exceeding the estimated scale of homogeneity), statistically-significant features in the distribution of matter in the Universe. The accumulating list of uLSSs raises questions about the assumption of homogeneity on large scales, which the Cosmological Principle --- the foundation of the standard cosmological model --- requires. I use a method of mapping intervening absorption features detected in the spectra of bright, background quasars, to trace the underlying matter distribution. In particular, singly-ionised magnesium (MgII) is well known to trace galaxies and galaxy clusters. Results: I will present the discovery of `A Giant Ring on the Sky’, which is a ring-like uLSS that appears to extend from the previously-reported Giant Arc (Lopez et al. 2022). The Giant Ring (GR) is an almost contiguous, overdense filament of MgII absorbers which appears as a Giant Ring, approximately 1Gpc across, from our line of sight. Previously, the Giant Arc (GA) and the Big Ring (BR; Lopez et al 2024) were reported in the literature as uLSS discoveries that are very interesting for cosmology due to their huge sizes, their close cosmological proximity to each other, and their curious ring-like morphologies. Following this, there were hints that the GA could extend into a GR (Lopez et al. 2025), which was investigated further. Conclusions: Substantial evidence now supports the reality of a GR: different observational methods affirm the presence of an overdense filament encompassed by underdense void regions, and multiple statistical tests confirm a >3 sigma detection of a GR. The Giant Ring was discovered in the same field, and at the same redshift as the two previously-reported uLSSs making this third discovery an even bigger curiosity for cosmology. Nested rings (such as the BR and GR) seem unlikely to occur in a FLRW homogeneous universe, so perhaps the explanation for these structures lies beyond standard cosmology; in either case, it could be productive to follow the hints that these structures are providing.

Abstract

Modern Deep Learning optimization is largely dominated by first-order methods such as Adam, yet their limitations in efficiently exploiting the curvature of the training loss motivate the search for improved alternatives. This talk provides a practical perspective on optimization, starting from the definition and limitations of the Adam optimizer and extending to recent advances that go beyond standard adaptive methods.

We present techniques that improve the computational efficiency of the optimization. In particular, we introduce DASH, a GPU-efficient implementation of the Shampoo optimizer that accelerates second-order preconditioning via improved parallelization and fast matrix inverse root approximations; and Trion, a low-rank version of Muon optimizer that replaces costly SVD/QR projections with more efficient, rank-independent alternatives. Together, these methods illustrate how careful algorithmic and systems-level design can overcome the practical limitations of existing optimizers, offering a path toward scalable and high-performance training beyond Adam.