MACSMIN 2024 : Mathematics and Computer Science for Materials Innovation
![]() |
The MACSMIN logo includes the basic examples of the rock-salt cubic crystal, the benzene ring, and a blue wave containing a local maximum and a local minimum. |
- Dates : 9-13 September 2024 in a hybrid form at Liverpool Materials Innovation Factory, UK.
- Conference organizer : Vitaliy Kurlin. To participate for free (in person or online), please e-mail.
- We plan 2-3 days in person including a conference dinner in Liverpool and 2-3 days on zoom.
- The conference is funded by the LMS through the network Applied Geometry and Topology.
- All talks will be aimed for a broad audience of scientists, see the invited speakers.
- Travel information for Liverpool (UK): venue, accommodation, trains, flights.
- Past meetings of the MACSMIN series: 2023, 2022, 2021, 2020.
- Invited speakers (more speakers will be added after their confirmations)
- Simon J. L. Billinge (Columbia University, US)
Title. Materials genomics, materials heredity and the structure definition problem.
Abstract. We have recently been thinking, somewhat whimsically, about the materials genome. The materials genome initiative (MGI) is a US government initiative from 2011 to speed up, and lower the cost of, the discovery of new advanced materials, and their deployment in technologies, by applying data analytic methods inspired by biological genomics. Of course, materials do not have a genome. However, if we generalize the concept of a genome as a 1D discrete quantity that codes for the 3-dimensional arrangement of atoms, then we do have quantities that could serve as this generalized genome. At MACSMIN 2023 I introduced our thinking on this idea in a general sense. In this talk I will briefly reiterate the main idea, and then discuss, developments in our thinking over the past year. Two new concepts emerge from this framing. One is the idea of the materials ribosome. The ribosome is the cellular machinery that converts a DNA code into protein molecules which then fold to unique 3D structures. For our materials genome, this would be machinery, either physical or computational, that can convert our materials genome code into a 3D structure. The other concept is that of heredity, whereby we can find new materials similar to existing ones by making small mutations to our materials genome. I will discuss how this way of thinking can guide us in our search for genomic codings for materials structure. Something that has emerged from this thinking is a realization that the field of crystallography doesn't have clear definitions of what constitutes a structure. I call this the "structure definition problem" and I suggest that, as a community it would be most beneficial if we could address this problem and formalize definitions for what is meant by materials structure. - Daniel Colquitt (University of Liverpool, UK)
- Lucas Foppa (NOMAD lab at the Fritz-Haber-Institute, Berlin, Germany)
Title. From Prediction to Action: Critical Role of Performance Estimation for Machine-Learning-Driven Materials Discovery.
Abstract. Materials discovery driven by statistical property models is an iterative decision process, during which an initial data collection is extended with new data proposed by a model-informed acquisition function--with the goal to maximize a certain "reward" over time, such as the maximum property value discovered so far. While the materials science community achieved much progress in developing property models that predict well on average with respect to the training distribution, this form of in-distribution performance measurement is not directly coupled with the discovery reward. This is because an iterative discovery process has a shifting reward distribution that is over-proportionally determined by the model performance for exceptional materials. We demonstrate this problem using the example of bulk modulus maximization among double perovskite oxides. We find that the in-distribution predictive performance suggests random forests as superior to Gaussian process regression, while the results are inverse in terms of the discovery rewards. We argue that the lack of proper performance estimation methods from pre-computed data collections is a fundamental problem for improving data-driven materials discovery, and we propose a novel such estimator that, in contrast to naïve reward estimation, successfully predicts Gaussian processes with the "expected improvement" acquisition function as the best out of four options in our demonstrational study for double perovskites. Importantly, it does so without requiring the over thousand ab initio computations that were needed to confirm this prediction. - John Helliwell (University of Manchester, UK)
Title. The Scientific Truth, the Whole Truth and Nothing But the Truth (based on this book).
Abstract. There is a massive thrust on Open Science from Governments, Organisations and Funding Agencies. Puzzlingly Trust is not emphasised. Peer review of articles with underpinning data is a tradition of crystallography including community agreed validation checks as standard to try and ensure Trust. Exemplars are IUCr’s Checkcif and PDB’s Validation Report. The question arises once editor (and their referees) and database validator are content with an article and underpinning data what are the standard uncertainties on atomic coordinates and atomic displacement parameters? Expansion of digital data archiving allows raw data preservation reaching close to objectivity in science. In law the truth, the whole truth and nothing but the truth is sought, why not in science as well?! - Richard D. James (University of Minnesota, US)
- Nicholas Kotov (University of Michigan, US)
- Gregory McColm (University of South Florida, US)
Title. Geometric Families of (Edge Transitive) Crystal Nets.
Abstract. A covalent crystal may be represented as a geometric graph whose vertices are atoms or molecular building blocks and whose edges are bonds or ligands. If edge transitive, such a crystal net may be derived from a voltage graph that encodes the vertex symmetries and edge displacements occurring within the crystal net. Say that two voltage graphs are homologous if they are isomorphic and have corresponding vertex symmetries, and this homological equivalence relation partitions the space of voltage graphs into topological spaces corresponding to topological spaces of the corresponding crystal nets. For any one equivalence class of voltage graphs, almost all of its crystal nets are of a common dimension and symmetry group, although there may be subspaces of crystal nets of greater symmetry, lower dimension, or some other reduction. We consider several examples of spaces of edge transitive crystal nets. - Cristian Micheletti (SISSA, Trieste, Italy)
Title. Designed self-assembly of molecular knots, links and topological gels.
Abstract. Supramolecular constructs with complex topologies are of great interest across soft-matter physics, biology and chemistry, and hold much promise as metamaterials with unusual mechanical properties. A particularly challenging problem is how to rationally design, and subsequently realize, these structures and the precise interlockings of their multiple molecular strands. Here we report on the combined use of theory and simulations to obtain complex supramolecular constructs via programmed self-assembly. Specifically, by controlling the geometry of the self-assembled monomers we show that the assembly process can be directed towards "privileged", addressable topologies of molecular knots, and extended linked structures, such as Olympic gels and catenanes. We conclude presenting an overview of the unique static and dynamical properties of linear catenanes. The talk will cover results based on publications [1-5].
[1] E. Orlandini and C.Micheletti, J. Phys. Condensed Matter, 34, 013002 (2022).
[2] M. Marenda, E. Orlandini, and C. Micheletti, Nat. Commun. 9, 3051 (2018).
[3] G. Polles, E. Orlandini, and C. Micheletti, ACS Macro Lett.5 , 931 (2016).
[4] G. Polles, D. Marenduzzo, E. Orlandini, and C. Micheletti, Nat. Commun. 6, 6423 (2015).
[5] M. Becchi, R. Capelli, C. Perego, G.M. Pavan, and C. Micheletti, Soft Matter 18, 8106 (2022).
For an actual hands-on demonstration of the designed self-assembly of "macroscopic" trefoil knots, see this video. - Peter Michor (University of Vienna, Austria)
Title. Closed surfaces with different shapes that are indistinguishable by the square root normal form.
Abstract. The Square Root Normal Field (SRNF), introduced by Jermyn et al. in 2012, provides a way of representing immersed surfaces in R3, and equipping the set of these immersions with a ``distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of R3. Thus, it induces a distance function on the shape space of immersions, i.e., the space of immersions modulo reparametrizations and rigid motions of R3.
In this talk, we give examples of the degeneracy of this distance function, i.e., examples of immersed surfaces (some closed and some open) that have the same SRNF, but are not the same up to reparametrization and rigid motions. We also prove that the SRNF does distinguish the shape of a standard sphere from the shape of any other immersed surface, and does distinguish between the shapes of any two embedded strictly convex surfaces. - Artem Mishchenko (University of Manchester, UK)
Title. Machine learning-driven discovery and classification of flat band materials.
Abstract. Flat bands are electronic energy states in crystalline materials where the electron energy remains nearly constant across a range of momentum values, appearing as horizontal lines in band structure diagrams. They are of great interest because they can lead to enhanced electron-electron interactions and exotic quantum phenomena, making them promising for novel technological applications such as quantum computing, high-temperature superconductivity, and next-generation electronics. High-throughput computational databases provide access to hundreds of thousands of computed materials, where many materials with flat bands are awaiting discovery. However, identifying and categorising flat band materials across vast computational databases remains challenging. We present a comprehensive machine learning framework that combines supervised and unsupervised techniques to efficiently discover and classify flat band materials. We developed a convolutional neural network (CNN) based approach to identify flat bands from electronic structure images in the 2DMatPedia (2D materials) and the Materials Project (3D materials) databases. We coupled CNN with density-based clustering of structural fingerprints to reveal families of flat band materials, uncovering new lattice structures beyond known paradigms. We then extended our approach beyond structural fingerprints, by training a convolutional autoencoder (CAE) to encode band structures into compact electronic fingerprints. Unsupervised clustering of these fingerprints efficiently mapped the electronic property spaces of flat band materials. To further advance the field, we propose a novel metric inspired by quantum geometry to quantify the triviality of flat band materials. This metric provides crucial insights into the nature of the flat bands and their potential for hosting exotic quantum phenomena.
In this talk, I will overview our recent progress in the field of autonomous materials discovery, including our current results and future directions. Our hybrid framework provides a powerful, generalisable tool to rapidly screen computational databases and identify promising flat band candidates. In the future, we aim to extend our framework to predict synthesis conditions for promising flat band materials and to incorporate experimental feedback for continuous learning and improvement of our models. - Alexander Movchan (University of Liverpool, UK)
Title. Modelling of waves in semi-infinite metamaterials clusters.
Abstract. The talk presents a class of models for waves in two-dimensional metamaterials systems containing clusters of resonators. Such waves are dispersive, and they are characterised by the dynamic anisotropy. Special attention is given to the wave localisation and lattice Green's functions. For semi-infinite clusters of resonators, the approach based on the Floquet theory would not be applicable. Instead, we derive and analyse the functional equations of the Wiener-Hopf type. In particular, the connection is drawn between the kernels of the Wiener-Hopf equations and the quasiperiodic lattice Green's functions for infinite doubly periodic clusters. The analytical results are accompanied by the numerical simulations and examples. - Anthony Nixon (Lancaster University, UK)
Title. A tour through rigidity theory.
Abstract. A bar-joint framework is a discrete structure made of fixed length bars connected at universal joints. Mathematically the framework is a combination of a graph and a realisation mapping the vertices into Euclidean space. Rigidity theory concerns the analysis of the rigidity and flexibility properties of such frameworks. In this talk I will survey the basic mathematical theory with a focus on past, present and future applications of rigidity theory to materials science, biology and engineering. - Marjorie Senechal (Smith College, US)
Title. Geometry and crystallography: a conversation.
Abstract. Throughout the century from Fedorov's enumeration of the five convex parallelohedra in 1885 to Schectman's 1982 discovery of aperiodic crystals, "geometrical crystallography" comprised lattices, point sets, symmetry groups, tilings, and other topics in discrete geometry. Today the field includes continuous models and measures. Models include "soft packings" in which cells overlap, or have soft corners, or are skeletal rather than solid. Indeed, the skeletal Fedorov five, together with the tilings they form, transform continuously into one! Though the older discrete classifications still distinguish periodic crystals, comparing the millions of known structures in materials databases requires continuous distance metrics. In this talk we imagine a conversation between crystallographers of 1924 and 2024. - Andy Zhang (Princeton University, US)
Title. Moment-based metrics for molecules computable from cryogenic electron microscopy images (based on this paper).
Abstract. TBA.
- Simon J. L. Billinge (Columbia University, US)
- Tutorials in Geometric Data Science by the DSTA group
developing geographic-style maps for continuous data spaces:
- Vitaliy Kurlin. Recent advances in Geometric Data Science.
- Olga Anosova. Continuous maps of the protein universe.
- Yury Elkin. Continuous maps of molecular shape spaces.
- Dan Widdowson. Continuous maps of crystal databases.
- Short talks by Will Jeffcott and Jonathan McManus.
- We invite to participate in-person and have a modest budget to cover travel and accommodation of invited speakers. However, since many colleagues have other important commitments, invited talks over zoom can also be arranged.
- MACSMIN has the MIF++ scientific style and encourages rigorous results justified by proofs, not only by examples.
Travel information : venue, accommodation, trains, flights
- All talks in person will be in the ground floor boardroom in the Materials Innovation Factory (MIF), Liverpool, UK. Address: 51 Oxford street, building 807 in the grid cell F5 on the campus map. The building has a secure entrance, so we will let the reception know about MACSMIN participants. The MIF is 15 min on foot from the Liverpool Lime Street station.
- If you contact us in advance, we can help with booking hotels. One option is the Liner hotel in a quiet street close to the Liverpool Lime Street main rail station. Explore other good hotels and attractions at the website visit Liverpool.
- The city has the Liverpool John Lennon airport with convenient buses to the centre. The larger Manchester airport has the train station with direct 90-min trains to the Liverpool Lime Street station. Check flights to nearby airports at Skyscanner.
Back to Top of this page | Back to MACSMIN | Back to Home page