BMC-BAMC Glasgow 2021
We organized a mini-symposium on the theme of “Integrating dynamical systems with data driven methods” (MS09). The invited speakers presented theory and applications of data driven methods in fluid mechanics and chemical reactions. The mini-symposium had the following four talks. The program for Day 1 along with the scheduled talks is available here
Coming soon: the recorded talks.
Peter Ashwin (Exeter)
Plant ER networks and the dynamics of anchored 2D foams subject to viscous flow
The Endoplasmic Reticulum in plant cells can form a variety of rapidly changing structures including networks of filaments that are anchored to the cell membrane at various points. We discuss progress in biophysical modelling of the interaction of these geometric networks with other processes in play within the cell, in particular actin-driven cross-connections and viscous flow associated with cytoplasmic streaming. We show these processes can maintain an anchored 2D foam of filaments and, maybe more surprisingly the foam retains memory of past streaming speed and direction. (Joint work with Congping Lin, Wuhan).
Stefan Klus (Surrey)
Kernel methods for detecting coherent structures
Over the last years, numerical methods for the analysis of large data sets have gained a lot of attention. Recently, different purely data-driven methods have been proposed which enable the user to extract relevant information about the global behavior of the underlying dynamical system, to identify low-order dynamics, and to compute finite-dimensional approximations of transfer operators associated with the system. However, due to the curse of dimensionality, analyzing high-dimensional systems is often infeasible using conventional methods since the amount of memory required to compute and store the results grows exponentially with the size of the system. We extend transfer operator theory to reproducing kernel Hilbert spaces and show that these operators are related to Hilbert space representations of conditional distributions, known as conditional mean embeddings in the machine learning community. One main benefit of the presented kernel-based approaches is that these methods can be applied to any domain where a similarity measure given by a kernel is available. We illustrate the results with the aid of guiding examples and highlight potential applications in molecular dynamics, fluid dynamics, and quantum mechanics.
Kamyar Azizzadenesheli (Purdue)
A Crash Course on Neural Operators
Neural Operators are a new advancement in machine learning, applied mathematics, and science, that allows for efficiently learning operators from infinite-dimensional spaces, e.g. function spaces. In this talk, we cover the basics of Neural Operators, their properties, architectures, computation powers, limitations, and the theory behind them. We concluded the talk with a few empirical study partial differential equations (PDEs) to elaborate on the broad applicability of these methods.
Cecilia Clementi (Freie Universität Berlin)
Designing molecular models by machine learning and experimental data
The last years have seen an immense increase in high-throughput and high-resolution technologies for experimental observation as well as high-performance techniques to simulate molecular systems at a microscopic level, resulting in vast and ever-increasing amounts of high-dimensional data. However, experiments provide only a partial view of macromolecular processes and are limited in their temporal and spatial resolution. On the other hand, atomistic simulations are still not able to sample the conformation space of large complexes, thus leaving significant gaps in our ability to study molecular processes at a biologically relevant scale. We present our efforts to bridge these gaps, by exploiting the available data and using state-of-the-art machine-learning methods to design optimal coarse models for complex macromolecular systems. We show that it is possible to define simplified molecular models to reproduce the essential information contained both in microscopic simulation and experimental measurements.