Computational mathematics for model reduction and predictive modelling in molecular and complex systems
- Anders Szepessy (KTH Royal Institute of Technology, Stockholm, Sweden)
- Petr Plechac (University of Delaware, USA)
- Markos A. Katsoulakis (University of Massachusetts, Amherst, USA)
- Ben Leimkuhler (University of Edinburgh , United Kingdom)
The Centre Interfacultaire Bernoulli (or CIB or Bernoulli Centre) is a research centre at the EPFL which runs semester long thematic programmes each focussed on a specific topic within mathematics and its applications. The semester activities typically involve a relatively small number of both long and short term visitors as well as a few week-long conferences with a larger number of participants. Recently a CIB semester programme "M^3+C^3: Multiscale Mathematical Modelling and Coarse-Grain Computational Chemistry", with overall organizers Carsten Hartmann (Cottbus), John H. Maddocks (Lausanne) and Christof Schuette (Berlin) has been approved for funding and will take place in Spring 2019. Part of the original CIB proposal, with the explicit agreement of both Directors, was to enhance natural synergies between CECAM-HQ and CIB (as well as the EPFL campus more widely) in activities concerning the domains of multi-scale modelling and coarse graining at scales bridging between the atomistic and continuum.
The M^3 + C^3 CIB semester programme is built around a central
core of applied mathematics as it concerns molecular and materials modelling from atomistic to continuum scales. Our aim in the programme is to bring together theoreticians and practitioners, both senior and junior, and from all of applied mathematics, statistics, engineering, physics and computational chemistry, to work on the development of a systematic account of available coarse-grain and multi-scale techniques, with a focus on data-driven and non-
asymptotic approaches. We believe that the requested complementary CECAM workshops will be an opportunity to attract more applications oriented senior scientists to the activities of the CIB programme and its conferences, and in particular to use CECAM Workshop discussion sessions to provide a fertile environment to establish high-level trans- and interdisciplinary links and a two-way information exchange between top flight scientists and applied
mathematicians who work on similar problems but perhaps from rather different perspectives.
The two specific CECAM Workshops that we propose are:
Workshop I (organized by M. Katsoulakis, B. Leimkuhler, P. Plechac, and A. Szepessy): "Mathematical methods, data-driven algorithms and predictive modelling of complex systems."
This workshop will address computational issues in stochastic modelling and model reduction in complex molecular systems, combining mathematical methodologies from different research
fields (including materials physics and chemistry, probabilistic modelling, scientific computing uncertainty quantification and machine learning) towards predictive materials modelling.
Workshop II (organized by C. Hartmann, F. Nobile, and T. Sullivan): "Predictive multiscale modelling—from homogenization theory to data-driven coarse graining."
This workshop is at the boundary between analytical (“bottom-up”) and data-driven coarse-graining methods, and will discuss ways to systematically use effective dynamics for performing system tasks such as estimation, filtering and prediction, in a data-driven framework, with a special focus on statistical and Bayesian inference techniques.
Both workshops are described in further detail in the attached pdf document. The topics of the two workshops have some important aspects in common, for example the perspective of uncertainty quantification (UQ) and statistical inference, predictive modelling, and data assimilation. It is therefore not a coincidence that several of the potential attendees proposed below are shared between the two workshops. One significant difference is that the first proposed workshop has a much stronger focus on computation, algorithms and software.
 P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos. Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework. J. Chem. Phys., 137:144103, 2012.
 C. Bayer, H. Hoel, A. Kadir, P. Plechac, M. Sandberg, A. Szepessy. Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. Appl. Math. Research Express, 2015:329–417, 2015.
 C. Hartmann, J.C. Latorre, W. Zhang, and G. A. Pavliotis. Optimal control of multiscale systems using reduced-order models. J. Computational Dynamics, 1:279–306, 2014.
 G. Hummer. Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilib-
rium and replica molecular dynamics simulations. New J. Phys., 7:34–48, 2005.
 T. Kirchdoerfer and M. Ortiz. Data-driven computational mechanics. Comp. Meth. Appl. Mech. Eng., 304:81–101, 2016.
 C. Kuehn. A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics. Physica D, 240(12):1020–1035, 2011.
 A.J. Majda and B. Gershgorin. Improving model fidelity and sensitivity for complex systems through
empirical information theory. Proc. Natl. Acad. Sci. USA, 108(25):10044–10049, 2011.
 H. Meidani, J. B. Hooper, D. Bedrov, and R. M. Kirby. Calibration and ranking of coarse-grained models
in molecular simulation using Bayesian formalism. Int. J. Uncertain. Quantif., 7(2):99–115, 2017.
 G. Pavliotis, Y. Pokern, and A.M. Stuart. Parameter estimation for multiscale diffusions: an overview. In: Statistical Methods for Stochastic Differential Equations. M. Kessler, A. Lindner, and M. Sorensen (Eds.), Chapman & Hall/CRC, pp. 429–471, 2012.
 F. Rizzi, H.N. Najm, B.J. Debusschere, K. Sargsyan, M. Salloum, H. Adalsteinsson, and O.M. Knio. Uncertainty Quantification in MD Simulations. Part I: Forward Propagation. Multiscale Model. Simul.,