At this colloquium, we are happy to welcome:

Lucio Galeati

Modelling turbulent fluids by noise: theoretical challenges

Incompressible fluids can display very irregular and chaotic behaviour in regions where they are turbulent, which makes them hard to model and predict. Mathematically, this is related to the challenge of understanding the Navier-Stokes equations, especially at very high Reynolds numbers. Kolmogorov first proposed in the '40s to switch to a more statistical perspective, in order to understand the universal patterns displayed by (homogeneous and isotropic) turbulent fluids. More recently, several theoretical works have suggested to incorporate a specific type of noise in PDEs of interest, as a proxy for the action of the turbulent small scales of a fluid. In this talk, I will first provide a short overview of these novel approaches and illustrate some theoretical results about the resulting stochastic PDEs (SPDEs). In the final part, I will then focus on some recent progress we are making in the mathematical understanding of a synthetic model for passive scalar turbulence, first proposed by Kraichnan in the 60s. Based on joint works with M. Maurelli, F. Grotto, U. Pappalettera and T. Drivas.

Fishbowl Discussion

From micro to macro: How to come up with simple macroscipic models based on the knowledge of the microscpic mathematical model of a system

Frank Noé

Scalable emulation of protein equilibrium ensembles with generative deep learning

Following the sequence and structure revolutions, predicting the dynamical mechanisms of proteins that implement biological function remains an outstanding scientific challenge. Several experimental techniques and molecular dynamics (MD) simulations can, in principle, determine conformational states, binding configurations and their probabilities, but suffer from low throughput. Here we develop a Biomolecular Emulator (BioEmu), a generative deep learning system that can generate thousands of statistically independent samples from the protein structure ensemble per hour on a single graphical processing unit. By leveraging novel training methods and vast data of protein structures, over 200 milliseconds of MD simulation, and experimental protein stabilities, BioEmu's protein ensembles represent equilibrium in a range of challenging and practically relevant metrics. Qualitatively, BioEmu samples many functionally relevant conformational changes, ranging from formation of cryptic pockets, over unfolding of specific protein regions, to large-scale domain rearrangements. Quantitatively, BioEmu samples protein conformations with relative free energy errors around 1 kcal/mol, as validated against millisecond-timescale MD simulation and experimentally-measured protein stabilities. By simultaneously emulating structural ensembles and thermodynamic properties, BioEmu reveals mechanistic insights, such as the causes for fold destabilization of mutants, and can efficiently provide experimentally-testable hypotheses.