Explore a seminar on weak convergence and invertible coarse-graining in probability theory and molecular dynamics. Delve into Prof. Grant M. Rotskoff's discussion of combining force-matching based coarse-graining with invertible neural networks to invert coarse-graining maps statistically. Learn about the thermodynamic equivalence principle, challenges in coarse-graining biomolecular systems, and the application of machine learning in this context. Discover how this approach can recover fine-grained free energy surfaces from coarse-grained sampling in non-trivial biomolecular systems. Gain insights into metastability in protein folding/misfolding and the capture of large- and small-scale observables through this innovative method.