Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an atomistic model for glass-forming liquids. This is a notoriously difficult task, as it amounts to ergodically exploring the complex free energy landscape of a disordered and frustrated many-body system. We optimize a normalizing flow model to successfully transform high-temperature configurations of a dense liquid into low-temperature ones, near the glass transition. We perform a detailed comparative analysis with established enhanced sampling techniques developed in the physics literature to assess and rank the performance of normalizing flows against state-of-the-art algorithms. We demonstrate that machine learning methods are very promising, showing a large speedup over conventional molecular dynamics. Normalizing flows show performances comparable to parallel tempering and population annealing, while still falling far behind the swap Monte Carlo algorithm. Our study highlights the potential of generative machine learning models in scientific computing for complex systems, but also points to some of its current limitations and the need for further improvement.

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Background: Radiological follow-up of diffuse low-grade gliomas (LGGs) growth is challenging. Approximative visual assessment still predominates over objective quantification due to the complexity of the pathology. The infiltrating character, diffuse borders and presence of surgical cavities demand LGG-based linear measurement rules to efficiently and precisely assess LGG evolution over time.Methods: We compared optimized 1D, 2D, and 3D linear measurements with manual volume segmentation as a reference to assess LGG tumor growth in 36 patients with LGG (340 magnetic resonance imaging scans), using the clinically important mean tumor diameter (MTD) and the velocity diameter expansion (VDE). LGG-specific progression thresholds were established using the high-grade gliomas-based RECIST, Macdonald, and RANO criteria, comparing the sensitivity to identify progression/non-progression for each linear method compared to the ground truth established by the manual segmentation.Results: 3D linear volume approximation correlated strongly with manually segmented volume. It also showed the highest sensitivity for progression detection. The MTD showed a comparable result, whereas the VDE highlighted that caution is warranted in the case of small tumors with multiple residues. Novel LGG-specific progression thresholds, or the critical change in estimated tumor volume, were increased for the 3D (from 40% to 52%) and 2D methods (from 25% to 33%) and decreased for the 1D method (from 20% to 16%). Using the 3D method allowed a ~5-minute time gain.Conclusions: While manual volumetric assessment remains the gold standard for calculating growth rate, the 3D linear method is the best time-efficient standardized alternative for radiological evaluation of LGGs in routine use.