Timothy S. Carpenter

Loïc Pottier, Konstantia Georgouli, Timothy S. Carpenter et al.

Computational models have become one of the prevalent methods to model complex phenomena. To accurately model complex interactions, such as detailed biomolecular interactions, scientists often rely on multiscale models comprised of several internal models operating at difference scales, ranging from microscopic to macroscopic length and time scales. Bridging the gap between different time and length scales has historically been challenging but the advent of newer machine learning (ML) approaches has shown promise for tackling that task. Multiscale models require massive amounts of computational power and a powerful workflow management system. Orchestrating ML-driven multiscale studies on parallel systems with thousands of nodes is challenging, the workflow must schedule, allocate and control thousands of simulations operating at different scales. Here, we discuss the massively parallel Multiscale Machine-Learned Modeling Infrastructure (MuMMI), a multiscale workflow management infrastructure, that can orchestrate thousands of molecular dynamics (MD) simulations operating at different timescales, spanning from millisecond to nanosecond. More specifically, we introduce a novel version of MuMMI called "mini-MuMMI". Mini-MuMMI is a curated version of MuMMI designed to run on modest HPC systems or even laptops whereas MuMMI requires larger HPC systems. We demonstrate mini-MuMMI utility by exploring RAS-RAF membrane interactions and discuss the different challenges behind the generalization of multiscale workflows and how mini-MuMMI can be leveraged to target a broader range of applications outside of MD and RAS-RAF interactions.

Timothy Carpenter, Ilias Diakonikolas, Anastasios Sidiropoulos et al.

We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the first upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on $\mathbb{R}^d$, for all $d \geq 4$. Prior to this work, no finite sample upper bound was known for this estimator in more than $3$ dimensions. In more detail, we prove that for any $d \geq 1$ and $ε>0$, given $\tilde{O}_d((1/ε)^{(d+3)/2})$ samples drawn from an unknown log-concave density $f_0$ on $\mathbb{R}^d$, the MLE outputs a hypothesis $h$ that with high probability is $ε$-close to $f_0$, in squared Hellinger loss. A sample complexity lower bound of $Ω_d((1/ε)^{(d+1)/2})$ was previously known for any learning algorithm that achieves this guarantee. We thus establish that the sample complexity of the log-concave MLE is near-optimal, up to an $\tilde{O}(1/ε)$ factor.