Networks beyond pairwise interactions: Structure and dynamics

Molecular dynamics (MD) simulation techniques are widely used for various natural science applications. Increasingly, machine learning (ML) force field (FF) models begin to replace ab-initio simulations by predicting forces directly from atomic structures. Despite significant progress in this area, such techniques are primarily benchmarked by their force/energy prediction errors, even though the practical use case would be to produce realistic MD trajectories. We aim to fill this gap by introducing a novel benchmark suite for ML MD simulation. We curate representative MD systems, including water, organic molecules, peptide, and materials, and design evaluation metrics corresponding to the scientific objectives of respective systems. We benchmark a collection of state-of-the-art (SOTA) ML FF models and illustrate, in particular, how the commonly benchmarked force accuracy is not well aligned with relevant simulation metrics. We demonstrate when and how selected SOTA methods fail, along with offering directions for further improvement. Specifically, we identify stability as a key metric for ML models to improve. Our benchmark suite comes with a comprehensive open-source codebase for training and simulation with ML FFs to facilitate further work.

Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations

Global machine learning force fields, with the capacity to capture collective interactions in molecular systems, now scale up to a few dozen atoms due to considerable growth of model complexity with system size. For larger molecules, locality assumptions are introduced, with the consequence that nonlocal interactions are not described. Here, we develop an exact iterative approach to train global symmetric gradient domain machine learning (sGDML) force fields (FFs) for several hundred atoms, without resorting to any potentially uncontrolled approximations. All atomic degrees of freedom remain correlated in the global sGDML FF, allowing the accurate description of complex molecules and materials that present phenomena with far-reaching characteristic correlation lengths. We assess the accuracy and efficiency of sGDML on a newly developed MD22 benchmark dataset containing molecules from 42 to 370 atoms. The robustness of our approach is demonstrated in nanosecond path-integral molecular dynamics simulations for supramolecular complexes in the MD22 dataset.

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Accurate global machine learning force fields for molecules with hundreds of atoms

In this paper, we investigate the network of information dissemination that emerges from group communication in the increasingly popular WhatsApp platform. We aim to reveal properties of the underlying structure that facilitates content spread in the system, despite limitations the application imposes in group membership. Our analyses reveal a number of strongly connected user communities that cross the boundaries of groups, suggesting that such boundaries offer little constraint to information spread. We also show that, despite frequent changes in community membership, there are consistent co-sharing activities among some users which, even while holding broad content diversity, lead to high coverage of the network in terms of groups and individual users.

Beyond Groups: Uncovering Dynamic Communities on the WhatsApp Network of Information Dissemination

In recent years, hypergraph generalizations of many graph cut problems have been introduced and analyzed as a way to better explore and understand complex systems and datasets characterized by multiway relationships. Recent work has made use of a generalized hypergraph cut function which for a hypergraph $\mathcal{H} = (V,E)$ can be defined by associating each hyperedge $e \in E$ with a splitting function ${\bf w}_e$, which assigns a penalty to each way of separating the nodes of $e$. When each ${\bf w}_e$ is a submodular cardinality-based splitting function, meaning that ${\bf w}_e(S) = g(|S|)$ for some concave function $g$, previous work has shown that a generalized hypergraph cut problem can be reduced to a directed graph cut problem on an augmented node set. However, existing reduction procedures often result in a dense graph, even when the hypergraph is sparse, which leads to slow runtimes for algorithms that run on the reduced graph. 
We introduce a new framework of sparsifying hypergraph-to-graph reductions, where a hypergraph cut defined by submodular cardinality-based splitting functions is $(1+\varepsilon)$-approximated by a cut on a directed graph. Our techniques are based on approximating concave functions using piecewise linear curves. For $\varepsilon > 0$ we need at most $O(\varepsilon^{-1}|e| \log |e|)$ edges to reduce any hyperedge $e$, which leads to faster runtimes for approximating generalized hypergraph $s$-$t$ cut problems. For the machine learning heuristic of a clique splitting function, our approach requires only $O(|e| \varepsilon^{-1/2} \log \log \frac{1}{\varepsilon})$ edges. This sparsification leads to faster approximate min $s$-$t$ graph cut algorithms for certain classes of co-occurrence graphs. Finally, we apply our sparsification techniques to develop approximation algorithms for minimizing sums of cardinality-based submodular functions.

Augmented Sparsifiers for Generalized Hypergraph Cuts.

Molecular dynamics (MD) simulation is the workhorse of various scientific domains but is limited by high computational cost. Learning-based force fields have made major progress in accelerating ab-initio MD simulation but are still not fast enough for many real-world applications that require long-time MD simulation. In this paper, we adopt a different machine learning approach where we coarse-grain a physical system using graph clustering, and model the system evolution with a very large time-integration step using graph neural networks. A novel score-based GNN refinement module resolves the long-standing challenge of long-time simulation instability. Despite only trained with short MD trajectory data, our learned simulator can generalize to unseen novel systems and simulate for much longer than the training trajectories. Properties requiring 10-100 ns level long-time dynamics can be accurately recovered at several-orders-of-magnitude higher speed than classical force fields. We demonstrate the effectiveness of our method on two realistic complex systems: (1) single-chain coarse-grained polymers in implicit solvent; (2) multi-component Li-ion polymer electrolyte systems.

Simulate Time-integrated Coarse-grained Molecular Dynamics with Geometric Machine Learning

Large Question-and-Answer (Q&A) platforms support diverse knowledge curation on the Web. While researchers have studied user behavior on the platforms in a variety of contexts, there is relatively little insight into important by-products of user behavior that also encode knowledge. Here, we analyze and model the macroscopic structure of tags applied by users to annotate and catalog questions, using a collection of 168 Stack Exchange websites. We find striking similarity in tagging structure across these Stack Exchange communities, even though each community evolves independently (albeit under similar guidelines). Using our empirical findings, we develop a simple generative model that creates random bipartite graphs of tags and questions. Our model accounts for the tag frequency distribution but does not explicitly account for co-tagging correlations. Even under these constraints, we demonstrate empirically and theoretically that our model can reproduce a number of statistical properties of the co-tagging graph that links tags appearing in the same post.

Modelling and analysis of tagging networks in Stack Exchange communities

Modeling and Analysis of Tagging Networks in Stack Exchange Communities

Current model-based reinforcement learning methods struggle when operating from complex visual scenes due to their inability to prioritize task-relevant features. To mitigate this problem, we propose learning Task Informed Abstractions (TIA) that explicitly separates reward-correlated visual features from distractors. For learning TIA, we introduce the formalism of Task Informed MDP (TiMDP) that is realized by training two models that learn visual features via cooperative reconstruction, but one model is adversarially dissociated from the reward signal. Empirical evaluation shows that TIA leads to significant performance gains over state-of-the-art methods on many visual control tasks where natural and unconstrained visual distractions pose a formidable challenge.

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Xiang Fu

Papers

Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations

Simulate Time-integrated Coarse-grained Molecular Dynamics with Geometric Machine Learning

Modelling and analysis of tagging networks in Stack Exchange communities

Modeling and Analysis of Tagging Networks in Stack Exchange Communities

Learning Task Informed Abstractions