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Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy. However, the simultaneous training of NNs on energies and forces, which are a prerequisite for, e.g., molecular dynamics simulations, can be demanding. In this work, we present an improved NN architecture based on the previous GM-NN model [V. Zaverkin and J. K\"astner, J. Chem. Theory Comput. 16, 5410-5421 (2020)], which shows an improved prediction accuracy and considerably reduced training times. Moreover, we extend the applicability of Gaussian moment-based interatomic potentials to periodic systems and demonstrate the overall excellent transferability and robustness of the respective models. The fast training by the improved methodology is a pre-requisite for training-heavy workflows such as active learning or learning-on-the-fly. Comment: Manuscript accepted for publication in J. Chem. Theory Comput.; Code published at https://gitlab.com/zaverkin_v/gmnn

Knowledge Distillation, as a model compression technique, has received great attention. The knowledge of a well-performed teacher is distilled to a student with a small architecture. The architecture of the small student is often chosen to be similar to their teacher's, with fewer layers or fewer channels, or both. However, even with the same number of FLOPs or parameters, the students with different architecture can achieve different generalization ability. The configuration of a student architecture requires intensive network architecture engineering. In this work, instead of designing a good student architecture manually, we propose to search for the optimal student automatically. Based on L1-norm optimization, a subgraph from the teacher network topology graph is selected as a student, the goal of which is to minimize the KL-divergence between student's and teacher's outputs. We verify the proposal on CIFAR10 and CIFAR100 datasets. The empirical experiments show that the learned student architecture achieves better performance than ones specified manually. We also visualize and understand the architecture of the found student.

In this paper we consider the next-to-next-to-leading order total cross section of Higgs boson pair production in the large top quark mass limit and compute four expansion terms in $1/m_t^2$. Good convergence is observed below the top quark threshold, which makes our results a valuable input for approximation methods which aim for next-to-next-to-leading order corrections over the whole kinematic range. We present details on various steps of our calculation; in particular, we provide results for three- and four-particle phase-space master integrals and describe in detail the evaluation of the collinear counterterms. 50 pages, 15 figures

In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically provide guarantees that such systems satisfy certain safety or invariance conditions. We analyze the possibility of automatically generating such guarantees in the form of constraints on parameters. We illustrate our methods on several examples 39 pages

We present a novel method to search for structures of coherently aligned patterns in ultra-high energy cosmic-ray arrival directions simultaneously across the entire sky. This method can be used to obtain information on the Galactic magnetic field, in particular the integrated component perpendicular to the line of sight, from cosmic-ray data only. Using a likelihood-ratio approach, neighboring cosmic rays are related by rotatable, elliptically shaped density distributions and the significance of their alignment with respect to circular distributions is evaluated. In this way, a vector field tangential to the celestial sphere is fitted which approximates the local deflections in cosmic magnetic fields if significant deflection structures are detected. The sensitivity of the method is evaluated on the basis of astrophysical simulations of the ultra-high energy cosmic-ray sky, where a discriminative power between isotropic and signal-induced scenarios is found. 14 pages, 15 figures

The study of fault-tolerant data structures for various network design problems is a prominent area of research in computer science. Likewise, the study of NP-Complete problems lies at the heart of computer science with numerous results in algorithms and complexity. In this paper we raise the question of computing fault tolerant solutions to NP-Complete problems; that is computing a solution that can survive the "failure" of a few constituent elements. This notion has appeared in a variety of theoretical and practical settings such as estimating network reliability, kernelization (aka instance compression), approximation algorithms and so on. In this paper, we seek to highlight these questions for further research. As a concrete example, we study the fault-tolerant version of the classical Feedback Vertex Set (FVS) problem, that we call Fault Tolerant Feedback Vertex Set (FT-FVS). Recall that, in FVS the input is a graph $G$ and the objective is to compute a minimum subset of vertices $S$ such that $G-S$ is a forest. In FT-FVS, the objective is to compute a minimum subset $S$ of vertices such that $G - (S \setminus \{v\})$ is a forest for any $v \in V(G)$. Here the vertex $v$ denotes a single vertex fault. We show that this problem is NP-Complete, and then present a constant factor approximation algorithm as well as an FPT-algorithm parameterized by the solution size. We believe that the question of computing fault tolerant solutions to various NP-Complete problems is an interesting direction for future research.

Abstract We analyze extremes of traffic flow profiles composed of traffic counts over a day. The data is essentially curves and determining which trajectory should be classified as extreme is not straight forward. To assess the extremes of the traffic flow curves in a coherent way, we use a directional definition of extremeness and apply the dimension reduction technique called principal component analysis (PCA) in an asymmetric norm. In the classical PCA one reduces the dimensions of the data by projecting it in the direction of the largest variation of the projection around its mean. In the PCA in an asymmetric norm one chooses the projection directions, such that the asymmetrically weighted variation around a tail index – an expectile – of the data is the largest possible. Expectiles are tail measures that generalize the mean in a similar manner as quantiles generalize the median. Focusing on the asymmetrically weighted variation around an expectile of the data, we find the appropriate projection directions and the low dimensional representation of the traffic flow profiles that uncover different patterns in their extremes. Using the traffic flow data from the roundabout on Ernst-Reuter-Platz in the city center of Berlin, Germany, we estimate, visualize and interpret the resulting principal expectile components. The corresponding directional extremes of the traffic flow profiles are simple to identify and to connect to their location- and time-related specifics. Their shapes are driven by their scores on each principal expectile component which is useful for extracting and analyzing traffic patterns. We utilize the double cross-validation for determining the optimal component number and forecast traffic flow profiles based on the estimated model. Our approach to dimensionality reduction towards the directional extremes of traffic flow extends the related methodological basis and gives promising results for subsequent analysis, prediction and control of the reflected patterns.

AbstractIn this paper our goal is to define a renormalized dissipative measure-valued (rDMV) solution of compressible Navier–Stokes system for fluids with non-monotone pressure–density relation. We prove existence of rDMV solutions and establish a suitable relative energy inequality. Moreover we obtain the weak (measure-valued)–strong uniqueness property of this rDMV solution with the help of relative energy inequality.