Modern HPC systems are increasingly relying on greater core counts and wider vector registers. Thus, applications need to be adapted to fully utilize these hardware capabilities. One class of applications that can benefit from this increase in parallelism are molecular dynamics simulations. In this paper, we describe our efforts at modernizing the ESPResSo++ molecular dynamics simulation package by restructuring its particle data layout for efficient memory accesses and applying vectorization techniques to benefit the calculation of short-range non-bonded forces, which results in an overall three times speedup and serves as a baseline for further optimizations. We also implement fine-grained parallelism for multi-core CPUs through HPX, a C++ runtime system which uses lightweight threads and an asynchronous many-task approach to maximize concurrency. Our goal is to evaluate the performance of an HPX-based approach compared to the bulk-synchronous MPI-based implementation. This requires the introduction of an additional layer to the domain decomposition scheme that defines the task granularity. On spatially inhomogeneous systems, which impose a corresponding load-imbalance in traditional MPI-based approaches, we demonstrate that by choosing an optimal task size, the efficient work-stealing mechanisms of HPX can overcome the overhead of communication resulting in an overall 1.4 times speedup compared to the baseline MPI version.
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Understanding how different networks relate to each other is key for obtaining a greater insight into complex systems. Here, we introduce an intuitive yet powerful framework to characterise the relationship between two networks comprising the same nodes. We showcase our framework by decomposing the shortest paths between nodes as being contributed uniquely by one or the other source network, or redundantly by either, or synergistically by the two together. Our approach takes into account the networks' full topology, and it also provides insights at multiple levels of resolution: from global statistics, to individual paths of different length. We show that this approach is widely applicable, from brains to the London public transport system. In humans and across 123 other mammalian species, we demonstrate that reliance on unique contributions by long-range white matter fibers is a conserved feature of mammalian structural brain networks. Across species, we also find that efficient communication relies on significantly greater synergy between long-range and short-range fibers than expected by chance, and significantly less redundancy. Our framework may find applications to help decide how to trade-off different desiderata when designing network systems, or to evaluate their relative presence in existing systems, whether biological or artificial.
Personalized recommendations form an important part of today's internet ecosystem, helping artists and creators to reach interested users, and helping users to discover new and engaging content. However, many users today are skeptical of platforms that personalize recommendations, in part due to historically careless treatment of personal data and data privacy. Now, businesses that rely on personalized recommendations are entering a new paradigm, where many of their systems must be overhauled to be privacy-first. In this article, we propose an algorithm for personalized recommendations that facilitates both precise and differentially-private measurement. We consider advertising as an example application, and conduct offline experiments to quantify how the proposed privacy-preserving algorithm affects key metrics related to user experience, advertiser value, and platform revenue compared to the extremes of both (private) non-personalized and non-private, personalized implementations.
Stochastic inversion problems are typically encountered when it is wanted to quantify the uncertainty affecting the inputs of computer models. They consist in estimating input distributions from noisy, observable outputs, and such problems are increasingly examined in Bayesian contexts where the targeted inputs are affected by stochastic uncertainties. In this regard, a stochastic input can be qualified as meaningful if it explains most of the output uncertainty. While such inverse problems are characterized by identifiability conditions, constraints of "signal to noise", that can formalize this meaningfulness, should be accounted for within the definition of the model, prior to inference. This article investigates the possibility of forcing a solution to be meaningful in the context of parametric uncertainty quantification, through the tools of global sensitivity analysis and information theory (variance, entropy, Fisher information). Such forcings have mainly the nature of constraints placed on the input covariance, and can be made explicit by considering linear or linearizable models. Simulated experiments indicate that, when injected into the modeling process, these constraints can limit the influence of measurement or process noise on the estimation of the input distribution, and let hope for future extensions in a full non-linear framework, for example through the use of linear Gaussian mixtures.
Multiphysics processes in fractured porous media is a research field of importance for several subsurface applications and has received considerable attention over the last decade. The dynamics are characterised by strong couplings between processes as well as interaction between the processes and the structure of the fractured medium itself. The rich range of behavior calls for explorative mathematical modelling, such as experimentation with constitutive laws and novel coupling concepts between physical processes. Moreover, efficient simulations of the strong couplings between multiphysics processes and geological structures require the development of tailored numerical methods. We present a modelling framework and its implementation in the open-source simulation toolbox PorePy, which is designed for rapid prototyping of multiphysics processes in fractured porous media. PorePy uses a mixed-dimensional representation of the fracture geometry and generally applies fully implicit couplings between processes. The code design follows the paradigms of modularity and differentiable programming, which together allow for extreme flexibility in experimentation with governing equations with minimal changes to the code base. The code integrity is supported by a multilevel testing framework ensuring the reliability of the code. We present our modelling framework within a context of thermo-poroelasticity in deformable fractured porous media, illustrating the close relation between the governing equations and the source code. We furthermore discuss the design of the testing framework and present simulations showcasing the extendibility of PorePy, as well as the type of results that can be produced by mixed-dimensional simulation tools.
Hardware implementations of Spiking Neural Networks (SNNs) represent a promising approach to edge-computing for applications that require low-power and low-latency, and which cannot resort to external cloud-based computing services. However, most solutions proposed so far either support only relatively small networks, or take up significant hardware resources, to implement large networks. To realize large-scale and scalable SNNs it is necessary to develop an efficient asynchronous communication and routing fabric that enables the design of multi-core architectures. In particular the core interface that manages inter-core spike communication is a crucial component as it represents the bottleneck of Power-Performance-Area (PPA) especially for the arbitration architecture and the routing memory. In this paper we present an arbitration mechanism with the corresponding asynchronous encoding pipeline circuits, based on hierarchical arbiter trees. The proposed scheme reduces the latency by more than 70% in sparse-event mode, compared to the state-of-the-art arbitration architectures, with lower area cost. The routing memory makes use of asynchronous Content Addressable Memory (CAM) with Current Sensing Completion Detection (CSCD), which saves approximately 46% energy, and achieves a 40% increase in throughput against conventional asynchronous CAM using configurable delay lines, at the cost of only a slight increase in area. In addition as it radically reduces the core interface resources in multi-core neuromorphic processors, the arbitration architecture and CAM architecture we propose can be also applied to a wide range of general asynchronous circuits and systems.
The application of deep learning to non-stationary temporal datasets can lead to overfitted models that underperform under regime changes. In this work, we propose a modular machine learning pipeline for ranking predictions on temporal panel datasets which is robust under regime changes. The modularity of the pipeline allows the use of different models, including Gradient Boosting Decision Trees (GBDTs) and Neural Networks, with and without feature engineering. We evaluate our framework on financial data for stock portfolio prediction, and find that GBDT models with dropout display high performance, robustness and generalisability with reduced complexity and computational cost. We then demonstrate how online learning techniques, which require no retraining of models, can be used post-prediction to enhance the results. First, we show that dynamic feature projection improves robustness by reducing drawdown in regime changes. Second, we demonstrate that dynamical model ensembling based on selection of models with good recent performance leads to improved Sharpe and Calmar ratios of out-of-sample predictions. We also evaluate the robustness of our pipeline across different data splits and random seeds with good reproducibility.
Sparse principal component analysis (SPCA) is a popular tool for dimensionality reduction in high-dimensional data. However, there is still a lack of theoretically justified Bayesian SPCA methods that can scale well computationally. One of the major challenges in Bayesian SPCA is selecting an appropriate prior for the loadings matrix, considering that principal components are mutually orthogonal. We propose a novel parameter-expanded coordinate ascent variational inference (PX-CAVI) algorithm. This algorithm utilizes a spike and slab prior, which incorporates parameter expansion to cope with the orthogonality constraint. Besides comparing to two popular SPCA approaches, we introduce the PX-EM algorithm as an EM analogue to the PX-CAVI algorithm for comparison. Through extensive numerical simulations, we demonstrate that the PX-CAVI algorithm outperforms these SPCA approaches, showcasing its superiority in terms of performance. We study the posterior contraction rate of the variational posterior, providing a novel contribution to the existing literature. The PX-CAVI algorithm is then applied to study a lung cancer gene expression dataset. The R package VBsparsePCA with an implementation of the algorithm is available on the Comprehensive R Archive Network (CRAN).
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.
This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression, regularization tools are needed to compute estimators for the functional slope. The traditional methods are based on dimension reduction or penalization combined with maximum likelihood or quasi--likelihood techniques and for that reason, they may be affected by misclassified points especially if they are associated to functional covariates with atypical behaviour. The proposal given in this paper adapts some of the best practices used when the covariates are finite--dimensional to provide reliable estimations. Under regularity conditions, consistency of the resulting estimators and rates of convergence for the predictions are derived. A numerical study illustrates the finite sample performance of the proposed method and reveals its stability under different contamination scenarios. A real data example is also presented.
In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geometry or a set of parametrizable geometries. Thus, there remains the need to train a new model for a new geometry, even if it is only slightly modified. With this work we introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization. This technique is based on a combination of a U-Net-like CNN and well established discretization methods from the field of the finite difference method.The results of our physics-aware CNN are compared to a state-of-the-art data-based approach. Additionally, it is also shown how our approach performs when combined with the data-based approach.
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