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Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models inadequately treat boundary conditions essential for the reliable prediction of such problems. In addition, because of the locally connected nature of GNNs, it is difficult to accurately predict the state after a long time, where interaction between vertices tends to be global. We present our approach termed physics-embedded neural networks that considers boundary conditions and predicts the state after a long time using an implicit method. It is built based on an E(n)-equivariant GNN, resulting in high generalization performance on various shapes. We demonstrate that our model learns flow phenomena in complex shapes and outperforms a well-optimized classical solver and a state-of-the-art machine learning model in speed-accuracy trade-off. Therefore, our model can be a useful standard for realizing reliable, fast, and accurate GNN-based PDE solvers. The code is available at //github.com/yellowshippo/penn-neurips2022.

Electricity grids have become an essential part of daily life, even if they are often not noticed in everyday life. We usually only become particularly aware of this dependence by the time the electricity grid is no longer available. However, significant changes, such as the transition to renewable energy (photovoltaic, wind turbines, etc.) and an increasing number of energy consumers with complex load profiles (electric vehicles, home battery systems, etc.), pose new challenges for the electricity grid. To address these challenges, we propose two first-of-its-kind datasets based on measurements in a broadband powerline communications (PLC) infrastructure. Both datasets FiN-1 and FiN-2, were collected during real practical use in a part of the German low-voltage grid that supplies around 4.4 million people and show more than 13 billion datapoints collected by more than 5100 sensors. In addition, we present different use cases in asset management, grid state visualization, forecasting, predictive maintenance, and novelty detection to highlight the benefits of these types of data. For these applications, we particularly highlight the use of novel machine learning architectures to extract rich information from real-world data that cannot be captured using traditional approaches. By publishing the first large-scale real-world dataset, we aim to shed light on the previously largely unrecognized potential of PLC data and emphasize machine-learning-based research in low-voltage distribution networks by presenting a variety of different use cases.

Finding the initial conditions that led to the current state of the universe is challenging because it involves searching over a vast input space of initial conditions, along with modeling their evolution via tools such as N-body simulations which are computationally expensive. Deep learning has emerged as an alternate modeling tool that can learn the mapping between the linear input of an N-body simulation and the final nonlinear displacements at redshift zero, which can significantly accelerate the forward modeling. However, this does not help reduce the search space for initial conditions. In this paper, we demonstrate for the first time that a deep learning model can be trained for the reverse mapping. We train a V-Net based convolutional neural network, which outputs the linear displacement of an N-body system, given the current time nonlinear displacement and the cosmological parameters of the system. We demonstrate that this neural network accurately recovers the initial linear displacement field over a wide range of scales ($<1$-$2\%$ error up to nearly $k = 1\ \mathrm{Mpc}^{-1}\,h$), despite the ill-defined nature of the inverse problem at smaller scales. Specifically, smaller scales are dominated by nonlinear effects which makes the backward dynamics much more susceptible to numerical and computational errors leading to highly divergent backward trajectories and a one-to-many backward mapping. The results of our method motivate that neural network based models can act as good approximators of the initial linear states and their predictions can serve as good starting points for sampling-based methods to infer the initial states of the universe.

In this paper we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm of the velocity in the convection dominated regime. This bound is pressure robust (the error bound of the velocity does not depend on the pressure) and also convection robust (the constants in the error bounds are independent of the Reynolds number).

The success of a football team depends on various individual skills and performances of the selected players as well as how cohesively they perform. This work proposes a two-stage process for selecting optimal playing eleven of a football team from its pool of available players. In the first stage, for the reference team, a LASSO-induced modified trinomial logistic regression model is derived to analyze the probabilities of the three possible outcomes. The model takes into account strengths of the players in the team as well as those of the opponent, home advantage, and also the effects of individual players and player combinations beyond the recorded performances of these players. Careful use of the LASSO technique acts as an appropriate enabler of the player selection exercise while keeping the number of variables at a reasonable level. Then, in the second stage, a GRASP-type meta-heuristic is implemented for the team selection which maximizes the probability of win for the team. The work is illustrated with English Premier League data from 2008/09 to 2015/16. The application demonstrates that the model in the first stage furnishes valuable insights about the deciding factors for different teams whereas the optimization steps can be effectively used to determine the best possible starting lineup under various circumstances. Based on the adopted model and methodology, we propose a measure of efficiency in team selection by the team management and analyze the performance of EPL teams on this front.

Permutation synchronization is an important problem in computer science that constitutes the key step of many computer vision tasks. The goal is to recover $n$ latent permutations from their noisy and incomplete pairwise measurements. In recent years, spectral methods have gained increasing popularity thanks to their simplicity and computational efficiency. Spectral methods utilize the leading eigenspace $U$ of the data matrix and its block submatrices $U_1,U_2,\ldots, U_n$ to recover the permutations. In this paper, we propose a novel and statistically optimal spectral algorithm. Unlike the existing methods which use $\{U_jU_1^\top\}_{j\geq 2}$, ours constructs an anchor matrix $M$ by aggregating useful information from all the block submatrices and estimates the latent permutations through $\{U_jM^\top\}_{j\geq 1}$. This modification overcomes a crucial limitation of the existing methods caused by the repetitive use of $U_1$ and leads to an improved numerical performance. To establish the optimality of the proposed method, we carry out a fine-grained spectral analysis and obtain a sharp exponential error bound that matches the minimax rate.

Recent works show that speech separation guided diarization (SSGD) is an increasingly promising direction, mainly thanks to the recent progress in speech separation. It performs diarization by first separating the speakers and then applying voice activity detection (VAD) on each separated stream. In this work we conduct an in-depth study of SSGD in the conversational telephone speech (CTS) domain, focusing mainly on low-latency streaming diarization applications. We consider three state-of-the-art speech separation (SSep) algorithms and study their performance both in online and offline scenarios, considering non-causal and causal implementations as well as continuous SSep (CSS) windowed inference. We compare different SSGD algorithms on two widely used CTS datasets: CALLHOME and Fisher Corpus (Part 1 and 2) and evaluate both separation and diarization performance. To improve performance, a novel, causal and computationally efficient leakage removal algorithm is proposed, which significantly decreases false alarms. We also explore, for the first time, fully end-to-end SSGD integration between SSep and VAD modules. Crucially, this enables fine-tuning on real-world data for which oracle speakers sources are not available. In particular, our best model achieves 8.8% DER on CALLHOME, which outperforms the current state-of-the-art end-to-end neural diarization model, despite being trained on an order of magnitude less data and having significantly lower latency, i.e., 0.1 vs. 1 seconds. Finally, we also show that the separated signals can be readily used also for automatic speech recognition, reaching performance close to using oracle sources in some configurations.

The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover's Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.

We review Quasi Maximum Likelihood estimation of factor models for high-dimensional panels of time series. We consider two cases: (1) estimation when no dynamic model for the factors is specified (Bai and Li, 2016); (2) estimation based on the Kalman smoother and the Expectation Maximization algorithm thus allowing to model explicitly the factor dynamics (Doz et al., 2012). Our interest is in approximate factor models, i.e., when we allow for the idiosyncratic components to be mildly cross-sectionally, as well as serially, correlated. Although such setting apparently makes estimation harder, we show, in fact, that factor models do not suffer of the curse of dimensionality problem, but instead they enjoy a blessing of dimensionality property. In particular, we show that if the cross-sectional dimension of the data, $N$, grows to infinity, then: (i) identification of the model is still possible, (ii) the mis-specification error due to the use of an exact factor model log-likelihood vanishes. Moreover, if we let also the sample size, $T$, grow to infinity, we can also consistently estimate all parameters of the model and make inference. The same is true for estimation of the latent factors which can be carried out by weighted least-squares, linear projection, or Kalman filtering/smoothing. We also compare the approaches presented with: Principal Component analysis and the classical, fixed $N$, exact Maximum Likelihood approach. We conclude with a discussion on efficiency of the considered estimators.

Liou-Steffen splitting (AUSM) schemes are popular for low Mach number simulations, however, like many numerical schemes for compressible flow they require careful modification to accurately resolve convective features in this regime. Previous analyses of these schemes usually focus only on a single discrete scheme at the convective limit, only considering flow with acoustic effects empirically, if at all. In our recent paper Hope-Collins & di Mare, 2023 we derived constraints on the artificial diffusion scaling of low Mach number schemes for flows both with and without acoustic effects, and applied this analysis to Roe-type finite-volume schemes. In this paper we form approximate diffusion matrices for the Liou-Steffen splitting, as well as the closely related Zha-Bilgen and Toro-Vasquez splittings. We use the constraints found in Hope-Collins & di Mare, 2023 to derive and analyse the required scaling of each splitting at low Mach number. By transforming the diffusion matrices to the entropy variables we can identify erroneous diffusion terms compared to the ideal form used in Hope-Collins & di Mare, 2023. These terms vanish asymptotically for the Liou-Steffen splitting, but result in spurious entropy generation for the Zha-Bilgen and Toro-Vasquez splittings unless a particular form of the interface pressure is used. Numerical examples for acoustic and convective flow verify the results of the analysis, and show the importance of considering the resolution of the entropy field when assessing schemes of this type.