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Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econometricians began to turn their attention to the problem in the presence of serial dependence. The existing procedure for testing cross-sectional independence with serial correlation is based on the sum of the sample cross-sectional correlations, which generally performs well when the alternative has dense cross-sectional correlations, but suffers from low power against sparse alternatives. To deal with sparse alternatives, we propose a test based on the maximum of the squared sample cross-sectional correlations. Furthermore, we propose a combined test to combine the p-values of the max based and sum based tests, which performs well under both dense and sparse alternatives. The combined test relies on the asymptotic independence of the max based and sum based test statistics, which we show rigorously. We show that the proposed max based and combined tests have attractive theoretical properties and demonstrate the superior performance via extensive simulation results. We apply the two new tests to analyze the weekly returns on the securities in the S\&P 500 index under the Fama-French three-factor model, and confirm the usefulness of the proposed combined test in detecting cross-sectional independence.

A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the discrete trial space, and more importantly, modifies the trilinear term in the stream-function vorticity formulation of the incompressible 2D Navier-Stokes and the von K\'{a}rm\'{a}n equations. This enables the first efficient and reliable a posteriori error estimates for the 2D Navier-Stokes equations in the stream-function vorticity formulation for Morley, two discontinuous Galerkin, $C^0$ interior penalty, and WOPSIP discretizations with piecewise quadratic polynomials.

Existing deepfake speech detection systems lack generalizability to unseen attacks (i.e., samples generated by generative algorithms not seen during training). Recent studies have explored the use of universal speech representations to tackle this issue and have obtained inspiring results. These works, however, have focused on innovating downstream classifiers while leaving the representation itself untouched. In this study, we argue that characterizing the long-term temporal dynamics of these representations is crucial for generalizability and propose a new method to assess representation dynamics. Indeed, we show that different generative models generate similar representation dynamics patterns with our proposed method. Experiments on the ASVspoof 2019 and 2021 datasets validate the benefits of the proposed method to detect deepfakes from methods unseen during training, significantly improving on several benchmark methods.

Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.

Current physics-informed (standard or operator) neural networks still rely on accurately learning the initial conditions of the system they are solving. In contrast, standard numerical methods evolve such initial conditions without needing to learn these. In this study, we propose to improve current physics-informed deep learning strategies such that initial conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a DeepONet is applied multiple times to time step a solution, the resulting function is continuous.

Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. As a result, simulating such phenomena becomes unaffordable for many-query applications, such as parametrized systems with multiple scale-dependent features. Traditional projection-based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales. Specifically, we employ sparse mesh-informed neural networks (MINNs), which handle both spatial dependencies in the solutions and model parameters simultaneously. We evaluate the performance of this strategy on benchmark problems and then apply it to approximate a real-life problem involving the impact of microcirculation in transport phenomena through the tissue microenvironment.

We present a training method with linguistic speech regularization that improves the robustness of spontaneous speech synthesis methods with filled pause (FP) insertion. Spontaneous speech synthesis is aimed at producing speech with human-like disfluencies, such as FPs. Because modeling the complex data distribution of spontaneous speech with a rich FP vocabulary is challenging, the quality of FP-inserted synthetic speech is often limited. To address this issue, we present a method for synthesizing spontaneous speech that improves robustness to diverse FP insertions. Regularization is used to stabilize the synthesis of the linguistic speech (i.e., non-FP) elements. To further improve robustness to diverse FP insertions, it utilizes pseudo-FPs sampled using an FP word prediction model as well as ground-truth FPs. Our experiments demonstrated that the proposed method improves the naturalness of synthetic speech with ground-truth and predicted FPs by 0.24 and 0.26, respectively.

We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can be recognized as monotonic and (weakly) scalable functions within the framework of nonlinear Perron-Frobenius theory. This fact enables us to provide conditions for the existence of fixed points of nonnegative neural networks having inputs and outputs of the same dimension, and these conditions are weaker than those recently obtained using arguments in convex analysis. Furthermore, we prove that the shape of the fixed point set of nonnegative neural networks with nonnegative weights and biases is an interval, which under mild conditions degenerates to a point. These results are then used to obtain the existence of fixed points of more general nonnegative neural networks. From a practical perspective, our results contribute to the understanding of the behavior of autoencoders, and the main theoretical results are verified in numerical simulations using the Modified National Institute of Standards and Technology (MNIST) dataset.

This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the generalization error of these algorithms with bounded updates, extending beyond the scope of previous works that only focused on Stochastic Gradient Descent (SGD). Our approach introduces two main novelties: 1) we reformulate the mutual information as the uncertainty of updates, providing a new perspective, and 2) instead of using the chaining rule of mutual information, we employ a variance decomposition technique to decompose information across iterations, allowing for a simpler surrogate process. We analyze our generalization bound under various settings and demonstrate improved bounds when the model dimension increases at the same rate as the number of training data samples. To bridge the gap between theory and practice, we also examine the previously observed scaling behavior in large language models. Ultimately, our work takes a further step for developing practical generalization theories.

We study scalable machine learning models for full event reconstruction in high-energy electron-positron collisions based on a highly granular detector simulation. Particle-flow (PF) reconstruction can be formulated as a supervised learning task using tracks and calorimeter clusters or hits. We compare a graph neural network and kernel-based transformer and demonstrate that both avoid quadratic memory allocation and computational cost while achieving realistic PF reconstruction. We show that hyperparameter tuning on a supercomputer significantly improves the physics performance of the models. We also demonstrate that the resulting model is highly portable across hardware processors, supporting Nvidia, AMD, and Intel Habana cards. Finally, we demonstrate that the model can be trained on highly granular inputs consisting of tracks and calorimeter hits, resulting in a competitive physics performance with the baseline. Datasets and software to reproduce the studies are published following the findable, accessible, interoperable, and reusable (FAIR) principles.