We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve PDE- and ODE-constrained optimization problems on scenes with a complex geometry. It support static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. We implement our approach on top of the open-source PolyFEM library, and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and in physical validations.
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Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples can be difficult through standard methods. Inference can also be highly sensitive to the choice of threshold. Too low a threshold choice leads to bias in the fit of the extreme value model, while too high a choice leads to unnecessary additional uncertainty in the estimation of model parameters. In this paper, we develop a novel methodology for automated threshold selection that directly tackles this bias-variance trade-off. We also develop a method to account for the uncertainty in this threshold choice and propagate this uncertainty through to high quantile inference. Through a simulation study, we demonstrate the effectiveness of our method for threshold selection and subsequent extreme quantile estimation. We apply our method to the well-known, troublesome example of the River Nidd dataset.
We present a novel metric for generative modeling evaluation, focusing primarily on generative networks. The method uses dendrograms to represent real and fake data, allowing for the divergence between training and generated samples to be computed. This metric focus on mode collapse, targeting generators that are not able to capture all modes in the training set. To evaluate the proposed method it is introduced a validation scheme based on sampling from real datasets, therefore the metric is evaluated in a controlled environment and proves to be competitive with other state-of-the-art approaches.
The migration of Twitter users to Mastodon following Elon Musk's acquisition presents a unique opportunity to study collective behavior and gain insights into the drivers of coordinated behavior in online media. We analyzed the social network and the public conversations of about 75,000 migrated users and observed that the temporal trace of their migrations is compatible with a phenomenon of social influence, as described by a compartmental epidemic model of information diffusion. Drawing from prior research on behavioral change, we delved into the factors that account for variations across different Twitter communities in the effectiveness of the spreading of the influence to migrate. Communities in which the influence process unfolded more rapidly exhibit lower density of social connections, higher levels of signaled commitment to migrating, and more emphasis on shared identity and exchange of factual knowledge in the community discussion. These factors account collectively for 57% of the variance in the observed data. Our results highlight the joint importance of network structure, commitment, and psycho-linguistic aspects of social interactions in describing grassroots collective action, and contribute to deepen our understanding of the mechanisms driving processes of behavior change of online groups.
Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions. Two regression methods based on fusion penalties are presented. The first one is a generalization of the variable fusion methodology based on the 1-nearest neighbor. The second one, called group fusion lasso, assumes some grouping structure of conditions and allows for homogeneity among the regression coefficient functions within groups. A finite sample numerical simulation and an application on EEG data are presented.
This paper considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are the noise in the sample values and the unstructured nature of the sample locations. This paper proposes the eigenmatrix, a data-driven construction with desired approximate eigenvalues and eigenvectors. The eigenmatrix offers a new way for these sparse recovery problems. Numerical results are provided to demonstrate the efficiency of the proposed method.
Accurately predicting the lifetime of battery cells in early cycles holds tremendous value for battery research and development as well as numerous downstream applications. This task is rather challenging because diverse conditions, such as electrode materials, operating conditions, and working environments, collectively determine complex capacity-degradation behaviors. However, current prediction methods are developed and validated under limited aging conditions, resulting in questionable adaptability to varied aging conditions and an inability to fully benefit from historical data collected under different conditions. Here we introduce a universal deep learning approach that is capable of accommodating various aging conditions and facilitating effective learning under low-resource conditions by leveraging data from rich conditions. Our key finding is that incorporating inter-cell feature differences, rather than solely considering single-cell characteristics, significantly increases the accuracy of battery lifetime prediction and its cross-condition robustness. Accordingly, we develop a holistic learning framework accommodating both single-cell and inter-cell modeling. A comprehensive benchmark is built for evaluation, encompassing 401 battery cells utilizing 5 prevalent electrode materials across 168 cycling conditions. We demonstrate remarkable capabilities in learning across diverse aging conditions, exclusively achieving 10% prediction error using the first 100 cycles, and in facilitating low-resource learning, almost halving the error of single-cell modeling in many cases. More broadly, by breaking the learning boundaries among different aging conditions, our approach could significantly accelerate the development and optimization of lithium-ion batteries.
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning ensemble forecasting model based on the Dirichlet process. Initially, the learning rate is sampled with three basis distributions as hyperparameters to convert the infinite mixture into a finite one. All checkpoints are collected to establish a deep learning sub-model pool, and weight adjustment and diversity strategies are developed during the combination process. The main advantage of this method is its ability to generate the required base learners through a single training process, utilizing the decaying strategy to tackle the challenge posed by the stochastic nature of gradient descent in determining the optimal learning rate. To ensure the method's generalizability and competitiveness, this paper conducts an empirical analysis using the weekly dataset from the M4 competition and explores sensitivity to the number of models to be combined. The results demonstrate that the ensemble model proposed offers substantial improvements in prediction accuracy and stability compared to a single benchmark model.
We present a new Krylov subspace recycling method for solving a linear system of equations, or a sequence of slowly changing linear systems. Our new method, named GMRES-SDR, combines randomized sketching and deflated restarting in a way that avoids orthogononalizing a full Krylov basis. We provide new theory which characterizes sketched GMRES with and without augmentation as a projection method using a semi-inner product. We present results of numerical experiments demonstrating the effectiveness of GMRES-SDR over competitor methods such as GMRES-DR and GCRO-DR.
We propose and compare methods for the analysis of extreme events in complex systems governed by PDEs that involve random parameters, in situations where we are interested in quantifying the probability that a scalar function of the system's solution is above a threshold. If the threshold is large, this probability is small and its accurate estimation is challenging. To tackle this difficulty, we blend theoretical results from large deviation theory (LDT) with numerical tools from PDE-constrained optimization. Our methods first compute parameters that minimize the LDT-rate function over the set of parameters leading to extreme events, using adjoint methods to compute the gradient of this rate function. The minimizers give information about the mechanism of the extreme events as well as estimates of their probability. We then propose a series of methods to refine these estimates, either via importance sampling or geometric approximation of the extreme event sets. Results are formulated for general parameter distributions and detailed expressions are provided when Gaussian distributions. We give theoretical and numerical arguments showing that the performance of our methods is insensitive to the extremeness of the events we are interested in. We illustrate the application of our approach to quantify the probability of extreme tsunami events on shore. Tsunamis are typically caused by a sudden, unpredictable change of the ocean floor elevation during an earthquake. We model this change as a random process, which takes into account the underlying physics. We use the one-dimensional shallow water equation to model tsunamis numerically. In the context of this example, we present a comparison of our methods for extreme event probability estimation, and find which type of ocean floor elevation change leads to the largest tsunamis on shore.
The increased use of AI systems is associated with multi-faceted societal, environmental, and economic consequences. These include non-transparent decision-making processes, discrimination, increasing inequalities, rising energy consumption and greenhouse gas emissions in AI model development and application, and an increasing concentration of economic power. By considering the multi-dimensionality of sustainability, this paper takes steps towards substantiating the call for an overarching perspective on "sustainable AI". It presents the SCAIS Framework (Sustainability Criteria and Indicators for Artificial Intelligence Systems) which contains a set 19 sustainability criteria for sustainable AI and 67 indicators that is based on the results of a critical review and expert workshops. This interdisciplinary approach contributes a unique holistic perspective to facilitate and structure the discourse on sustainable AI. Further, it provides a concrete framework that lays the foundation for developing standards and tools to support the conscious development and application of AI systems.
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