Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical methods. This study examines a collection of exponential integration methods, known for their good numerical properties on wave representation, to investigate their efficacy in solving the wave equation with ABC. The purpose of this research is to assess the performance of these methods. We compare a recently proposed Exponential Integration based on Faber polynomials with well-established Krylov exponential methods alongside a high-order Runge-Kutta scheme and low-order classical methods. Through our analysis, we found that the exponential integrator based on the Krylov subspace exhibits the best convergence results among the high-order methods. We also discovered that high-order methods can achieve computational efficiency similar to lower-order methods while allowing for considerably larger time steps. Most importantly, the possibility of undertaking large time steps could be used for important memory savings in full waveform inversion imaging problems.
相關內容
Integration：Integration, the VLSI Journal。
Explanation：集成，VLSI雜志。
Publisher：Elsevier。
SIT：
The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using reproducing kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function.
In this manuscript, we combine non-intrusive reduced order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM. The prediction of the mixed formulation is given by a convex linear combination of the predictions of some previously-trained ROMs, where we assign to each model a space-dependent weight. The ROMs taken into account to build the mixed model exploit different reduction techniques, such as Proper Orthogonal Decomposition (POD) and AutoEncoders (AE), and/or different approximation techniques, namely a Radial Basis Function Interpolation (RBF), a Gaussian Process Regression (GPR) or a feed-forward Artificial Neural Network (ANN). The contribution of each model is retained with higher weights in the regions where the model performs best, and, vice versa, with smaller weights where the model has a lower accuracy with respect to the other models. Finally, a regression technique, namely a Random Forest, is exploited to evaluate the weights for unseen conditions. The performance of the aggregated model is evaluated on two different test cases: the 2D flow past a NACA 4412 airfoil, with an angle of attack of 5 degrees, having as parameter the Reynolds number varying between 1e5 and 1e6 and a transonic flow over a NACA 0012 airfoil, considering as parameter the angle of attack. In both cases, the mixed-ROM has provided improved accuracy with respect to each individual ROM technique.
The sparsity-ranked lasso (SRL) has been developed for model selection and estimation in the presence of interactions and polynomials. The main tenet of the SRL is that an algorithm should be more skeptical of higher-order polynomials and interactions *a priori* compared to main effects, and hence the inclusion of these more complex terms should require a higher level of evidence. In time series, the same idea of ranked prior skepticism can be applied to the possibly seasonal autoregressive (AR) structure of the series during the model fitting process, becoming especially useful in settings with uncertain or multiple modes of seasonality. The SRL can naturally incorporate exogenous variables, with streamlined options for inference and/or feature selection. The fitting process is quick even for large series with a high-dimensional feature set. In this work, we discuss both the formulation of this procedure and the software we have developed for its implementation via the **fastTS** R package. We explore the performance of our SRL-based approach in a novel application involving the autoregressive modeling of hourly emergency room arrivals at the University of Iowa Hospitals and Clinics. We find that the SRL is considerably faster than its competitors, while producing more accurate predictions.
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based on exponentially decaying entries of the global system matrices and an appropriate partition of unity, it is proved that the superposition of localized solutions is appropriately close to the solution of the (global) implicit scheme. It is thereby justified that the localized (and especially parallel) computation on multiple overlapping subdomains is reasonable. Moreover, a re-start is introduced after a certain amount of time steps to maintain a moderate overlap of the subdomains. Overall, the approach may be understood as a domain decomposition strategy in space on successive short time intervals that completely avoids inner iterations. Numerical examples are presented.
We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen to be, up to negligeable remainders, independent. We use Stein-Malliavin calculus to prove that this wavelet variation satisfies a multidimensional Central Limit Theorem, with an explicit bound for the Wasserstein distance.
Aqueous solubility is a valuable yet challenging property to predict. Computing solubility using first-principles methods requires accounting for the competing effects of entropy and enthalpy, resulting in long computations for relatively poor accuracy. Data-driven approaches, such as deep learning, offer improved accuracy and computational efficiency but typically lack uncertainty quantification. Additionally, ease of use remains a concern for any computational technique, resulting in the sustained popularity of group-based contribution methods. In this work, we addressed these problems with a deep learning model with predictive uncertainty that runs on a static website (without a server). This approach moves computing needs onto the website visitor without requiring installation, removing the need to pay for and maintain servers. Our model achieves satisfactory results in solubility prediction. Furthermore, we demonstrate how to create molecular property prediction models that balance uncertainty and ease of use. The code is available at //github.com/ur-whitelab/mol.dev, and the model is usable at //mol.dev.
Modern consumer devices must execute multimedia applications that exhibit high resource utilization. In order to efficiently execute these applications, the dynamic memory subsystem needs to be optimized. This complex task can be tackled in two complementary ways: optimizing the application source code or designing custom dynamic memory management mechanisms. Currently, the first approach has been well established, and several automatic methodologies have been proposed. Regarding the second approach, software engineers often write custom dynamic memory managers from scratch, which is a difficult and error-prone work. This paper presents a novel way to automatically generate custom dynamic memory managers optimizing both performance and memory usage of the target application. The design space is pruned using grammatical evolution converging to the best dynamic memory manager implementation for the target application. Our methodology achieves important improvements (62.55\% and 30.62\% better on average in performance and memory usage, respectively) when its results are compared to five different general-purpose dynamic memory managers.
One of the main challenges for interpreting black-box models is the ability to uniquely decompose square-integrable functions of non-independent random inputs into a sum of functions of every possible subset of variables. However, dealing with dependencies among inputs can be complicated. We propose a novel framework to study this problem, linking three domains of mathematics: probability theory, functional analysis, and combinatorics. We show that, under two reasonable assumptions on the inputs (non-perfect functional dependence and non-degenerate stochastic dependence), it is always possible to decompose such a function uniquely. This generalizes the well-known Hoeffding decomposition. The elements of this decomposition can be expressed using oblique projections and allow for novel interpretability indices for evaluation and variance decomposition purposes. The properties of these novel indices are studied and discussed. This generalization offers a path towards a more precise uncertainty quantification, which can benefit sensitivity analysis and interpretability studies whenever the inputs are dependent. This decomposition is illustrated analytically, and the challenges for adopting these results in practice are discussed.
Implicit solvers for atmospheric models are often accelerated via the solution of a preconditioned system. For block preconditioners this typically involves the factorisation of the (approximate) Jacobian for the coupled system into a Helmholtz equation for some function of the pressure. Here we present a preconditioner for the compressible Euler equations with a flux form representation of the potential temperature on the Lorenz grid using mixed finite elements. This formulation allows for spatial discretisations that conserve both energy and potential temperature variance. By introducing the dry thermodynamic entropy as an auxiliary variable for the solution of the algebraic system, the resulting preconditioner is shown to have a similar block structure to an existing preconditioner for the material form transport of potential temperature on the Charney-Phillips grid, and to be more efficient and stable than either this or a previous Helmholtz preconditioner for the flux form transport of density weighted potential temperature on the Lorenz grid for a one dimensional thermal bubble configuration. The new preconditioner is further verified against standard two dimensional test cases in a vertical slice geometry.
Time-lapse seismic monitoring necessitates integrated workflows that combine seismic and reservoir modeling to enhance reservoir property estimation. We present a feasibility study of an end-to-end inversion framework that directly inverts for permeability from prestack time-lapse seismic data. To assess the method's robustness, we design experiments focusing on its sensitivity to initial models and potential errors in modeling. Our study leverages the Compass model to simulate CO2 storage in saline aquifers, which is derived from well and seismic data from the North Sea, a candidate site for geological carbon storage.
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