The optimization of open-loop shallow geothermal systems, which includes both design and operational aspects, is an important research area aimed at improving their efficiency and sustainability and the effective management of groundwater as a shallow geothermal resource. This paper investigates various approaches to address optimization problems arising from these research and implementation questions about GWHP systems. The identified optimization approaches are thoroughly analyzed based on criteria such as computational cost and applicability. Moreover, a novel classification scheme is introduced that categorizes the approaches according to the types of groundwater simulation model and the optimization algorithm used. Simulation models are divided into two types: numerical and simplified (analytical or data-driven) models, while optimization algorithms are divided into gradient-based and derivative-free algorithms. Finally, a comprehensive review of existing approaches in the literature is provided, highlighting their strengths and limitations and offering recommendations for both the use of existing approaches and the development of new, improved ones in this field.
相關內容
The statistical analysis of group studies in neuroscience is particularly challenging due to the complex spatio-temporal nature of the data, its multiple levels and the inter-individual variability in brain responses. In this respect, traditional ANOVA-based studies and linear mixed effects models typically provide only limited exploration of the dynamic of the group brain activity and variability of the individual responses potentially leading to overly simplistic conclusions and/or missing more intricate patterns. In this study we propose a novel method based on functional Principal Components Analysis and Bayesian model-based clustering to simultaneously assess group effects and individual deviations over the most important temporal features in the data. This method provides a thorough exploration of group differences and individual deviations in neuroscientific group studies without compromising on the spatio-temporal nature of the data. By means of a simulation study we demonstrate that the proposed model returns correct classification in different clustering scenarios under low and high of noise levels in the data. Finally we consider a case study using Electroencephalogram data recorded during an object recognition task where our approach provides new insights into the underlying brain mechanisms generating the data and their variability.
In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function $\mathfrak{J}$ defined on dyadic cubes. We determine the exact upper order in terms of the critical value of the corresponding $\mathfrak{J}$-partition function, and we are able to provide upper and lower bounds in term of fractal-geometric quantities. With properly chosen $\mathfrak{J}$, our new approach has applications in many different areas of mathematics, including the spectral theory of Krein-Feller operators, quantization dimensions of compactly supported probability measures, and the exact asymptotic order for Kolmogorov, Gelfand and linear widths for Sobolev embeddings into $L_{\mu}^p$-spaces.
A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The computational model can be thought of as a two-stage alternating iterative method, which well suits to the well-known Hermitian and skew-Hermitian splitting (HSS) approach, with the particularity here of considering only one inner iteration. Experimental parallel performance comparison is conducted between the generalized minimal residual (GMRES) algorithm, the standard HSS and our asynchronous variant, on both real and complex non-Hermitian linear systems respectively arising from convection-diffusion and structural dynamics problems. A significant gain on execution time is observed in both cases.
In recent literature, for modeling reasons, fractional differential problems have been considered equipped with anti-symmetric boundary conditions. Twenty years ago the anti-reflective boundary conditions were introduced in a context of signal processing and imaging for increasing the quality of the reconstruction of a blurred signal/image contaminated by noise and for reducing the overall complexity to that of few fast sine transforms i.e. to $O(N\log N)$ real arithmetic operations, where $N$ is the number of pixels. Here we consider the anti-symmetric boundary conditions and we introduce the anti-reflective boundary conditions in the context of nonlocal problems of fractional differential type. In the latter context, we study both types of boundary conditions, which in reality are similar in the essentials, from the perspective of computational efficiency, by considering nontruncated and truncated versions. Several numerical tests, tables, and visualizations are provided and critically discussed.
We consider the numerical approximation of variational problems with orthotropic growth, that is those where the integrand depends strongly on the coordinate directions with possibly different growth in each direction. Under realistic regularity assumptions we derive optimal error estimates. These estimates depend on the existence of an orthotropically stable interpolation operator. Over certain meshes we construct an orthotropically stable interpolant that is also a projection. Numerical experiments illustrate and explore the limits of our theory.
In PDE-constrained optimization, one aims to find design parameters that minimize some objective, subject to the satisfaction of a partial differential equation. A major challenges is computing gradients of the objective to the design parameters, as applying the chain rule requires computing the Jacobian of the design parameters to the PDE's state. The adjoint method avoids this Jacobian by computing partial derivatives of a Lagrangian. Evaluating these derivatives requires the solution of a second PDE with the adjoint differential operator to the constraint, resulting in a backwards-in-time simulation. Particle-based Monte Carlo solvers are often used to compute the solution to high-dimensional PDEs. However, such solvers have the drawback of introducing noise to the computed results, thus requiring stochastic optimization methods. To guarantee convergence in this setting, both the constraint and adjoint Monte Carlo simulations should simulate the same particle trajectories. For large simulations, storing full paths from the constraint equation for re-use in the adjoint equation becomes infeasible due to memory limitations. In this paper, we provide a reversible extension to the family of permuted congruential pseudorandom number generators (PCG). We then use such a generator to recompute these time-reversed paths for the heat equation, avoiding these memory issues.
We develop a theory for the representation of opaque solids as volumetric models. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using exponential volumetric transport. We also derive expressions for the volumetric attenuation coefficient as a functional of the probability distributions of the underlying indicator functions. We generalize our theory to account for isotropic and anisotropic scattering at different parts of the solid, and for representations of opaque solids as implicit surfaces. We derive our volumetric representation from first principles, which ensures that it satisfies physical constraints such as reciprocity and reversibility. We use our theory to explain, compare, and correct previous volumetric representations, as well as propose meaningful extensions that lead to improved performance in 3D reconstruction tasks.
Understanding normalization in contrastive representation learning and out-of-distribution detection
Contrastive representation learning has emerged as an outstanding approach for anomaly detection. In this work, we explore the $\ell_2$-norm of contrastive features and its applications in out-of-distribution detection. We propose a simple method based on contrastive learning, which incorporates out-of-distribution data by discriminating against normal samples in the contrastive layer space. Our approach can be applied flexibly as an outlier exposure (OE) approach, where the out-of-distribution data is a huge collective of random images, or as a fully self-supervised learning approach, where the out-of-distribution data is self-generated by applying distribution-shifting transformations. The ability to incorporate additional out-of-distribution samples enables a feasible solution for datasets where AD methods based on contrastive learning generally underperform, such as aerial images or microscopy images. Furthermore, the high-quality features learned through contrastive learning consistently enhance performance in OE scenarios, even when the available out-of-distribution dataset is not diverse enough. Our extensive experiments demonstrate the superiority of our proposed method under various scenarios, including unimodal and multimodal settings, with various image datasets.
We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical investigation, which reveals that for high-dimensional data, the proposed approach may be more efficient than the alternative ones. The accompanying code repository is provided at \url{//shorturl.at/rtuy5}.
We propose an adaptive model-predictive controller that balances driving the system to a goal state and seeking system observations that are informative with respect to the parameters of a nonlinear autoregressive exogenous model. The controller's objective function is derived from an expected free energy functional and contains information-theoretic terms expressing uncertainty over model parameters and output predictions. Experiments illustrate how parameter uncertainty affects the control objective and evaluate the proposed controller for a pendulum swing-up task.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191