In this work we present a mixed-dimensional mathematical model to obtain the electric potential and current density in direct current simulations when a thin liner is included in the modelled domain. The liner is used in landfill management to prevent leakage of leachate from the waste body into the underground and is made of a highly-impermeable high-resistivity plastic material. The electrodes and the liner have diameters and thickness respectively that are much smaller than their other dimensions, thus their numerical simulation might be too costly in an equi-dimensional setting. Our approach is to approximate them as objects of lower dimension and derive the corresponding equations. The obtained mixed-dimensional model is validated against laboratory experiments of increasing complexity showing the reliability of the proposed mathematical model.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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We present a novel approach to leverage prior knowledge encapsulated in pre-trained text-to-image diffusion models for blind super-resolution (SR). Specifically, by employing our time-aware encoder, we can achieve promising restoration results without altering the pre-trained synthesis model, thereby preserving the generative prior and minimizing training cost. To remedy the loss of fidelity caused by the inherent stochasticity of diffusion models, we introduce a controllable feature wrapping module that allows users to balance quality and fidelity by simply adjusting a scalar value during the inference process. Moreover, we develop a progressive aggregation sampling strategy to overcome the fixed-size constraints of pre-trained diffusion models, enabling adaptation to resolutions of any size. A comprehensive evaluation of our method using both synthetic and real-world benchmarks demonstrates its superiority over current state-of-the-art approaches.
In data poisoning attacks, an adversary tries to change a model's prediction by adding, modifying, or removing samples in the training data. Recently, ensemble-based approaches for obtaining provable defenses against data poisoning have been proposed where predictions are done by taking a majority vote across multiple base models. In this work, we show that merely considering the majority vote in ensemble defenses is wasteful as it does not effectively utilize available information in the logits layers of the base models. Instead, we propose Run-Off Election (ROE), a novel aggregation method based on a two-round election across the base models: In the first round, models vote for their preferred class and then a second, Run-Off election is held between the top two classes in the first round. Based on this approach, we propose DPA+ROE and FA+ROE defense methods based on Deep Partition Aggregation (DPA) and Finite Aggregation (FA) approaches from prior work. We evaluate our methods on MNIST, CIFAR-10, and GTSRB and obtain improvements in certified accuracy by up to 3%-4%. Also, by applying ROE on a boosted version of DPA, we gain improvements around 12%-27% comparing to the current state-of-the-art, establishing a new state-of-the-art in (pointwise) certified robustness against data poisoning. In many cases, our approach outperforms the state-of-the-art, even when using 32 times less computational power.
We introduce the Collection Space Navigator (CSN), a browser-based visualization tool to explore, research, and curate large collections of visual digital artifacts that are associated with multidimensional data, such as vector embeddings or tables of metadata. Media objects such as images are often encoded as numerical vectors, for e.g. based on metadata or using machine learning to embed image information. Yet, while such procedures are widespread for a range of applications, it remains a challenge to explore, analyze, and understand the resulting multidimensional spaces in a more comprehensive manner. Dimensionality reduction techniques such as t-SNE or UMAP often serve to project high-dimensional data into low dimensional visualizations, yet require interpretation themselves as the remaining dimensions are typically abstract. Here, the Collection Space Navigator provides a customizable interface that combines two-dimensional projections with a set of configurable multidimensional filters. As a result, the user is able to view and investigate collections, by zooming and scaling, by transforming between projections, by filtering dimensions via range sliders, and advanced text filters. Insights that are gained during the interaction can be fed back into the original data via ad hoc exports of filtered metadata and projections. This paper comes with a functional showcase demo using a large digitized collection of classical Western art. The Collection Space Navigator is open source. Users can reconfigure the interface to fit their own data and research needs, including projections and filter controls. The CSN is ready to serve a broad community.
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, given an approximate factor structure, if the cross-sectional dimension of the data, $N$, grows to infinity, we show that: (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.
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value function of optimal control problems, which partially mitigates the dimensionality problem. The method is based on a greedy Hermite kernel interpolation scheme and incorporates context-knowledge by its structure. Especially, the value function surrogate is elegantly enforced to be 0 in the target state, non-negative and constructed as a correction of a linearized model. The algorithm is proposed in a matrix-free way, which circumvents the large-matrix-problem for multivariate Hermite interpolation. For finite time horizons, both convergence of the surrogate to the value function as well as for the surrogate vs. the optimal controlled dynamical system are proven. Experiments support the effectiveness of the scheme, using among others a new academic model that has a scalable dimension and an explicitly given value function. It may also be useful for the community to validate other optimal control approaches.
Statistical data simulation is essential in the development of statistical models and methods as well as in their performance evaluation. To capture complex data structures, in particular for high-dimensional data, a variety of simulation approaches have been introduced including parametric and the so-called plasmode simulations. While there are concerns about the realism of parametrically simulated data, it is widely claimed that plasmodes come very close to reality with some aspects of the "truth'' known. However, there are no explicit guidelines or state-of-the-art on how to perform plasmode data simulations. In the present paper, we first review existing literature and introduce the concept of statistical plasmode simulation. We then discuss advantages and challenges of statistical plasmodes and provide a step-wise procedure for their generation, including key steps to their implementation and reporting. Finally, we illustrate the concept of statistical plasmodes as well as the proposed plasmode generation procedure by means of a public real RNA dataset on breast carcinoma patients.
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting computes empirical risk on a holdout set and halts once (or flags that/when) it begins to increase. Such practice often helps in outputting a well-generalizing model, but justification for why it works is primarily heuristic. We discuss the overfitting problem and explain why standard asymptotic and concentration results do not hold for evaluation with training data. We then proceed to introduce and argue for a hypothesis test by means of which both model performance may be evaluated using training data, and overfitting quantitatively defined and detected. We rely on said concentration bounds which guarantee that empirical means should, with high probability, approximate their true mean to conclude that they should approximate each other. We stipulate conditions under which this test is valid, describe how the test may be used for identifying overfitting, articulate a further nuance according to which distributional shift may be flagged, and highlight an alternative notion of learning which usefully captures generalization in the absence of uniform PAC guarantees.
When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with Bayesian consistency. Otherwise, the resultant probability density function for the difficult to measure quantity or field will not be appropriately clustered around the truth. In particular, the inverse problem should be formulated by evaluating the numerical solution at the true point locations for direct comparison with the point data source. If the data are first fitted to a gridded or meshed field on the computational grid or mesh, and the inverse problem formulated by comparing the numerical solution to the fitted field, the benefits of additional point data values below the grid density will be lost. We demonstrate, with examples in the fields of groundwater hydrology and glaciology, that a consistent formulation can increase the accuracy of results and aid discourse between modellers and observationalists. To do this, we bring point data into the finite element method ecosystem as discontinuous fields on meshes of disconnected vertices. Point evaluation can then be formulated as a finite element interpolation operation (dual-evaluation). This new abstraction is well-suited to automation, including automatic differentiation. We demonstrate this through implementation in Firedrake, which generates highly optimised code for solving PDEs with the finite element method. Our solution integrates with dolfin-adjoint/pyadjoint, allowing PDE-constrained optimisation problems, such as data assimilation, to be solved through forward and adjoint mode automatic differentiation.
Invariant approaches have been remarkably successful in tackling the problem of domain generalization, where the objective is to perform inference on data distributions different from those used in training. In our work, we investigate whether it is possible to leverage domain information from the unseen test samples themselves. We propose a domain-adaptive approach consisting of two steps: a) we first learn a discriminative domain embedding from unsupervised training examples, and b) use this domain embedding as supplementary information to build a domain-adaptive model, that takes both the input as well as its domain into account while making predictions. For unseen domains, our method simply uses few unlabelled test examples to construct the domain embedding. This enables adaptive classification on any unseen domain. Our approach achieves state-of-the-art performance on various domain generalization benchmarks. In addition, we introduce the first real-world, large-scale domain generalization benchmark, Geo-YFCC, containing 1.1M samples over 40 training, 7 validation, and 15 test domains, orders of magnitude larger than prior work. We show that the existing approaches either do not scale to this dataset or underperform compared to the simple baseline of training a model on the union of data from all training domains. In contrast, our approach achieves a significant improvement.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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