Wildfire forecasting is notoriously hard due to the complex interplay of different factors such as weather conditions, vegetation types and human activities. Deep learning models show promise in dealing with this complexity by learning directly from data. However, to inform critical decision making, we argue that we need models that are right for the right reasons; that is, the implicit rules learned should be grounded by the underlying processes driving wildfires. In that direction, we propose integrating causality with Graph Neural Networks (GNNs) that explicitly model the causal mechanism among complex variables via graph learning. The causal adjacency matrix considers the synergistic effect among variables and removes the spurious links from highly correlated impacts. Our methodology's effectiveness is demonstrated through superior performance forecasting wildfire patterns in the European boreal and mediterranean biome. The gain is especially prominent in a highly imbalanced dataset, showcasing an enhanced robustness of the model to adapt to regime shifts in functional relationships. Furthermore, SHAP values from our trained model further enhance our understanding of the model's inner workings.
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We propose a test problem for Navier-Stokes solvers based on the flow around a cylinder. We choose a range of Reynolds numbers for which the flow is time-dependent but can be characterized as essentially two-dimensional. The test problem requires accurate resolution of chaotic dynamics over a long time interval. It also requires the use of a relatively large computational domain, part of which is curved, and it requires evaluation of derivatives of the solution and pressure on the curved boundary. We review the performance of different finite element methods for the proposed range of Reynolds numbers. These tests indicate that some of the most established methods do not capture the correct behavior.
We provide a condition monitoring system for wind farms, based on normal behaviour modelling using a probabilistic multi-layer perceptron with transfer learning via fine-tuning. The model predicts the output power of the wind turbine under normal behaviour based on features retrieved from supervisory control and data acquisition (SCADA) systems. Its advantages are that (i) it can be trained with SCADA data of at least a few years, (ii) it can incorporate all SCADA data of all wind turbines in a wind farm as features, (iii) it assumes that the output power follows a normal density with heteroscedastic variance and (iv) it can predict the output of one wind turbine by borrowing strength from the data of all other wind turbines in a farm. Probabilistic guidelines for condition monitoring are given via a CUSUM control chart. We illustrate the performance of our model in a real SCADA data example which provides evidence that it outperforms other probabilistic prediction models.
Unsupervised clustering of wafer map defect patterns is challenging because the appearance of certain defect patterns varies significantly. This includes changing shape, location, density, and rotation of the defect area on the wafer. We present a harvesting approach, which can cluster even challenging defect patterns of wafer maps well. Our approach makes use of a well-known, three-step procedure: feature extraction, dimension reduction, and clustering. The novelty in our approach lies in repeating dimensionality reduction and clustering iteratively while filtering out one cluster per iteration according to its silhouette score. This method leads to an improvement of clustering performance in general and is especially useful for difficult defect patterns. The low computational effort allows for a quick assessment of large datasets and can be used to support manual labeling efforts. We benchmark against related approaches from the literature and show improved results on a real-world industrial dataset.
Myocardial Infarction is a main cause of mortality globally, and accurate risk prediction is crucial for improving patient outcomes. Machine Learning techniques have shown promise in identifying high-risk patients and predicting outcomes. However, patient data often contain vast amounts of information and missing values, posing challenges for feature selection and imputation methods. In this article, we investigate the impact of the data preprocessing task and compare three ensembles boosted tree methods to predict the risk of mortality in patients with myocardial infarction. Further, we use the Tree Shapley Additive Explanations method to identify relationships among all the features for the performed predictions, leveraging the entirety of the available data in the analysis. Notably, our approach achieved a superior performance when compared to other existing machine learning approaches, with an F1-score of 91,2% and an accuracy of 91,8% for LightGBM without data preprocessing.
We show that (local) confluence of terminating locally constrained rewrite systems is undecidable, even when the underlying theory is decidable. Several confluence criteria for logically constrained rewrite systems are known. These were obtained by replaying existing proofs for plain term rewrite systems in a constrained setting, involving a non-trivial effort. We present a simple transformation from logically constrained rewrite systems to term rewrite systems such that critical pairs of the latter correspond to constrained critical pairs of the former. The usefulness of the transformation is illustrated by lifting the advanced confluence results based on (almost) development closed critical pairs as well as on parallel critical pairs to the constrained setting.
Time series forecasting is an important problem and plays a key role in a variety of applications including weather forecasting, stock market, and scientific simulations. Although transformers have proven to be effective in capturing dependency, its quadratic complexity of attention mechanism prevents its further adoption in long-range time series forecasting, thus limiting them attend to short-range range. Recent progress on state space models (SSMs) have shown impressive performance on modeling long range dependency due to their subquadratic complexity. Mamba, as a representative SSM, enjoys linear time complexity and has achieved strong scalability on tasks that requires scaling to long sequences, such as language, audio, and genomics. In this paper, we propose to leverage a hybrid framework Mambaformer that internally combines Mamba for long-range dependency, and Transformer for short range dependency, for long-short range forecasting. To the best of our knowledge, this is the first paper to combine Mamba and Transformer architecture in time series data. We investigate possible hybrid architectures to combine Mamba layer and attention layer for long-short range time series forecasting. The comparative study shows that the Mambaformer family can outperform Mamba and Transformer in long-short range time series forecasting problem. The code is available at //github.com/XiongxiaoXu/Mambaformerin-Time-Series.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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