We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations. We present extensive experiments and theoretical error estimates to demonstrate that PINNs provide a very easy to implement, fast, robust and accurate method for simulating radiative transfer. We also present a PINN based algorithm for simulating inverse problems for radiative transfer efficiently.
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Embedding methods transform the knowledge graph into a continuous, low-dimensional space, facilitating inference and completion tasks. Existing methods are mainly divided into two types: translational distance models and semantic matching models. A key challenge in translational distance models is their inability to effectively differentiate between 'head' and 'tail' entities in graphs. To address this problem, a novel location-sensitive embedding (LSE) method has been developed. LSE innovatively modifies the head entity using relation-specific mappings, conceptualizing relations as linear transformations rather than mere translations. The theoretical foundations of LSE, including its representational capabilities and its connections to existing models, have been thoroughly examined. A more streamlined variant, LSE-d, which employs a diagonal matrix for transformations to enhance practical efficiency, is also proposed. Experiments conducted on four large-scale KG datasets for link prediction show that LSEd either outperforms or is competitive with state-of-the-art related works.
Jet tagging is a critical yet challenging classification task in particle physics. While deep learning has transformed jet tagging and significantly improved performance, the lack of a large-scale public dataset impedes further enhancement. In this work, we present JetClass, a new comprehensive dataset for jet tagging. The JetClass dataset consists of 100 M jets, about two orders of magnitude larger than existing public datasets. A total of 10 types of jets are simulated, including several types unexplored for tagging so far. Based on the large dataset, we propose a new Transformer-based architecture for jet tagging, called Particle Transformer (ParT). By incorporating pairwise particle interactions in the attention mechanism, ParT achieves higher tagging performance than a plain Transformer and surpasses the previous state-of-the-art, ParticleNet, by a large margin. The pre-trained ParT models, once fine-tuned, also substantially enhance the performance on two widely adopted jet tagging benchmarks. The dataset, code and models are publicly available at //github.com/jet-universe/particle_transformer.
This study introduces the Lower Ricci Curvature (LRC), a novel, scalable, and scale-free discrete curvature designed to enhance community detection in networks. Addressing the computational challenges posed by existing curvature-based methods, LRC offers a streamlined approach with linear computational complexity, making it well-suited for large-scale network analysis. We further develop an LRC-based preprocessing method that effectively augments popular community detection algorithms. Through comprehensive simulations and applications on real-world datasets, including the NCAA football league network, the DBLP collaboration network, the Amazon product co-purchasing network, and the YouTube social network, we demonstrate the efficacy of our method in significantly improving the performance of various community detection algorithms.
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions deviating from strict linearity up to some adjustable threshold, thereby accommodating a comprehensive and pragmatically relevant set of functions. The derived confidence regions can be cast as constraints within a Mixed Integer Linear Programming framework, enabling optimisation of linear objectives. This representation enables robust optimization and the extraction of confidence intervals for specific parameter coordinates. Unlike previous methods, the confidence region can be empty, which can be used for hypothesis testing. Finally, we validate the empirical applicability of our method on synthetic data.
The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of differential-algebraic equations (DAEs). Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness.
Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
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