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Register a new userUsing Deep Learning to Explore Local Physical Similarity for Global-scale Bridging in Thermal-hydraulic Simulation
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Current system thermal-hydraulic codes have limited credibility in simulating real plant conditions, especially when the geometry and boundary conditions are extrapolated beyond the range of test facilities. This paper proposes a data-driven approach, Feature Similarity Measurement FFSM), to establish a technical basis to overcome these difficulties by exploring local patterns using machine learning. The underlying local patterns in multiscale data are represented by a set of physical features that embody the information from a physical system of interest, empirical correlations, and the effect of mesh size. After performing a limited number of high-fidelity numerical simulations and a sufficient amount of fast-running coarse-mesh simulations, an error database is built, and deep learning is applied to construct and explore the relationship between the local physical features and simulation errors. Case studies based on mixed convection have been designed for demonstrating the capability of data-driven models in bridging global scale gaps.
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Several applications in the scientific simulation of physical systems can be formulated as control/optimization problems. The computational models for such systems generally contain hyperparameters, which control solution fidelity and computational expense. The tuning of these parameters is non-trivial and the general approach is to manually `spot-check for good combinations. This is because optimal hyperparameter configuration search becomes impractical when the parameter space is large and when they may vary dynamically. To address this issue, we present a framework based on deep reinforcement learning (RL) to train a deep neural network agent that controls a model solve by varying parameters dynamically. First, we validate our RL framework for the problem of controlling chaos in chaotic systems by dynamically changing the parameters of the system. Subsequently, we illustrate the capabilities of our framework for accelerating the convergence of a steady-state CFD solver by automatically adjusting the relaxation factors of discretized Navier-Stokes equations during run-time. The results indicate that the run-time control of the relaxation factors by the learned policy leads to a significant reduction in the number of iterations for convergence compared to the random selection of the relaxation factors. Our results point to potential benefits for learning adaptive hyperparameter learning strategies across different geometries and boundary conditions with implications for reduced computational campaign expenses. footnote{Data and codes available at url{https://github.com/Romit-Maulik/PAR-RL}}
Numerical simulation models associated with hydraulic engineering take a wide array of data into account to produce predictions: rainfall contribution to the drainage basin (characterized by soil nature, infiltration capacity and moisture), current water height in the river, topography, nature and geometry of the river bed, etc. This data is tainted with uncertainties related to an imperfect knowledge of the field, measurement errors on the physical parameters calibrating the equations of physics, an approximation of the latter, etc. These uncertainties can lead the model to overestimate or underestimate the flow and height of the river. Moreover, complex assimilation models often require numerous evaluations of physical solvers to evaluate these uncertainties, limiting their use for some real-time operational applications. In this study, we explore the possibility of building a predictor for river height at an observation point based on drainage basin time series data. An array of data-driven techniques is assessed for this task, including statistical models, machine learning techniques and deep neural network approaches. These are assessed on several metrics, offering an overview of the possibilities related to hydraulic time-series. An important finding is that for the same hydraulic quantity, the best predictors vary depending on whether the data is produced using a physical model or real observations.
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a visual Sudok problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.
While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity learning has considered either global-level graph-graph interactions or low-level node-node interactions, however ignoring the rich cross-level interactions (e.g., between each node of one graph and the other whole graph). In this paper, we propose a multi-level graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects in an end-to-end fashion. In particular, the proposed MGMN consists of a node-graph matching network for effectively learning cross-level interactions between each node of one graph and the other whole graph, and a siamese graph neural network to learn global-level interactions between two input graphs. Furthermore, to compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks with different sizes in order to evaluate the effectiveness and robustness of our models. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks. Compared with previous work, MGMN also exhibits stronger robustness as the sizes of the two input graphs increase.
We propose a novel learning framework to answer questions such as if a user is purchasing a shirt, what other items will (s)he need with the shirt? Our framework learns distributed representations for items from available textual data, with the learned representations representing items in a latent space expressing functional complementarity as well similarity. In particular, our framework places functionally similar items close together in the latent space, while also placing complementary items closer than non-complementary items, but farther away than similar items. In this study, we introduce a new dataset of similar, complementary, and negative items derived from the Amazon co-purchase dataset. For evaluation purposes, we focus our approach on clothing and fashion verticals. As per our knowledge, this is the first attempt to learn similar and complementary relationships simultaneously through just textual title metadata. Our framework is applicable across a broad set of items in the product catalog and can generate quality complementary item recommendations at scale.
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