Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMeaningful uncertainties from deep neural network surrogates of large-scale numerical simulations
60
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural networks (DNNs) can serve as highly-accurate surrogate models, with the capacity to handle diverse datatypes, offering tremendous speed-ups for prediction and many other downstream tasks. An important use-case for these surrogates is the comparison between simulations and experiments; prediction uncertainty estimates are crucial for making such comparisons meaningful, yet standard DNNs do not provide them. In this work we define the fundamental requirements for a DNN to be useful for scientific applications, and demonstrate a general variational inference approach to equip predictions of scalar and image data from a DNN surrogate model trained on inertial confinement fusion simulations with calibrated Bayesian uncertainties. Critically, these uncertainties are interpretable, meaningful and preserve physics-correlations in the predicted quantities.
rate research
Read More
Faced with continuously increasing scale of data, original back-propagation neural network based machine learning algorithm presents two non-trivial challenges: huge amount of data makes it difficult to maintain both efficiency and accuracy; redundant data aggravates the system workload. This project is mainly focused on the solution to the issues above, combining deep learning algorithm with cloud computing platform to deal with large-scale data. A MapReduce-based handwriting character recognizer will be designed in this project to verify the efficiency improvement this mechanism will achieve on training and practical large-scale data. Careful discussion and experiment will be developed to illustrate how deep learning algorithm works to train handwritten digits data, how MapReduce is implemented on deep learning neural network, and why this combination accelerates computation. Besides performance, the scalability and robustness will be mentioned in this report as well. Our system comes with two demonstration software that visually illustrates our handwritten digit recognition/encoding application.
Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as $mathrm{NNGP}$. While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of $mathrm{NNGP}$ for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. Especially, with certain scale priors, we obtain heavy-tailed stochastic processes, and we recover Students $t$ processes in the case of inverse gamma priors. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for $mathrm{NNGP}$. We present a practical posterior-inference algorithm for the scale mixture of $mathrm{NNGP}$ and empirically demonstrate its usefulness on regression and classification tasks.
This study proposes a novel Graph Convolutional Neural Network with Data-driven Graph Filter (GCNN-DDGF) model that can learn hidden heterogeneous pairwise correlations between stations to predict station-level hourly demand in a large-scale bike-sharing network. Two architectures of the GCNN-DDGF model are explored; GCNNreg-DDGF is a regular GCNN-DDGF model which contains the convolution and feedforward blocks, and GCNNrec-DDGF additionally contains a recurrent block from the Long Short-term Memory neural network architecture to capture temporal dependencies in the bike-sharing demand series. Furthermore, four types of GCNN models are proposed whose adjacency matrices are based on various bike-sharing system data, including Spatial Distance matrix (SD), Demand matrix (DE), Average Trip Duration matrix (ATD), and Demand Correlation matrix (DC). These six types of GCNN models and seven other benchmark models are built and compared on a Citi Bike dataset from New York City which includes 272 stations and over 28 million transactions from 2013 to 2016. Results show that the GCNNrec-DDGF performs the best in terms of the Root Mean Square Error, the Mean Absolute Error and the coefficient of determination (R2), followed by the GCNNreg-DDGF. They outperform the other models. Through a more detailed graph network analysis based on the learned DDGF, insights are obtained on the black box of the GCNN-DDGF model. It is found to capture some information similar to details embedded in the SD, DE and DC matrices. More importantly, it also uncovers hidden heterogeneous pairwise correlations between stations that are not revealed by any of those matrices.
Computer simulations are invaluable tools for scientific discovery. However, accurate simulations are often slow to execute, which limits their applicability to extensive parameter exploration, large-scale data analysis, and uncertainty quantification. A promising route to accelerate simulations by building fast emulators with machine learning requires large training datasets, which can be prohibitively expensive to obtain with slow simulations. Here we present a method based on neural architecture search to build accurate emulators even with a limited number of training data. The method successfully accelerates simulations by up to 2 billion times in 10 scientific cases including astrophysics, climate science, biogeochemistry, high energy density physics, fusion energy, and seismology, using the same super-architecture, algorithm, and hyperparameters. Our approach also inherently provides emulator uncertainty estimation, adding further confidence in their use. We anticipate this work will accelerate research involving expensive simulations, allow more extensive parameters exploration, and enable new, previously unfeasible computational discovery.
We show experimentally that the accuracy of a trained neural network can be predicted surprisingly well by looking only at its weights, without evaluating it on input data. We motivate this task and introduce a formal setting for it. Even when using simple statistics of the weights, the predictors are able to rank neural networks by their performance with very high accuracy (R2 score more than 0.98). Furthermore, the predictors are able to rank networks trained on different, unobserved datasets and with different architectures. We release a collection of 120k convolutional neural networks trained on four different datasets to encourage further research in this area, with the goal of understanding network training and performance better.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
