Purpose: In surgical navigation, pre-operative organ models are presented to surgeons during the intervention to help them in efficiently finding their target. In the case of soft tissue, these models need to be deformed and adapted to the current situation by using intra-operative sensor data. A promising method to realize this are real-time capable biomechanical models. Methods: We train a fully convolutional neural network to estimate a displacement field of all points inside an organ when given only the displacement of a part of the organ's surface. The network trains on entirely synthetic data of random organ-like meshes, which allows us to generate much more data than is otherwise available. The input and output data is discretized into a regular grid, allowing us to fully utilize the capabilities of convolutional operators and to train and infer in a highly parallelized manner. Results: The system is evaluated on in-silico liver models, phantom liver data and human in-vivo breathing data. We test the performance with varying material parameters, organ shapes and amount of visible surface. Even though the network is only trained on synthetic data, it adapts well to the various cases and gives a good estimation of the internal organ displacement. The inference runs at over 50 frames per second. Conclusions: We present a novel method for training a data-driven, real-time capable deformation model. The accuracy is comparable to other registration methods, it adapts very well to previously unseen organs and does not need to be re-trained for every patient. The high inferring speed makes this method useful for many applications such as surgical navigation and real-time simulation.
Our method is inspired by the work of @cite_21 , who have used neural networks to estimate the results of fluid dynamics simulations for real-time applications. One major difference is that fluid dynamics are often computed on regular grids with a fixed number of cells which makes them easier to handle with neural networks. In contrast to this, we need to re-sample the irregular simulation domain before we pass the data to the network.
@cite_21
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Physically based fluid simulation requires much time in numerical calculation to solve Navier-Stokes equations. Especially in grid-based fluid simulation, because of iterative computation, the projection step is much more time-consuming than other steps. In this paper, we propose a novel data-driven projection method using an artificial neural network to avoid iterative computation. Once the grid resolution is decided, our data-driven method could obtain projection results in relatively constant time per grid cell, which is independent of scene complexity. Experimental results demonstrated that our data-driven method drastically speeded up the computation in the projection step. With the growth of grid resolution, the speed-up would increase strikingly. In addition, our method is still applicable in different fluid scenes with some alterations, when computational cost is more important than physical accuracy. Copyright © 2016 John Wiley & Sons, Ltd. Our work explores methods for the data-driven inference of temporal evolutions of physical functions with deep learning techniques. More specifically, we target fluid flow problems, and we propose a novel LSTM-based approach to predict the changes of the pressure field over time. The central challenge in this context is the high dimensionality of Eulerian space-time data sets. Key for arriving at a feasible algorithm is a technique for dimensionality reduction based on convolutional neural networks, as well as a special architecture for temporal prediction. We demonstrate that dense 3D+time functions of physics system can be predicted with neural networks, and we arrive at a neural-network based simulation algorithm with significant practical speed-ups. We demonstrate the capabilities of our method with a series of complex liquid simulations, and with a set of single-phase buoyancy simulations. With a set of trained networks, our method is more than two orders of magnitudes faster than a traditional pressure solver. Additionally, we present and discuss a series of detailed evaluations for the different components of our algorithm. Traditional fluid simulations require large computational resources even for an average sized scene with the main bottleneck being a very small time step size, required to guarantee the stability of the solution. Despite a large progress in parallel computing and efficient algorithms for pressure computation in the recent years, realtime fluid simulations have been possible only under very restricted conditions. In this paper we propose a novel machine learning based approach, that formulates physics-based fluid simulation as a regression problem, estimating the acceleration of every particle for each frame. We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a large time step setting on yet unseen test videos. We used a regression forest to approximate the behaviour of particles observed in the large training set of simulations obtained using a traditional solver. Our GPU implementation led to a speed-up of one to three orders of magnitude compared to the state-of-the-art position-based fluid solver and runs in real-time for systems with up to 2 million particles. In aerodynamics related design, analysis and optimization problems, flow fields are simulated using computational fluid dynamics (CFD) solvers. However, CFD simulation is usually a computationally expensive, memory demanding and time consuming iterative process. These drawbacks of CFD limit opportunities for design space exploration and forbid interactive design. We propose a general and flexible approximation model for real-time prediction of non-uniform steady laminar flow in a 2D or 3D domain based on convolutional neural networks (CNNs). We explored alternatives for the geometry representation and the network architecture of CNNs. We show that convolutional neural networks can estimate the velocity field two orders of magnitude faster than a GPU-accelerated CFD solver and four orders of magnitude faster than a CPU-based CFD solver at a cost of a low error rate. This approach can provide immediate feedback for real-time design iterations at the early stage of design. Compared with existing approximation models in the aerodynamics domain, CNNs enable an efficient estimation for the entire velocity field. Furthermore, designers and engineers can directly apply the CNN approximation model in their design space exploration algorithms without training extra lower-dimensional surrogate models. It was only a matter of time before deep neural networks (DNNs) – deep learning – made their mark in turbulence modelling, or more broadly, in the general area of high-dimensional, complex dynamical systems. In the last decade, DNNs have become a dominant data mining tool for big data applications. Although neural networks have been applied previously to complex fluid flows, the article featured here ( , J. Fluid Mech. , vol. 807, 2016, pp. 155–166) is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models. As one often expects with modern DNNs, performance gains are achieved over competing state-of-the-art methods, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows. We propose the use of deep convolutional neural networks to estimate the transient attributes of a scene from a single image. Transient scene attributes describe both the objective conditions, such as the weather, time of day, and the season, and subjective properties of a scene, such as whether or not the scene seems busy. Recently, convolutional neural networks have been used to achieve state-of-the-art results for many vision problems, from object detection to scene classification, but have not previously been used for estimating transient attributes. We compare several methods for adapting an existing network architecture and present state-of-the-art results on two benchmark datasets. Our method is more accurate and significantly faster than previous methods, enabling real-world applications. Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional functions, potentially of great use in computational and applied mathematics. That said, there are few rigorous results about the representation error and trainability of neural networks. Here we characterize both the error and the scaling of the error with the size of the network by reinterpreting the standard optimization algorithm used in machine learning applications, stochastic gradient descent, as the evolution of a particle system with interactions governed by a potential related to the objective or "loss" function used to train the network. We show that, when the number @math of parameters is large, the empirical distribution of the particles descends on a convex landscape towards a minimizer at a rate independent of @math . We establish a Law of Large Numbers and a Central Limit Theorem for the empirical distribution, which together show that the approximation error of the network universally scales as @math . Remarkably, these properties do not depend on the dimensionality of the domain of the function that we seek to represent. Our analysis also quantifies the scale and nature of the noise introduced by stochastic gradient descent and provides guidelines for the step size and batch size to use when training a neural network. We illustrate our findings on examples in which we train neural network to learn the energy function of the continuous 3-spin model on the sphere. The approximation error scales as our analysis predicts in as high a dimension as @math . Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems. Also, conventional networks fix the architecture before training starts; as a result, training cannot improve the architecture. To address these limitations, we describe a method to reduce the storage and computation required by neural networks by an order of magnitude without affecting their accuracy by learning only the important connections. Our method prunes redundant connections using a three-step method. First, we train the network to learn which connections are important. Next, we prune the unimportant connections. Finally, we retrain the network to fine tune the weights of the remaining connections. On the ImageNet dataset, our method reduced the number of parameters of AlexNet by a factor of 9x, from 61 million to 6.7 million, without incurring accuracy loss. Similar experiments with VGG-16 found that the number of parameters can be reduced by 13x, from 138 million to 10.3 million, again with no loss of accuracy. Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems. Also, conventional networks fix the architecture before training starts; as a result, training cannot improve the architecture. To address these limitations, we describe a method to reduce the storage and computation required by neural networks by an order of magnitude without affecting their accuracy by learning only the important connections. Our method prunes redundant connections using a three-step method. First, we train the network to learn which connections are important. Next, we prune the unimportant connections. Finally, we retrain the network to fine tune the weights of the remaining connections. On the ImageNet dataset, our method reduced the number of parameters of AlexNet by a factor of 9x, from 61 million to 6.7 million, without incurring accuracy loss. Similar experiments with VGG-16 found that the total number of parameters can be reduced by 13x, from 138 million to 10.3 million, again with no loss of accuracy. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modelling uncertainty is one of the key features of Bayesian methods. Bayesian DNNs that use dropout-based variational distributions and scale to complex tasks have recently been proposed. We evaluate Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We compare these Bayesian DNNs ability to represent their uncertainty about their outputs through sampling during inference. We tested the calibration of these Bayesian fully connected and convolutional DNNs on two visual inference tasks (MNIST and CIFAR-10). By adding different levels of Gaussian noise to the test images, we assessed how these DNNs represented their uncertainty about regions of input space not covered by the training set. These Bayesian DNNs represented their own uncertainty more accurately than traditional DNNs with a softmax output. We find that sampling of weights, whether Gaussian or Bernoulli, led to more accurate representation of uncertainty compared to sampling of units. However, sampling units using either Gaussian or Bernoulli dropout led to increased convolutional neural network (CNN) classification accuracy. Based on these findings we use both Bernoulli dropout and Gaussian dropconnect concurrently, which approximates the use of a spike-and-slab variational distribution. We find that networks with spike-and-slab sampling combine the advantages of the other methods: they classify with high accuracy and robustly represent the uncertainty of their classifications for all tested architectures. Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better robustness to over-fitting on small data than traditional approaches. This is by placing a probability distribution over the CNN's kernels. We approximate our model's intractable posterior with Bernoulli variational distributions, requiring no additional model parameters. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. This allows us to implement our model using existing tools in deep learning with no increase in time complexity, while highlighting a negative result in the field. We show a considerable improvement in classification accuracy compared to standard techniques and improve on published state-of-the-art results for CIFAR-10. Convolutional neural networks (CNN) have achieved impressive performance on the wide variety of tasks (classification, detection, etc.) across multiple domains at the cost of high computational and memory requirements. Thus, leveraging CNNs for real-time applications necessitates model compression approaches that not only reduce the total number of parameters but reduce the overall computation as well. In this work, we present a stability-based approach for filter-level pruning of CNNs. We evaluate our proposed approach on different architectures (LeNet, VGG-16, ResNet, and Faster RCNN) and datasets and demonstrate its generalizability through extensive experiments. Moreover, our compressed models can be used at run-time without requiring any special libraries or hardware. Our model compression method reduces the number of FLOPS by an impressive factor of 6.03X and GPU memory footprint by more than 17X, significantly outperforming other state-of-the-art filter pruning methods. Recent work has shown that convolutional neural networks (CNNs) can be used to estimate optical flow with high quality and fast runtime. This makes them preferable for real-world applications. However, such networks require very large training datasets. Engineering the training data is difficult and or laborious. This paper shows how to augment a network trained on an existing synthetic dataset with large amounts of additional unlabelled data. In particular, we introduce a selection mechanism to assemble from multiple estimates a joint optical flow field, which outperforms that of all input methods. The latter can be used as proxy-ground-truth to train a network on real-world data and to adapt it to specific domains of interest. Our experimental results show that the performance of networks improves considerably, both, in cross-domain and in domain-specific scenarios. As a consequence, we obtain state-of-the-art results on the KITTI benchmarks. The need to model visual information with compact representations has existed since the early days of computer vision. We implemented in the past a segmentation and model recovery method for range images which is unfortunately too slow for current size of 3D point clouds and type of applications. Recently, neural networks have become the popular choice for quick and effective processing of visual data. In this article we demonstrate that with a convolutional neural network we could achieve comparable results, that is to determine and model all objects in a given 3D point cloud scene. We started off with a simple architecture that could predict the parameters of a single object in a scene. Then we expanded it with an architecture similar to Faster R-CNN, that could predict the parameters for any number of objects in a scene. The results of the initial neural network were satisfactory. The second network, that performed also segmentation, still gave decent results comparable to the original method, but compared to the initial one, performed somewhat worse. Results, however, are encouraging but further experiments are needed to build CNNs that will be able to replace the state-of-the-art method. To attain a favorable performance on large-scale datasets, convolutional neural networks (CNNs) are usually designed to have very high capacity involving millions of parameters. In this work, we aim at optimizing the number of neurons in a network, thus the number of parameters. We show that, by incorporating sparse constraints into the objective function, it is possible to decimate the number of neurons during the training stage. As a result, the number of parameters and the memory footprint of the neural network are also reduced, which is also desirable at the test time. We evaluated our method on several well-known CNN structures including AlexNet, and VGG over different datasets including ImageNet. Extensive experimental results demonstrate that our method leads to compact networks. Taking first fully connected layer as an example, our compact CNN contains only (30 , ) of the original neurons without any degradation of the top-1 classification accuracy. Following a number of studies that have interrogated the usability of an autoencoder neural network in various classification and regression approximation problems, this manuscript focuses on its usability in water demand predictive modelling, with the Gauteng Province of the Republic of South Africa being chosen as a case study. Water demand predictive modelling is a regression approximation problem. This autoencoder network is constructed from a simple multi-layer network, with a total of 6 parameters in both the input and output units, and 5 nodes in the hidden unit. These 6 parameters include a figure that represents population size and water demand values of 5 consecutive days. The water demand value of the fifth day is the variable of interest, that is, the variable that is being predicted. The optimum number of nodes in the hidden unit is determined through the use of a simple, less computationally expensive technique. The performance of this network is measured against prediction accuracy, average prediction error, and the time it takes the network to generate a single output. The dimensionality of the network is also taken into consideration. In order to benchmark the performance of this autoencoder network, a conventional neural network is also implemented and evaluated using the same measures of performance. The conventional network is slightly outperformed by the autoencoder network. We explore a model-based approach to reinforcement learning where partially or totally unknown dynamics are learned and explicit planning is performed. We learn dynamics with neural networks, and plan behaviors with differential dynamic programming (DDP). In order to handle complicated dynamics, such as manipulating liquids (pouring), we consider temporally decomposed dynamics. We start from our recent work [1] where we used locally weighted regression (LWR) to model dynamics. The major contribution of this paper is making use of deep learning in the form of neural networks with stochastic DDP, and showing the advantages of neural networks over LWR. For this purpose, we extend neural networks for: (1) modeling prediction error and output noise, (2) computing an output probability distribution for a given input distribution, and (3) computing gradients of output expectation with respect to an input. Since neural networks have nonlinear activation functions, these extensions were not easy. We provide an analytic solution for these extensions using some simplifying assumptions. We verified this method in pouring simulation experiments. The learning performance with neural networks was better than that of LWR. The amount of spilled materials was reduced. We also present early results of robot experiments using a PR2. Accompanying video: https: youtu.be aM3hE1J5W98 We propose a new method for creating computationally efficient convolutional neural networks (CNNs) by using low-rank representations of convolutional filters. Rather than approximating filters in previously-trained networks with more efficient versions, we learn a set of small basis filters from scratch; during training, the network learns to combine these basis filters into more complex filters that are discriminative for image classification. To train such networks, a novel weight initialization scheme is used. This allows effective initialization of connection weights in convolutional layers composed of groups of differently-shaped filters. We validate our approach by applying it to several existing CNN architectures and training these networks from scratch using the CIFAR, ILSVRC and MIT Places datasets. Our results show similar or higher accuracy than conventional CNNs with much less compute. Applying our method to an improved version of VGG-11 network using global max-pooling, we achieve comparable validation accuracy using 41 less compute and only 24 of the original VGG-11 model parameters; another variant of our method gives a 1 percentage point increase in accuracy over our improved VGG-11 model, giving a top-5 center-crop validation accuracy of 89.7 while reducing computation by 16 relative to the original VGG-11 model. Applying our method to the GoogLeNet architecture for ILSVRC, we achieved comparable accuracy with 26 less compute and 41 fewer model parameters. Applying our method to a near state-of-the-art network for CIFAR, we achieved comparable accuracy with 46 less compute and 55 fewer parameters. The representation of nonlinear subgrid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric subgrid processes in a climate model by learning from a multiscale model in which convection is treated explicitly. The trained neural network then replaces the traditional subgrid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multiyear simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth system model development could play a key role in reducing climate prediction uncertainty in the coming decade. We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.