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Efficient exploration remains a challenging problem in reinforcement learning, especially for tasks where extrinsic rewards from environments are sparse or even totally disregarded. Significant advances based on intrinsic motivation show promising results in simple environments but often get stuck in environments with multimodal and stochastic dynamics. In this work, we propose a variational dynamic model based on the conditional variational inference to model the multimodality and stochasticity. We consider the environmental state-action transition as a conditional generative process by generating the next-state prediction under the condition of the current state, action, and latent variable, which provides a better understanding of the dynamics and leads a better performance in exploration. We derive an upper bound of the negative log-likelihood of the environmental transition and use such an upper bound as the intrinsic reward for exploration, which allows the agent to learn skills by self-supervised exploration without observing extrinsic rewards. We evaluate the proposed method on several image-based simulation tasks and a real robotic manipulating task. Our method outperforms several state-of-the-art environment model-based exploration approaches.

Temporally consistent depth estimation is crucial for real-time applications such as augmented reality. While stereo depth estimation has received substantial attention that led to improvements on a frame-by-frame basis, there is relatively little work focused on maintaining temporal consistency across frames. Indeed, based on our analysis, current stereo depth estimation techniques still suffer from poor temporal consistency. Stabilizing depth temporally in dynamic scenes is challenging due to concurrent object and camera motion. In an online setting, this process is further aggravated because only past frames are available. In this paper, we present a technique to produce temporally consistent depth estimates in dynamic scenes in an online setting. Our network augments current per-frame stereo networks with novel motion and fusion networks. The motion network accounts for both object and camera motion by predicting a per-pixel SE3 transformation. The fusion network improves consistency in prediction by aggregating the current and previous predictions with regressed weights. We conduct extensive experiments across varied datasets (synthetic, outdoor, indoor and medical). In both zero-shot generalization and domain fine-tuning, we demonstrate that our proposed approach outperforms competing methods in terms of temporal stability and per-frame accuracy, both quantitatively and qualitatively. Our code will be available online.

The absorption of light by molecules in the atmosphere of Earth is a complication for ground-based observations of astrophysical objects. Comprehensive information on various molecular species is required to correct for this so called telluric absorption. We present a neural network autoencoder approach for extracting a telluric transmission spectrum from a large set of high-precision observed solar spectra from the HARPS-N radial velocity spectrograph. We accomplish this by reducing the data into a compressed representation, which allows us to unveil the underlying solar spectrum and simultaneously uncover the different modes of variation in the observed spectra relating to the absorption of $\mathrm{H_2O}$ and $\mathrm{O_2}$ in the atmosphere of Earth. We demonstrate how the extracted components can be used to remove $\mathrm{H_2O}$ and $\mathrm{O_2}$ tellurics in a validation observation with similar accuracy and at less computational expense than a synthetic approach with molecfit.

The Ensemble Kalman inversion (EKI), proposed by Iglesias et al. for the solution of Bayesian inverse problems of type $y=A u^\dagger +\varepsilon$, with $u^\dagger$ being an unknown parameter and $y$ a given datum, is a powerful tool usually derived from a sequential Monte Carlo point of view. It describes the dynamics of an ensemble of particles $\{u^j(t)\}_{j=1}^J$, whose initial empirical measure is sampled from the prior, evolving over an artificial time $t$ towards an approximate solution of the inverse problem. Using spectral techniques, we provide a complete description of the deterministic dynamics of EKI and their asymptotic behavior in parameter space. In particular, we analyze the dynamics of deterministic EKI and mean-field EKI. We demonstrate that the Bayesian posterior can only be recovered with the mean-field limit and not with finite sample sizes or deterministic EKI. Furthermore, we show that -- even in the deterministic case -- residuals in parameter space do not decrease monotonously in the Euclidean norm and suggest a problem-adapted norm, where monotonicity can be proved. Finally, we derive a system of ordinary differential equations governing the spectrum and eigenvectors of the covariance matrix.

We are motivated by the problem of learning policies for robotic systems with rich sensory inputs (e.g., vision) in a manner that allows us to guarantee generalization to environments unseen during training. We provide a framework for providing such generalization guarantees by leveraging a finite dataset of real-world environments in combination with a (potentially inaccurate) generative model of environments. The key idea behind our approach is to utilize the generative model in order to implicitly specify a prior over policies. This prior is updated using the real-world dataset of environments by minimizing an upper bound on the expected cost across novel environments derived via Probably Approximately Correct (PAC)-Bayes generalization theory. We demonstrate our approach on two simulated systems with nonlinear/hybrid dynamics and rich sensing modalities: (i) quadrotor navigation with an onboard vision sensor, and (ii) grasping objects using a depth sensor. Comparisons with prior work demonstrate the ability of our approach to obtain stronger generalization guarantees by utilizing generative models. We also present hardware experiments for validating our bounds for the grasping task.

Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions, and the interaction between wakes. Physics-based models that capture the wake flow-field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional \emph{latent} space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow-fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.

We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states as measured by von Neumann entropy and entanglement capacity. The focus is on the variance of von Neumann entropy and the mean entanglement capacity that belong to the so-defined second-order statistics. The main results are the exact yet explicit formulas of the two considered second-order statistics for fixed subsystem dimension differences. We also conjecture the exact variance of von Neumann entropy valid for arbitrary subsystem dimensions. Based on the obtained results, we analytically study the numerically observed phenomena of Gaussianity of von Neumann entropy and linear growth of average capacity.

In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compute the mean and covariance function from realizations of available stochastic models, e.g., from realizations of governing stochastic partial differential equations solutions. Such constructed Gaussian process generally is non-stationary, and does not assume a specific form of the covariance function. Our approach avoids the optimization step in data-driven GPR methods to identify the hyperparameters. More importantly, we prove that the physical constraints in the form of a deterministic linear operator are guaranteed in the resulting prediction. We also provide an error estimate in preserving the physical constraints when errors are included in the stochastic model realizations. To reduce the computational cost of obtaining stochastic model realizations, we propose a multilevel Monte Carlo estimate of the mean and covariance functions. Further, we present an active learning algorithm that guides the selection of additional observation locations. The efficiency and accuracy of PhIK are demonstrated for reconstructing a partially known modified Branin function, studying a three-dimensional heat transfer problem and learning a conservative tracer distribution from sparse concentration measurements.

Applying image processing algorithms independently to each frame of a video often leads to undesired inconsistent results over time. Developing temporally consistent video-based extensions, however, requires domain knowledge for individual tasks and is unable to generalize to other applications. In this paper, we present an efficient end-to-end approach based on deep recurrent network for enforcing temporal consistency in a video. Our method takes the original unprocessed and per-frame processed videos as inputs to produce a temporally consistent video. Consequently, our approach is agnostic to specific image processing algorithms applied on the original video. We train the proposed network by minimizing both short-term and long-term temporal losses as well as the perceptual loss to strike a balance between temporal stability and perceptual similarity with the processed frames. At test time, our model does not require computing optical flow and thus achieves real-time speed even for high-resolution videos. We show that our single model can handle multiple and unseen tasks, including but not limited to artistic style transfer, enhancement, colorization, image-to-image translation and intrinsic image decomposition. Extensive objective evaluation and subject study demonstrate that the proposed approach performs favorably against the state-of-the-art methods on various types of videos.