A Temporally Consistent Image-based Sun Tracking Algorithm for Solar Energy Forecasting Applications

Improving irradiance forecasting is critical to further increase the share of solar in the energy mix. On a short time scale, fish-eye cameras on the ground are used to capture cloud displacements causing the local variability of the electricity production. As most of the solar radiation comes directly from the Sun, current forecasting approaches use its position in the image as a reference to interpret the cloud cover dynamics. However, existing Sun tracking methods rely on external data and a calibration of the camera, which requires access to the device. To address these limitations, this study introduces an image-based Sun tracking algorithm to localise the Sun in the image when it is visible and interpolate its daily trajectory from past observations. We validate the method on a set of sky images collected over a year at SIRTA's lab. Experimental results show that the proposed method provides robust smooth Sun trajectories with a mean absolute error below 1% of the image size.Comment: Accepted as a workshop paper at NeurIPS 202

Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere

We present a significantly-improved data-driven global weather forecasting framework using a deep convolutional neural network (CNN) to forecast several basic atmospheric variables on a global grid. New developments in this framework include an offline volume-conservative mapping to a cubed-sphere grid, improvements to the CNN architecture, and the minimization of the loss function over multiple steps in a prediction sequence. The cubed-sphere remapping minimizes the distortion on the cube faces on which convolution operations are performed and provides natural boundary conditions for padding in the CNN. Our improved model produces weather forecasts that are indefinitely stable and produce realistic weather patterns at lead times of several weeks and longer. For short- to medium-range forecasting, our model significantly outperforms persistence, climatology, and a coarse-resolution dynamical numerical weather prediction (NWP) model. Unsurprisingly, our forecasts are worse than those from a high-resolution state-of-the-art operational NWP system. Our data-driven model is able to learn to forecast complex surface temperature patterns from few input atmospheric state variables. On annual time scales, our model produces a realistic seasonal cycle driven solely by the prescribed variation in top-of-atmosphere solar forcing. Although it is currently less accurate than operational weather forecasting models, our data-driven CNN executes much faster than those models, suggesting that machine learning could prove to be a valuable tool for large-ensemble forecasting.Comment: Manuscript submitted to Journal of Advances in Modeling Earth System

Orientation-aware semantic segmentation on icosahedron spheres

© 2019 IEEE. We address semantic segmentation on omnidirectional images, to leverage a holistic understanding of the surrounding scene for applications like autonomous driving systems. For the spherical domain, several methods recently adopt an icosahedron mesh, but systems are typically rotation invariant or require significant memory and parameters, thus enabling execution only at very low resolutions. In our work, we propose an orientation-aware CNN framework for the icosahedron mesh. Our representation allows for fast network operations, as our design simplifies to standard network operations of classical CNNs, but under consideration of north-aligned kernel convolutions for features on the sphere. We implement our representation and demonstrate its memory efficiency up-to a level-8 resolution mesh (equivalent to 640 x 1024 equirectangular images). Finally, since our kernels operate on the tangent of the sphere, standard feature weights, pretrained on perspective data, can be directly transferred with only small need for weight refinement. In our evaluation our orientation-aware CNN becomes a new state of the art for the recent 2D3DS dataset, and our Omni-SYNTHIA version of SYNTHIA. Rotation invariant classification and segmentation tasks are additionally presented for comparison to prior art

Learning Equivariant Representations

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of this principle, their defining characteristic being the shift-equivariance. By sliding a filter over the input, when the input shifts, the response shifts by the same amount, exploiting the structure of natural images where semantic content is independent of absolute pixel positions. This property is essential to the success of CNNs in audio, image and video recognition tasks. In this thesis, we extend equivariance to other kinds of transformations, such as rotation and scaling. We propose equivariant models for different transformations defined by groups of symmetries. The main contributions are (i) polar transformer networks, achieving equivariance to the group of similarities on the plane, (ii) equivariant multi-view networks, achieving equivariance to the group of symmetries of the icosahedron, (iii) spherical CNNs, achieving equivariance to the continuous 3D rotation group, (iv) cross-domain image embeddings, achieving equivariance to 3D rotations for 2D inputs, and (v) spin-weighted spherical CNNs, generalizing the spherical CNNs and achieving equivariance to 3D rotations for spherical vector fields. Applications include image classification, 3D shape classification and retrieval, panoramic image classification and segmentation, shape alignment and pose estimation. What these models have in common is that they leverage symmetries in the data to reduce sample and model complexity and improve generalization performance. The advantages are more significant on (but not limited to) challenging tasks where data is limited or input perturbations such as arbitrary rotations are present

Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds

Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold. The underlying reason for this ambiguity is that general manifolds do not come with a canonical choice of reference frames (gauge). Kernels and features therefore have to be expressed relative to arbitrary coordinates. We argue that the particular choice of coordinatization should not affect a network's inference -- it should be coordinate independent. A simultaneous demand for coordinate independence and weight sharing is shown to result in a requirement on the network to be equivariant under local gauge transformations (changes of local reference frames). The ambiguity of reference frames depends thereby on the G-structure of the manifold, such that the necessary level of gauge equivariance is prescribed by the corresponding structure group G. Coordinate independent convolutions are proven to be equivariant w.r.t. those isometries that are symmetries of the G-structure. The resulting theory is formulated in a coordinate free fashion in terms of fiber bundles. To exemplify the design of coordinate independent convolutions, we implement a convolutional network on the M\"obius strip. The generality of our differential geometric formulation of convolutional networks is demonstrated by an extensive literature review which explains a large number of Euclidean CNNs, spherical CNNs and CNNs on general surfaces as specific instances of coordinate independent convolutions.Comment: The implementation of orientation independent M\"obius convolutions is publicly available at https://github.com/mauriceweiler/MobiusCNN