Learning Matchable Image Transformations for Long-term Metric Visual Localization

Long-term metric self-localization is an essential capability of autonomous mobile robots, but remains challenging for vision-based systems due to appearance changes caused by lighting, weather, or seasonal variations. While experience-based mapping has proven to be an effective technique for bridging the `appearance gap,' the number of experiences required for reliable metric localization over days or months can be very large, and methods for reducing the necessary number of experiences are needed for this approach to scale. Taking inspiration from color constancy theory, we learn a nonlinear RGB-to-grayscale mapping that explicitly maximizes the number of inlier feature matches for images captured under different lighting and weather conditions, and use it as a pre-processing step in a conventional single-experience localization pipeline to improve its robustness to appearance change. We train this mapping by approximating the target non-differentiable localization pipeline with a deep neural network, and find that incorporating a learned low-dimensional context feature can further improve cross-appearance feature matching. Using synthetic and real-world datasets, we demonstrate substantial improvements in localization performance across day-night cycles, enabling continuous metric localization over a 30-hour period using a single mapping experience, and allowing experience-based localization to scale to long deployments with dramatically reduced data requirements.Comment: In IEEE Robotics and Automation Letters (RA-L) and presented at the IEEE International Conference on Robotics and Automation (ICRA'20), Paris, France, May 31-June 4, 202

Surrogate-assisted Bayesian inversion for landscape and basin evolution models

The complex and computationally expensive features of the forward landscape and sedimentary basin evolution models pose a major challenge in the development of efficient inference and optimization methods. Bayesian inference provides a methodology for estimation and uncertainty quantification of free model parameters. In our previous work, parallel tempering Bayeslands was developed as a framework for parameter estimation and uncertainty quantification for the landscape and basin evolution modelling software Badlands. Parallel tempering Bayeslands features high-performance computing with dozens of processing cores running in parallel to enhance computational efficiency. Although parallel computing is used, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape and basin evolution problems, a single model evaluation can take from several minutes to hours, and in certain cases, even days. Surrogate-assisted optimization has been with successfully applied to a number of engineering problems. This motivates its use in optimisation and inference methods suited for complex models in geology and geophysics. Surrogates can speed up parallel tempering Bayeslands by developing computationally inexpensive surrogates to mimic expensive models. In this paper, we present an application of surrogate-assisted parallel tempering where that surrogate mimics a landscape evolution model including erosion, sediment transport and deposition, by estimating the likelihood function that is given by the model. We employ a machine learning model as a surrogate that learns from the samples generated by the parallel tempering algorithm. The results show that the methodology is effective in lowering the overall computational cost significantly while retaining the quality of solutions.Comment: Under review. arXiv admin note: text overlap with arXiv:1811.0868

Hierarchical Emulation & Data Assimilation into the Sediment Transport Model

AbstractSynthetic observations of the suspended sediment concentration in an idealised macro-tidal estuary are assimilated into the 3d sediment transport model. The assimilation scheme relies on fast and cheap surrogates of the complex model (called emulators) to update the model's state variables and its 2 parameters. A scenario with a hierarchically structured emulator is contrasted to the scenario with a more conventional non-hierarchical emulator. Numerical experiments indicate that for a given size of the ensemble an emulator which replicates a hierarchical structure of the model tends to provide a better approximation of that model. Improving the quality of the emulator translates into the improved quality of the assimilation products

Fast ocean data assimilation and forecasting using a neural-network reduced-space regional ocean model of the north Brazil current

Data assimilation is computationally demanding, typically many times slower than model forecasts. Fast and reliable ocean assimilation methods are attractive for multiple applications such as emergency situations, search and rescue, and oil spills. A novel framework which performs fast data assimilation with sufficient accuracy is proposed for the first time for the open ocean. Speed improvement is achieved by performing the data assimilation on a reduced-space rather than on a full-space. A surface 10km resolution hindcast of the North Brazil current from the Regional Ocean Modelling System (ROMS) serves as the full-space state. The target variables are sea surface height, sea surface temperature, and surface currents. A dimension reduction of the full-state is made by an Empirical Orthogonal Function analysis while retaining most of the explained variance. The dynamics are replicated by a state-of-the-art neural network trained on the truncated principal components of the full-state. An Ensemble Kalman filter assimilates the data in the reduced-space, where the trained neural network produces short-range forecasts from perturbed ensembles. The Ensemble Kalman filter of the reduced-space is successful in reducing the root mean squared error by ∼ 45% and increases the correlations between state variables and data. The performance is similar to other full-space data assimilation studies. However, the computations are three to four orders of magnitude faster than for other full-space data assimilation schemes. The forecast of ocean variables is a computationally demanding task in terms of speed and accuracy. This framework manages to create fast forecasts in ∼ 30 seconds, once data have been assimilated. The forecasts are obtained using the trained neural network. We performed additional experiments using data and forecasts from July 2015 and January 2016. The analysis and forecasts in our framework yield a higher skill score and high spatial correlation when compared to the operational dataset Global Ocean Physics Analysis and Forecast by the UK MetOffice. Forcing the neural network with 10 m surface winds in order to improve the total surface currents forecast was considered. There is no additional skill in the forecasts using wind forcing because of the low Ekman component compared to the dominant geostrophic currents. The reduced model approach could be a useful tool when full physics regional models are not available to make a forecast.Open Acces

PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.Comment: Project website: https://phlippe.github.io/PDERefiner

Advancing coastal ocean modelling, analysis, and prediction for the US Integrated Ocean Observing System

Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Journal of Operational Oceanography 10 (2017): 115-126, doi:10.1080/1755876X.2017.1322026.This paper outlines strategies that would advance coastal ocean modeling, analysis and prediction as a complement to the observing and data management activities of the coastal components of the U.S. Integrated Ocean Observing System (IOOS®) and the Global Ocean Observing System (GOOS). The views presented are the consensus of a group of U.S. based researchers with a cross-section of coastal oceanography and ocean modeling expertise and community representation drawn from Regional and U.S. Federal partners in IOOS. Priorities for research and development are suggested that would enhance the value of IOOS observations through model-based synthesis, deliver better model-based information products, and assist the design, evaluation and operation of the observing system itself. The proposed priorities are: model coupling, data assimilation, nearshore processes, cyberinfrastructure and model skill assessment, modeling for observing system design, evaluation and operation, ensemble prediction, and fast predictors. Approaches are suggested to accomplish substantial progress in a 3-8 year timeframe. In addition, the group proposes steps to promote collaboration between research and operations groups in Regional Associations, U.S. Federal Agencies, and the international ocean research community in general that would foster coordination on scientific and technical issues, and strengthen federal-academic partnerships benefiting IOOS stakeholders and end users.2018-05-2

Error analysis for deep neural network approximations of parametric hyperbolic conservation laws

We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that the approximation error can be made as small as desired with ReLU neural networks that overcome the curse of dimensionality. In addition, we provide an explicit upper bound on the generalization error in terms of the training error, number of training samples and the neural network size. The theoretical results are illustrated by numerical experiments