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Semi-Lagrangian (SL) schemes are highly efficient for simulating transport equations and are widely used across various applications. Despite their success, designing genuinely multi-dimensional and conservative SL schemes remains a significant challenge. Building on our previous work [Chen et al., J. Comput. Phys., V490 112329, (2023)], we introduce a conservative machine-learning-based SL finite difference (FD) method that allows for extra-large time step evolution. At the core of our approach is a novel dynamical graph neural network designed to handle the complexities associated with tracking accurately upstream points along characteristics. This proposed neural transport solver learns the conservative SL FD discretization directly from data, improving accuracy and efficiency compared to traditional numerical schemes, while significantly simplifying algorithm implementation. We validate the method' s effectiveness and efficiency through numerical tests on benchmark transport equations in both one and two dimensions, as well as the nonlinear Vlasov-Poisson system., Comment: arXiv admin note: text overlap with arXiv:2309.04943

Hyperspectral Imagery (HSI) has been used in many applications to non-destructively determine the material and/or chemical compositions of samples. There is growing interest in creating 3D hyperspectral reconstructions, which could provide both spatial and spectral information while also mitigating common HSI challenges such as non-Lambertian surfaces and translucent objects. However, traditional 3D reconstruction with HSI is difficult due to technological limitations of hyperspectral cameras. In recent years, Neural Radiance Fields (NeRFs) have seen widespread success in creating high quality volumetric 3D representations of scenes captured by a variety of camera models. Leveraging recent advances in NeRFs, we propose computing a hyperspectral 3D reconstruction in which every point in space and view direction is characterized by wavelength-dependent radiance and transmittance spectra. To evaluate our approach, a dataset containing nearly 2000 hyperspectral images across 8 scenes and 2 cameras was collected. We perform comparisons against traditional RGB NeRF baselines and apply ablation testing with alternative spectra representations. Finally, we demonstrate the potential of hyperspectral NeRFs for hyperspectral super-resolution and imaging sensor simulation. We show that our hyperspectral NeRF approach enables creating fast, accurate volumetric 3D hyperspectral scenes and enables several new applications and areas for future study., Comment: Main paper: 15 pages + 2 pages references. Supplemental/Appendix: 6 pages

Machine-learning (ML) based discretization has been developed to simulate complex partial differential equations (PDEs) with tremendous success across various fields. These learned PDE solvers can effectively resolve the underlying solution structures of interest and achieve a level of accuracy which often requires an order-of-magnitude finer grid for a conventional numerical method using polynomial-based approximations. In a previous work in [13], we introduced a learned finite volume discretization that further incorporates the semi-Lagrangian (SL) mechanism, enabling larger CFL numbers for stability. However, the efficiency and effectiveness of such methodology heavily rely on the availability of abundant high-resolution training data, which can be prohibitively expensive to obtain. To address this challenge, in this paper, we propose a novel multi-fidelity ML-based SL method for transport equations. This method leverages a combination of a small amount of high-fidelity data and sufficient but cheaper low-fidelity data. The approach is designed based on a composite convolutional neural network architecture that explore the inherent correlation between high-fidelity and low-fidelity data. The proposed method demonstrates the capability to achieve a reasonable level of accuracy, particularly in scenarios where a single-fidelity model fails to generalize effectively. We further extend the method to the nonlinear Vlasov-Poisson system by employing high order Runge-Kutta exponential integrators. A collection of numerical tests are provided to validate the efficiency and accuracy of the proposed method.

Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather prediction, among others. In this work, we develop a novel machine learning-assisted approach to accelerate the conventional SL finite volume (FV) schemes. The proposed scheme avoids the expensive tracking of upstream cells but attempts to learn the SL discretization from the data by incorporating specific inductive biases in the neural network, significantly simplifying the algorithm implementation and leading to improved efficiency. In addition, the method delivers sharp shock transitions and a level of accuracy that would typically require a much finer grid with traditional transport solvers. Numerical tests demonstrate the effectiveness and efficiency of the proposed method., Comment: 24 pages

We propose a novel hybrid cable-based robot with manipulator and camera for high-accuracy, medium-throughput plant monitoring in a vertical hydroponic farm and, as an example application, demonstrate non-destructive plant mass estimation. Plant monitoring with high temporal and spatial resolution is important to both farmers and researchers to detect anomalies and develop predictive models for plant growth. The availability of high-quality, off-the-shelf structure-from-motion (SfM) and photogrammetry packages has enabled a vibrant community of roboticists to apply computer vision for non-destructive plant monitoring. While existing approaches tend to focus on either high-throughput (e.g. satellite, unmanned aerial vehicle (UAV), vehicle-mounted, conveyor-belt imagery) or high-accuracy/robustness to occlusions (e.g. turn-table scanner or robot arm), we propose a middle-ground that achieves high accuracy with a medium-throughput, highly automated robot. Our design pairs the workspace scalability of a cable-driven parallel robot (CDPR) with the dexterity of a 4 degree-of-freedom (DoF) robot arm to autonomously image many plants from a variety of viewpoints. We describe our robot design and demonstrate it experimentally by collecting daily photographs of 54 plants from 64 viewpoints each. We show that our approach can produce scientifically useful measurements, operate fully autonomously after initial calibration, and produce better reconstructions and plant property estimates than those of over-canopy methods (e.g. UAV). As example applications, we show that our system can successfully estimate plant mass with a Mean Absolute Error (MAE) of 0.586g and, when used to perform hypothesis testing on the relationship between mass and age, produces p-values comparable to ground-truth data (p=0.0020 and p=0.0016, respectively)., Comment: 8 pages (6-content, 2-citations), 10 figures, 4 tables, submitted to ICRA 2023