Rotation Prevents Finite-Time Breakdown

We consider a two-dimensional convection model augmented with the rotational Coriolis forcing, $U_t + U\cdot\nabla_x U = 2k U^\perp$, with a fixed $2k$ being the inverse Rossby number. We ask whether the action of dispersive rotational forcing alone, $U^\perp$, prevents the generic finite time breakdown of the free nonlinear convection. The answer provided in this work is a conditional yes. Namely, we show that the rotating Euler equations admit global smooth solutions for a subset of generic initial configurations. With other configurations, however, finite time breakdown of solutions may and actually does occur. Thus, global regularity depends on whether the initial configuration crosses an intrinsic, ${\mathcal O}(1)$ critical threshold, which is quantified in terms of the initial vorticity, $\omega_0=\nabla \times U_0$, and the initial spectral gap associated with the $2\times 2$ initial velocity gradient, $\eta_0:=\lambda_2(0)-\lambda_1(0), \lambda_j(0)= \lambda_j(\nabla U_0)$. Specifically, global regularity of the rotational Euler equation is ensured if and only if $4k \omega_0(\alpha) +\eta^2_0(\alpha) <4k^2, \forall \alpha \in \R^2$ . We also prove that the velocity field remains smooth if and only if it is periodic. We observe yet another remarkable periodic behavior exhibited by the {\em gradient} of the velocity field. The spectral dynamics of the Eulerian formulation reveals that the vorticity and the eigenvalues (and hence the divergence) of the flow evolve with their own path-dependent period. We conclude with a kinetic formulation of the rotating Euler equation

Model reduction for the material point method via an implicit neural representation of the deformation map

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that restricts deformation trajectories to reside on a low-dimensional manifold. By explicitly approximating the deformation map, its spatiotemporal gradients -- in particular the deformation gradient and the velocity -- can be computed via analytical differentiation. In contrast to typical model-reduction techniques that construct a linear or nonlinear manifold to approximate the (finite number of) degrees of freedom characterizing a given spatial discretization, the use of an implicit neural representation enables the proposed method to approximate the $\textit{continuous}$ deformation map. This allows the kinematic approximation to remain agnostic to the discretization. Consequently, the technique supports dynamic discretizations -- including resolution changes -- during the course of the online reduced-order-model simulation. To generate $\textit{dynamics}$ for the generalized coordinates, we propose a family of projection techniques. At each time step, these techniques: (1) Calculate full-space kinematics at quadrature points, (2) Calculate the full-space dynamics for a subset of `sample' material points, and (3) Calculate the reduced-space dynamics by projecting the updated full-space position and velocity onto the low-dimensional manifold and tangent space, respectively. We achieve significant computational speedup via hyper-reduction that ensures all three steps execute on only a small subset of the problem's spatial domain. Large-scale numerical examples with millions of material points illustrate the method's ability to gain an order of magnitude computational-cost saving -- indeed $\textit{real-time simulations}$ -- with negligible errors

LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields

Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial discretization, and then serves to accelerate simulations with the same discretization. This discretization-dependence is restrictive. Becoming independent of a specific discretization would provide flexibility to mix and match mesh resolutions, connectivity, and type (tetrahedral, hexahedral) in training data; to accelerate simulations with novel discretizations unseen during training; and to accelerate adaptive simulations that temporally or parametrically change the discretization. We present a flexible, discretization-independent approach to reduced-order modeling. Like traditional ROM, we represent the configuration as a linear combination of displacement fields. Unlike traditional ROM, our displacement fields are continuous maps from every point on the reference domain to a corresponding displacement vector; these maps are represented as implicit neural fields. With linear continuous ROM (LiCROM), our training set can include multiple geometries undergoing multiple loading conditions, independent of their discretization. This opens the door to novel applications of reduced order modeling. We can now accelerate simulations that modify the geometry at runtime, for instance via cutting, hole punching, and even swapping the entire mesh. We can also accelerate simulations of geometries unseen during training. We demonstrate one-shot generalization, training on a single geometry and subsequently simulating various unseen geometries

Implementing Reinforcement Learning Datacenter Congestion Control in NVIDIA NICs

As communication protocols evolve, datacenter network utilization increases. As a result, congestion is more frequent, causing higher latency and packet loss. Combined with the increasing complexity of workloads, manual design of congestion control (CC) algorithms becomes extremely difficult. This calls for the development of AI approaches to replace the human effort. Unfortunately, it is currently not possible to deploy AI models on network devices due to their limited computational capabilities. Here, we offer a solution to this problem by building a computationally-light solution based on a recent reinforcement learning CC algorithm [arXiv:2207.02295]. We reduce the inference time of RL-CC by x500 by distilling its complex neural network into decision trees. This transformation enables real-time inference within the $\mu$-sec decision-time requirement, with a negligible effect on quality. We deploy the transformed policy on NVIDIA NICs in a live cluster. Compared to popular CC algorithms used in production, RL-CC is the only method that performs well on all benchmarks tested over a large range of number of flows. It balances multiple metrics simultaneously: bandwidth, latency, and packet drops. These results suggest that data-driven methods for CC are feasible, challenging the prior belief that handcrafted heuristics are necessary to achieve optimal performance

Neural Stress Fields for Reduced-order Elastoplasticity and Fracture

We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation elastoplasticity and fracture mechanics. However, their long runtime and large memory consumption render them unsuitable for applications constrained by computation time and memory usage, e.g., virtual reality. To overcome these barriers, we propose a reduced-order framework. Our key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. This low-dimensional neural stress field (NSF) enables efficient evaluations of stress values and, correspondingly, internal forces at arbitrary spatial locations. In addition, we also train neural deformation and affine fields to build low-dimensional manifolds for the deformation and affine momentum fields. These neural stress, deformation, and affine fields share the same low-dimensional latent space, which uniquely embeds the high-dimensional simulation state. After training, we run new simulations by evolving in this single latent space, which drastically reduces the computation time and memory consumption. Our general continuum-mechanics-based reduced-order framework is applicable to any phenomena governed by the elastodynamics equation. To showcase the versatility of our framework, we simulate a wide range of material behaviors, including elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision. We demonstrate dimension reduction by up to 100,000X and time savings by up to 10X

CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a smooth, low-dimensional manifold of the continuous vector fields themselves, not their discretization. We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations. We validate our approach on an extensive range of PDEs with training data from voxel grids, meshes, and point clouds. Compared to prior discretization-dependent ROM methods, such as linear subspace proper orthogonal decomposition (POD) and nonlinear manifold neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, and applicability to any discretization. For equal latent space dimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and 39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencoder methods, respectively. Experiments demonstrate 109$\times$ and 89$\times$ wall-clock speedups over unreduced models on CPUs and GPUs, respectively

Towards Transcervical Ultrasound Image Guidance for Transoral Robotic Surgery

Purpose: Trans-oral robotic surgery (TORS) using the da Vinci surgical robot is a new minimally-invasive surgery method to treat oropharyngeal tumors, but it is a challenging operation. Augmented reality (AR) based on intra-operative ultrasound (US) has the potential to enhance the visualization of the anatomy and cancerous tumors to provide additional tools for decision-making in surgery. Methods: We propose and carry out preliminary evaluations of a US-guided AR system for TORS, with the transducer placed on the neck for a transcervical view. Firstly, we perform a novel MRI-transcervical 3D US registration study. Secondly, we develop a US-robot calibration method with an optical tracker and an AR system to display the anatomy mesh model in the real-time endoscope images inside the surgeon console. Results: Our AR system reaches a mean projection error of 26.81 and 27.85 pixels for the projection from the US to stereo cameras in a water bath experiment. The average target registration error for MRI to 3D US is 8.90 mm for the 3D US transducer and 5.85 mm for freehand 3D US, and the average distance between the vessel centerlines is 2.32 mm. Conclusion: We demonstrate the first proof-of-concept transcervical US-guided AR system for TORS and the feasibility of trans-cervical 3D US-MRI registration. Our results show that trans-cervical 3D US is a promising technique for TORS image guidance.Comment: 12 pages, 8 figures. Accepted by Information Processing for Computer Assisted Interventions (IPCAI 2023

User Association and Resource Allocation Optimization in LTE Cellular Networks

International audienceAs the demand for higher data rates is growing exponentially, homogeneous cellular networks have been facing limitations when handling data traffic. These limitations are related to the available spectrum and the capacity of the network. Heterogeneous Networks (HetNets), composed of Macro Cells (MCs) and Small Cells (SCs), are seen as the key solution to improve spectral efficiency per unit area and to eliminate coverage holes. Due to the large imbalance in transmit power between MCs and SCs in HetNets, intelligent User Association (UA) is required to perform load balancing and to favor some SCs attraction against MCs. As Long Term Evolution (LTE) cellular networks use the same frequency sub-bands, User Equipments (UEs) may experience strong Inter-Cell Interference (ICI), especially at cell edge. Therefore, there is a need to coordinate the Resource Allocation (RA) among the cells and to minimize the ICI. In this paper, we propose a generic algorithm to optimize user Association and resource allocation in LTE networks. Our solution, based on game theory, permits to compute Cell Individual Offset (CIO) and a pattern of power transmission over frequency and time domain for each cell. Simulation results show significant benefits in the average throughput and also cell edge user throughput of 40% and 55% gains respectively. Furthermore, we also obtain a meaningful improvement in energy efficiency

Online Mobile User Speed Estimation: Performance and Tradeoff Considerations

International audienceThis paper presents an online algorithm for mobile user speed estimation in 3GPP Long Term Evolution (LTE)/LTE-Advanced (LTE-A) networks. The proposed method leverages on uplink (UL) sounding reference signal (SRS) power measurements performed at the base station, also known as eNodeB (eNB), and remains effective even under large sampling period. Extensive performance evaluation of the proposed algorithm is carried out using field traces from realistic environment. The on-line solution is proven highly efficient in terms of computational requirement, estimation delay, and accuracy. In particular, we show that the proposed algorithm can allow for the first speed estimation to be obtained after 10 seconds and with an average speed underestimation error of 14 kmph. After the first speed acquisition, subsequent speed estimations can be obtained much faster (e.g., each second) with limited implementation cost and still provide high accuracy

Effect of carbon nanotubes on calcium carbonate/calcium silicate phase and morphology

The composition and microstructure of different CaCO3-Ca2SiO4-carbon nanotube composites have been studied. Materials have been characterized by X-ray diffraction (XRD), high resolution scanning electron microscopy (SEM), thermogravimetric/differential thermal analysis (TG/DTA), and Fourier-transform infrared (FTIR) spectroscopy. The morphology and structure of the inorganic systems are affected by the presence of multiwall carbon nanotubes (MWCNT) during the hydration processes and the nature of the MWCNT/SDS interface plays a role in the curing stages of the composite enhancing the growth of calcium silicate