Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as our computational capabilities. Rigorous upscaling techniques enable efficient computation while bounding/tracking errors and making informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions for upscaled models break down. Here, we present a non-intrusive two-way coupled hybrid model, applied to thermal runaway in battery packs, that combines fine- and upscaled equations in the same numerical simulation to achieve predictive accuracy while limiting computational costs. First, we develop two methods with different orders of accuracy to enforce continuity at the coupling boundary. Then, we derive weak (i.e., variational) formulations of the fine-scale and upscaled governing equations for finite element (FE) discretization and numerical implementation in FEniCS. We demonstrate that hybrid simulations can accurately predict the average temperature fields within error bounds determined a priori by homogenization theory. Finally, we demonstrate the computational efficiency of the hybrid algorithm against fine-scale simulations.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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Reinforcement learning (RL) problems over general state and action spaces are notoriously challenging. In contrast to the tableau setting, one can not enumerate all the states and then iteratively update the policies for each state. This prevents the application of many well-studied RL methods especially those with provable convergence guarantees. In this paper, we first present a substantial generalization of the recently developed policy mirror descent method to deal with general state and action spaces. We introduce new approaches to incorporate function approximation into this method, so that we do not need to use explicit policy parameterization at all. Moreover, we present a novel policy dual averaging method for which possibly simpler function approximation techniques can be applied. We establish linear convergence rate to global optimality or sublinear convergence to stationarity for these methods applied to solve different classes of RL problems under exact policy evaluation. We then define proper notions of the approximation errors for policy evaluation and investigate their impact on the convergence of these methods applied to general-state RL problems with either finite-action or continuous-action spaces. To the best of our knowledge, the development of these algorithmic frameworks as well as their convergence analysis appear to be new in the literature.
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive mesh-refinement and the inexact iterative solution of the arising linear systems. More precisely, the iterative solver employs, as an outer loop, the so-called Zarantonello iteration to symmetrize the system and, as an inner loop, a uniformly contractive algebraic solver, e.g., an optimally preconditioned conjugate gradient method or an optimal geometric multigrid algorithm. We prove that the proposed inexact adaptive iteratively symmetrized finite element method (AISFEM) leads to full linear convergence and, for sufficiently small adaptivity parameters, to optimal convergence rates with respect to the overall computational cost, i.e., the total computational time. Numerical experiments underline the theory.
The ParaOpt algorithm was recently introduced as a time-parallel solver for optimal-control problems with a terminal-cost objective, and convergence results have been presented for the linear diffusive case with implicit-Euler time integrators. We reformulate ParaOpt for tracking problems and provide generalized convergence analyses for both objectives. We focus on linear diffusive equations and prove convergence bounds that are generic in the time integrators used. For large problem dimensions, ParaOpt's performance depends crucially on having a good preconditioner to solve the arising linear systems. For the case where ParaOpt's cheap, coarse-grained propagator is linear, we introduce diagonalization-based preconditioners inspired by recent advances in the ParaDiag family of methods. These preconditioners not only lead to a weakly-scalable ParaOpt version, but are themselves invertible in parallel, making maximal use of available concurrency. They have proven convergence properties in the linear diffusive case that are generic in the time discretization used, similarly to our ParaOpt results. Numerical results confirm that the iteration count of the iterative solvers used for ParaOpt's linear systems becomes constant in the limit of an increasing processor count. The paper is accompanied by a sequential MATLAB implementation.
Modern DNN workloads increasingly rely on activation functions consisting of computationally complex operations. This poses a challenge to current accelerators optimized for convolutions and matrix-matrix multiplications. This work presents Flex-SFU, a lightweight hardware accelerator for activation functions implementing non-uniform piecewise interpolation supporting multiple data formats. Non-Uniform segments and floating-point numbers are enabled by implementing a binary-tree comparison within the address decoding unit. An SGD-based optimization algorithm with heuristics is proposed to find the interpolation function reducing the mean squared error. Thanks to non-uniform interpolation and floating-point support, Flex-SFU achieves on average 22.3x better mean squared error compared to previous piecewise linear interpolation approaches. The evaluation with more than 700 computer vision and natural language processing models shows that Flex-SFU can, on average, improve the end-to-end performance of state-of-the-art AI hardware accelerators by 35.7%, achieving up to 3.3x speedup with negligible impact in the models' accuracy when using 32 segments, and only introducing an area and power overhead of 5.9% and 0.8% relative to the baseline vector processing unit.
We present a unified model for connected antenna arrays with a large number of tightly integrated (i.e., coupled) antennas in a compact space within the context of massive multiple-input multiple-output (MIMO) communication. We refer to this system as tightly-coupled massive MIMO. From an information-theoretic perspective, scaling the design of tightly-coupled massive MIMO systems in terms of the number of antennas, the operational bandwidth, and form factor was not addressed in prior art. We investigate this open research problem using a physically consistent modeling approach for far-field (FF) MIMO communication based on multi-port circuit theory. In doing so, we turn mutual coupling (MC) from a foe to a friend of MIMO systems design, thereby challenging a basic percept in antenna systems engineering that promotes MC mitigation/compensation. We show that tight MC widens the operational bandwidth of antenna arrays thereby unleashing a missing MIMO gain that we coin "bandwidth gain". Furthermore, we derive analytically the asymptotically optimum spacing-to-antenna-size ratio by establishing a condition for tight coupling in the limit of large-size antenna arrays with quasi-continuous apertures. We also optimize the antenna array size while maximizing the achievable rate under fixed transmit power and inter-element spacing. Then, we study the impact of MC on the achievable rate of MIMO systems under line-of-sight (LoS) and Rayleigh fading channels. These results reveal new insights into the design of tightly-coupled massive antenna arrays as opposed to the widely-adopted "disconnected" designs that disregard MC by putting faith in the half-wavelength spacing rule.
We consider the problem of allocating orders to multiple stations and sequencing the interlinked order and rack processing flows in each station in the robot-assisted KIVA warehouse. The various decisions involved in the problem, which are closely associated and must be solved in real time, are often tackled separately for ease of treatment. However, exploiting the synergy between order assignment and picking station scheduling benefits picking efficiency. We develop a comprehensive mathematical model that takes the synergy into consideration to minimize the total number of rack visits. To solve this intractable problem, we develop an efficient algorithm based on simulated annealing and beam search. Computational studies show that our proposed approach outperforms the rule-based greedy policy and the independent picking station scheduling method in terms of solution quality, saving over one-third and one-fifth of rack visits compared with the former and latter, respectively.
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed Neural Networks (MINNs), a class of architectures specifically tailored to handle mesh based functional data, and thus of particular interest for reduced order modeling of parametrized Partial Differential Equations (PDEs). The driving idea behind MINNs is to embed hidden layers into discrete functional spaces of increasing complexity, obtained through a sequence of meshes defined over the underlying spatial domain. The approach leads to a natural pruning strategy which enables the design of sparse architectures that are able to learn general nonlinear operators. We assess this strategy through an extensive set of numerical experiments, ranging from nonlocal operators to nonlinear diffusion PDEs, where MINNs are compared against more traditional architectures, such as classical fully connected Deep Neural Networks, but also more recent ones, such as DeepONets and Fourier Neural Operators. Our results show that MINNs can handle functional data defined on general domains of any shape, while ensuring reduced training times, lower computational costs, and better generalization capabilities, thus making MINNs very well-suited for demanding applications such as Reduced Order Modeling and Uncertainty Quantification for PDEs.
Gathering knowledge about surroundings and generating situational awareness for IoT devices is of utmost importance for systems developed for smart urban and uncontested environments. For example, a large-area surveillance system is typically equipped with multi-modal sensors such as cameras and LIDARs and is required to execute deep learning algorithms for action, face, behavior, and object recognition. However, these systems face power and memory constraints due to their ubiquitous nature, making it crucial to optimize data processing, deep learning algorithm input, and model inference communication. In this paper, we propose a self-adaptive optimization framework for a testbed comprising two Unmanned Ground Vehicles (UGVs) and two NVIDIA Jetson devices. This framework efficiently manages multiple tasks (storage, processing, computation, transmission, inference) on heterogeneous nodes concurrently. It involves compressing and masking input image frames, identifying similar frames, and profiling devices to obtain boundary conditions for optimization.. Finally, we propose and optimize a novel parameter split-ratio, which indicates the proportion of the data required to be offloaded to another device while considering the networking bandwidth, busy factor, memory (CPU, GPU, RAM), and power constraints of the devices in the testbed. Our evaluations captured while executing multiple tasks (e.g., PoseNet, SegNet, ImageNet, DetectNet, DepthNet) simultaneously, reveal that executing 70% (split-ratio=70%) of the data on the auxiliary node minimizes the offloading latency by approx. 33% (18.7 ms/image to 12.5 ms/image) and the total operation time by approx. 47% (69.32s to 36.43s) compared to the baseline configuration (executing on the primary node).
Since 2010, multiple cyber incidents on industrial infrastructure, such as Stuxnet and CrashOverride, have exposed the vulnerability of Industrial Control Systems (ICS) to cyber threats. The industrial systems are commissioned for longer duration amounting to decades, often resulting in non-compliance to technological advancements in industrial cybersecurity mechanisms. The unavailability of network infrastructure information makes designing the security policies or configuring the cybersecurity countermeasures such as Network Intrusion Detection Systems (NIDS) challenging. An empirical solution is to self-learn the network infrastructure information of an industrial system from its monitored network traffic to make the network transparent for downstream analyses tasks such as anomaly detection. In this work, a Python-based industrial communication paradigm-aware framework, named PROFINET Operations Enumeration and Tracking (POET), that enumerates different industrial operations executed in a deterministic order of a PROFINET-based industrial system is reported. The operation-driving industrial network protocol frames are dissected for enumeration of the operations. For the requirements of capturing the transitions between industrial operations triggered by the communication events, the Finite State Machines (FSM) are modelled to enumerate the PROFINET operations of the device, connection and system. POET extracts the network information from network traffic to instantiate appropriate FSM models (Device, Connection or System) and track the industrial operations. It successfully detects and reports the anomalies triggered by a network attack in a miniaturized PROFINET-based industrial system, executed through valid network protocol exchanges and resulting in invalid PROFINET operation transition for the device.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
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