The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the differential equations stiff, calling for computationally demanding implicit integration schemes. We suggest to tackle this issue by using exponential integrators, a long-standing class of integration schemes (first introduced in the 60's) that in recent years has enjoyed a resurgence of interest. We show that this scheme can be easily applied to multi-body systems subject to stiff viscoelastic contacts, producing accurate results at lower computational cost than \changed{classic explicit or implicit schemes}. In our tests with quadruped and biped robots, our method demonstrated stable behaviors with large time steps (10 ms) and stiff contacts ($10^5$ N/m). Its excellent properties, especially for fast and coarse simulations, make it a valuable candidate for many applications in robotics, such as simulation, Model Predictive Control, Reinforcement Learning, and controller design.
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Integration：Integration, the VLSI Journal。
Explanation：集成，VLSI雜志。
Publisher：Elsevier。
SIT：
Accurate camera pose estimation is a fundamental requirement for numerous applications, such as autonomous driving, mobile robotics, and augmented reality. In this work, we address the problem of estimating the global 6 DoF camera pose from a single RGB image in a given environment. Previous works consider every part of the image valuable for localization. However, many image regions such as the sky, occlusions, and repetitive non-distinguishable patterns cannot be utilized for localization. In addition to adding unnecessary computation efforts, extracting and matching features from such regions produce many wrong matches which in turn degrades the localization accuracy and efficiency. Our work addresses this particular issue and shows by exploiting an interesting concept of sparse 3D models that we can exploit discriminatory environment parts and avoid useless image regions for the sake of a single image localization. Interestingly, through avoiding selecting keypoints from non-reliable image regions such as trees, bushes, cars, pedestrians, and occlusions, our work acts naturally as an outlier filter. This makes our system highly efficient in that minimal set of correspondences is needed and highly accurate as the number of outliers is low. Our work exceeds state-ofthe-art methods on outdoor Cambridge Landmarks dataset. With only relying on single image at inference, it outweighs in terms of accuracy methods that exploit pose priors and/or reference 3D models while being much faster. By choosing as little as 100 correspondences, it surpasses similar methods that localize from thousands of correspondences, while being more efficient. In particular, it achieves, compared to these methods, an improvement of localization by 33% on OldHospital scene. Furthermore, It outstands direct pose regressors even those that learn from sequence of images
We develop an \textit{a posteriori} error analysis for a numerical estimate of the time at which a functional of the solution to a partial differential equation (PDE) first achieves a threshold value on a given time interval. This quantity of interest (QoI) differs from classical QoIs which are modeled as bounded linear (or nonlinear) functionals {of the solution}. Taylor's theorem and an adjoint-based \textit{a posteriori} analysis is used to derive computable and accurate error estimates in the case of semi-linear parabolic and hyperbolic PDEs. The accuracy of the error estimates is demonstrated through numerical solutions of the one-dimensional heat equation and linearized shallow water equations (SWE), representing parabolic and hyperbolic cases, respectively.
Most machine learning methods are used as a black box for modelling. We may try to extract some knowledge from physics-based training methods, such as neural ODE (ordinary differential equation). Neural ODE has advantages like a possibly higher class of represented functions, the extended interpretability compared to black-box machine learning models, ability to describe both trend and local behaviour. Such advantages are especially critical for time series with complicated trends. However, the known drawback is the high training time compared to the autoregressive models and long-short term memory (LSTM) networks widely used for data-driven time series modelling. Therefore, we should be able to balance interpretability and training time to apply neural ODE in practice. The paper shows that modern neural ODE cannot be reduced to simpler models for time-series modelling applications. The complexity of neural ODE is compared to or exceeds the conventional time-series modelling tools. The only interpretation that could be extracted is the eigenspace of the operator, which is an ill-posed problem for a large system. Spectra could be extracted using different classical analysis methods that do not have the drawback of extended time. Consequently, we reduce the neural ODE to a simpler linear form and propose a new view on time-series modelling using combined neural networks and an ODE system approach.
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate stochastic processes. Parameters like the spectral density matrix and its inverse, the coherence or the partial coherence, encode comprehensively the complex linear relations between the component processes of the multivariate system. In this paper, we develop inference procedures for such parameters in a high-dimensional, time series setup. In particular, we first focus on the derivation of consistent estimators of the coherence and, more importantly, of the partial coherence which possess manageable limiting distributions that are suitable for testing purposes. Statistical tests of the hypothesis that the maximum over frequencies of the coherence, respectively, of the partial coherence, do not exceed a prespecified threshold value are developed. Our approach allows for testing hypotheses for individual coherences and/or partial coherences as well as for multiple testing of large sets of such parameters. In the latter case, a consistent procedure to control the false discovery rate is developed. The finite sample performance of the inference procedures proposed is investigated by means of simulations and applications to the construction of graphical interaction models for brain connectivity based on EEG data are presented.
The great quest for adopting AI-based computation for safety-/mission-critical applications motivates the interest towards methods for assessing the robustness of the application w.r.t. not only its training/tuning but also errors due to faults, in particular soft errors, affecting the underlying hardware. Two strategies exist: architecture-level fault injection and application-level functional error simulation. We present a framework for the reliability analysis of Convolutional Neural Networks (CNNs) via an error simulation engine that exploits a set of validated error models extracted from a detailed fault injection campaign. These error models are defined based on the corruption patterns of the output of the CNN operators induced by faults and bridge the gap between fault injection and error simulation, exploiting the advantages of both approaches. We compared our methodology against SASSIFI for the accuracy of functional error simulation w.r.t. fault injection, and against TensorFI in terms of speedup for the error simulation strategy. Experimental results show that our methodology achieves about 99\% accuracy of the fault effects w.r.t. SASSIFI, and a speedup ranging from 44x up to 63x w.r.t. TensorFI, that only implements a limited set of error models.
Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective macroscopic equations which eliminates the small scales by exploiting scale separation. An accurate homogenized model avoids the computationally-expensive task of numerically solving the underlying balance laws at a fine scale, thereby rendering a numerical solution of the balance laws more computationally tractable. In complex settings, homogenization only defines the constitutive model implicitly, and machine learning can be used to learn the constitutive model explicitly from localized fine-scale simulations. In the case of one-dimensional viscoelasticity, the linearity of the model allows for a complete analysis. We establish that the homogenized constitutive model may be approximated by a recurrent neural network (RNN) that captures the memory. The memory is encapsulated in the evolution of an appropriate finite set of internal variables, discovered through the learning process and dependent on the history of the strain. Simulations are presented which validate the theory. Guidance for the learning of more complex models, such as arise in plasticity, by similar techniques, is given.
High-dimensional parabolic partial integro-differential equations (PIDEs) appear in many applications in insurance and finance. Existing numerical methods suffer from the curse of dimensionality or provide solutions only for a given space-time point. This gave rise to a growing literature on deep learning based methods for solving partial differential equations; results for integro-differential equations on the other hand are scarce. In this paper we consider an extension of the deep splitting scheme due to arXiv:1907.03452 and arXiv:2006.01496v3 to PIDEs. Our main contribution is an analysis of the approximation error which yields convergence rates in terms of the number of neurons for shallow neural networks. Moreover we discuss several test case studies to show the viability of our approach.
Accelerating hydrodynamic simulations of urban drainage systems with physics-guided machine learning
We propose and demonstrate a new approach for fast and accurate surrogate modelling of urban drainage system hydraulics based on physics-guided machine learning. The surrogates are trained against a limited set of simulation results from a hydrodynamic (HiFi) model. Our approach reduces simulation times by one to two orders of magnitude compared to a HiFi model. It is thus slower than e.g. conceptual hydrological models, but it enables simulations of water levels, flows and surcharges in all nodes and links of a drainage network and thus largely preserves the level of detail provided by HiFi models. Comparing time series simulated by the surrogate and the HiFi model, R2 values in the order of 0.9 are achieved. Surrogate training times are currently in the order of one hour. However, they can likely be reduced through the application of transfer learning and graph neural networks. Our surrogate approach will be useful for interactive workshops in initial design phases of urban drainage systems, as well as for real time applications. In addition, our model formulation is generic and future research should investigate its application for simulating other water systems.
The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
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