5,180 research outputs found
Trajectory inference of unknown linear systems based on partial states measurements
Proliferation of cheaper autonomous system prototypes has magnified the threat space for attacks across the manufacturing, transport, and smart living sectors. An accurate trajectory inference algorithm is required for monitoring and early detection of autonomous misbehavior and to take relevant countermeasures. This article presents a trajectory inference algorithm based on a CLOE approach using partial states measurements. The approach is based on a physics informed state parameteterization that combines the main advantages of state estimation and identification algorithms. Noise attenuation and parameter estimates convergence are obtained if the output trajectories fulfill a persistent excitation condition. Known and unknown desired reference/destination cases are considered. The stability and convergence of the proposed approach are assessed via Lyapunov stability theory under the fulfillment of a persistent excitation condition. Simulation studies are carried out to verify the effectiveness of the proposed approach
Backpropagation Beyond the Gradient
Automatic differentiation is a key enabler of deep learning: previously, practitioners were limited to models
for which they could manually compute derivatives. Now, they can create sophisticated models with almost
no restrictions and train them using first-order, i. e. gradient, information. Popular libraries like PyTorch
and TensorFlow compute this gradient efficiently, automatically, and conveniently with a single line of
code. Under the hood, reverse-mode automatic differentiation, or gradient backpropagation, powers the
gradient computation in these libraries. Their entire design centers around gradient backpropagation.
These frameworks are specialized around one specific task—computing the average gradient in a mini-batch.
This specialization often complicates the extraction of other information like higher-order statistical moments
of the gradient, or higher-order derivatives like the Hessian. It limits practitioners and researchers to methods
that rely on the gradient. Arguably, this hampers the field from exploring the potential of higher-order
information and there is evidence that focusing solely on the gradient has not lead to significant recent
advances in deep learning optimization.
To advance algorithmic research and inspire novel ideas, information beyond the batch-averaged gradient
must be made available at the same level of computational efficiency, automation, and convenience.
This thesis presents approaches to simplify experimentation with rich information beyond the gradient
by making it more readily accessible. We present an implementation of these ideas as an extension to the
backpropagation procedure in PyTorch. Using this newly accessible information, we demonstrate possible use
cases by (i) showing how it can inform our understanding of neural network training by building a diagnostic
tool, and (ii) enabling novel methods to efficiently compute and approximate curvature information.
First, we extend gradient backpropagation for sequential feedforward models to Hessian backpropagation
which enables computing approximate per-layer curvature. This perspective unifies recently proposed block-
diagonal curvature approximations. Like gradient backpropagation, the computation of these second-order
derivatives is modular, and therefore simple to automate and extend to new operations.
Based on the insight that rich information beyond the gradient can be computed efficiently and at the
same time, we extend the backpropagation in PyTorch with the BackPACK library. It provides efficient and
convenient access to statistical moments of the gradient and approximate curvature information, often at a
small overhead compared to computing just the gradient.
Next, we showcase the utility of such information to better understand neural network training. We build
the Cockpit library that visualizes what is happening inside the model during training through various
instruments that rely on BackPACK’s statistics. We show how Cockpit provides a meaningful statistical
summary report to the deep learning engineer to identify bugs in their machine learning pipeline, guide
hyperparameter tuning, and study deep learning phenomena.
Finally, we use BackPACK’s extended automatic differentiation functionality to develop ViViT, an approach
to efficiently compute curvature information, in particular curvature noise. It uses the low-rank structure
of the generalized Gauss-Newton approximation to the Hessian and addresses shortcomings in existing
curvature approximations. Through monitoring curvature noise, we demonstrate how ViViT’s information
helps in understanding challenges to make second-order optimization methods work in practice.
This work develops new tools to experiment more easily with higher-order information in complex deep
learning models. These tools have impacted works on Bayesian applications with Laplace approximations,
out-of-distribution generalization, differential privacy, and the design of automatic differentia-
tion systems. They constitute one important step towards developing and establishing more efficient deep
learning algorithms
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
X-ICP: Localizability-Aware LiDAR Registration for Robust Localization in Extreme Environments
Modern robotic systems are required to operate in challenging environments,
which demand reliable localization under challenging conditions. LiDAR-based
localization methods, such as the Iterative Closest Point (ICP) algorithm, can
suffer in geometrically uninformative environments that are known to
deteriorate point cloud registration performance and push optimization toward
divergence along weakly constrained directions. To overcome this issue, this
work proposes i) a robust fine-grained localizability detection module, and ii)
a localizability-aware constrained ICP optimization module, which couples with
the localizability detection module in a unified manner. The proposed
localizability detection is achieved by utilizing the correspondences between
the scan and the map to analyze the alignment strength against the principal
directions of the optimization as part of its fine-grained LiDAR localizability
analysis. In the second part, this localizability analysis is then integrated
into the scan-to-map point cloud registration to generate drift-free pose
updates by enforcing controlled updates or leaving the degenerate directions of
the optimization unchanged. The proposed method is thoroughly evaluated and
compared to state-of-the-art methods in simulated and real-world experiments,
demonstrating the performance and reliability improvement in LiDAR-challenging
environments. In all experiments, the proposed framework demonstrates accurate
and generalizable localizability detection and robust pose estimation without
environment-specific parameter tuning.Comment: 20 Pages, 20 Figures Submitted to IEEE Transactions On Robotics.
Supplementary Video: https://youtu.be/SviLl7q69aA Project Website:
https://sites.google.com/leggedrobotics.com/x-ic
Learning and Control of Dynamical Systems
Despite the remarkable success of machine learning in various domains in recent years, our understanding of its fundamental limitations remains incomplete. This knowledge gap poses a grand challenge when deploying machine learning methods in critical decision-making tasks, where incorrect decisions can have catastrophic consequences. To effectively utilize these learning-based methods in such contexts, it is crucial to explicitly characterize their performance. Over the years, significant research efforts have been dedicated to learning and control of dynamical systems where the underlying dynamics are unknown or only partially known a priori, and must be inferred from collected data. However, much of these classical results have focused on asymptotic guarantees, providing limited insights into the amount of data required to achieve desired control performance while satisfying operational constraints such as safety and stability, especially in the presence of statistical noise.
In this thesis, we study the statistical complexity of learning and control of unknown dynamical systems. By utilizing recent advances in statistical learning theory, high-dimensional statistics, and control theoretic tools, we aim to establish a fundamental understanding of the number of samples required to achieve desired (i) accuracy in learning the unknown dynamics, (ii) performance in the control of the underlying system, and (iii) satisfaction of the operational constraints such as safety and stability. We provide finite-sample guarantees for these objectives and propose efficient learning and control algorithms that achieve the desired performance at these statistical limits in various dynamical systems. Our investigation covers a broad range of dynamical systems, starting from fully observable linear dynamical systems to partially observable linear dynamical systems, and ultimately, nonlinear systems.
We deploy our learning and control algorithms in various adaptive control tasks in real-world control systems and demonstrate their strong empirical performance along with their learning, robustness, and stability guarantees. In particular, we implement one of our proposed methods, Fourier Adaptive Learning and Control (FALCON), on an experimental aerodynamic testbed under extreme turbulent flow dynamics in a wind tunnel. The results show that FALCON achieves state-of-the-art stabilization performance and consistently outperforms conventional and other learning-based methods by at least 37%, despite using 8 times less data. The superior performance of FALCON arises from its physically and theoretically accurate modeling of the underlying nonlinear turbulent dynamics, which yields rigorous finite-sample learning and performance guarantees. These findings underscore the importance of characterizing the statistical complexity of learning and control of unknown dynamical systems.</p
Proceedings of SIRM 2023 - The 15th European Conference on Rotordynamics
It was our great honor and pleasure to host the SIRM Conference after 2003 and 2011 for the third time in Darmstadt. Rotordynamics covers a huge variety of different applications and challenges which are all in the scope of this conference. The conference was opened with a keynote lecture given by Rainer Nordmann, one of the three founders of SIRM “Schwingungen in rotierenden Maschinen”. In total 53 papers passed our strict review process and were presented. This impressively shows that rotordynamics is relevant as ever. These contributions cover a very wide spectrum of session topics: fluid bearings and seals; air foil bearings; magnetic bearings; rotor blade interaction; rotor fluid interactions; unbalance and balancing; vibrations in turbomachines; vibration control; instability; electrical machines; monitoring, identification and diagnosis; advanced numerical tools and nonlinearities as well as general rotordynamics. The international character of the conference has been significantly enhanced by the Scientific Board since the 14th SIRM resulting on one hand in an expanded Scientific Committee which meanwhile consists of 31 members from 13 different European countries and on the other hand in the new name “European Conference on Rotordynamics”. This new international profile has also been
emphasized by participants of the 15th SIRM coming from 17 different countries out of three continents. We experienced a vital discussion and dialogue between industry and academia at the conference where roughly one third of the papers were presented by industry and two thirds by academia being an excellent basis to follow a bidirectional transfer what we call xchange at Technical University of Darmstadt. At this point we also want to give our special thanks to the eleven industry sponsors for their great support of the conference. On behalf of the Darmstadt Local Committee I welcome you to read the papers of the 15th SIRM giving you further insight into the topics and presentations
Development, Implementation, and Optimization of a Modern, Subsonic/Supersonic Panel Method
In the early stages of aircraft design, engineers consider many different design concepts, examining the trade-offs between different component arrangements and sizes, thrust and power requirements, etc. Because so many different designs are considered, it is best in the early stages of design to use simulation tools that are fast; accuracy is secondary. A common simulation tool for early design and analysis is the panel method. Panel methods were first developed in the 1950s and 1960s with the advent of modern computers. Despite being reasonably accurate and very fast, their development was abandoned in the late 1980s in favor of more complex and accurate simulation methods. The panel methods developed in the 1980s are still in use by aircraft designers today because of their accuracy and speed. However, they are cumbersome to use and limited in applicability. The purpose of this work is to reexamine panel methods in a modern context. In particular, this work focuses on the application of panel methods to supersonic aircraft (a supersonic aircraft is one that flies faster than the speed of sound). Various aspects of the panel method, including the distributions of the unknown flow variables on the surface of the aircraft and efficiently solving for these unknowns, are discussed. Trade-offs between alternative formulations are examined and recommendations given. This work also serves to bring together, clarify, and condense much of the literature previously published regarding panel methods so as to assist future developers of panel methods
Autonomous Vehicles an overview on system, cyber security, risks, issues, and a way forward
This chapter explores the complex realm of autonomous cars, analyzing their
fundamental components and operational characteristics. The initial phase of
the discussion is elucidating the internal mechanics of these automobiles,
encompassing the crucial involvement of sensors, artificial intelligence (AI)
identification systems, control mechanisms, and their integration with
cloud-based servers within the framework of the Internet of Things (IoT). It
delves into practical implementations of autonomous cars, emphasizing their
utilization in forecasting traffic patterns and transforming the dynamics of
transportation. The text also explores the topic of Robotic Process Automation
(RPA), illustrating the impact of autonomous cars on different businesses
through the automation of tasks. The primary focus of this investigation lies
in the realm of cybersecurity, specifically in the context of autonomous
vehicles. A comprehensive analysis will be conducted to explore various risk
management solutions aimed at protecting these vehicles from potential threats
including ethical, environmental, legal, professional, and social dimensions,
offering a comprehensive perspective on their societal implications. A
strategic plan for addressing the challenges and proposing strategies for
effectively traversing the complex terrain of autonomous car systems,
cybersecurity, hazards, and other concerns are some resources for acquiring an
understanding of the intricate realm of autonomous cars and their ramifications
in contemporary society, supported by a comprehensive compilation of resources
for additional investigation.
Keywords: RPA, Cyber Security, AV, Risk, Smart Car
An extended generalized Markov model for the spread risk and its calibration by using filtering techniques in Solvency II framework
The Solvency II regulatory regime requires the calculation of a capital requirement, the Solvency Capital Requirement (SCR), for the insurance and reinsurance companies, that is based on a market-consistent evaluation of the Basic Own Funds probability distribution forecast over a one-year time horizon. This work proposes an extended generalized Markov model for rating-based pricing of risky securities for spread risk assessment and management within the Solvency II framework, under an internal model or partial internal model. This model is based on Jarrow, Lando and Turnbull (1997), Lando (1998) and Gambaro et al. (2018) and models the credit rating transitions and the default process using an extension of a time-homogeneous Markov chain and two subordinator processes. This approach allows simultaneous modeling of credit spreads for different rating classes and credit spreads to fluctuate randomly even when the rating does not change.
The estimation methodologies used in this work are consistent with the scope of the work and the scope of the proposed model, i.e., pricing of defaultable bonds and calculation of SCR for the spread risk sub-module, and with the market-consistency principle required by Solvency II. For this purpose, estimation techniques on time series known as filtering techniques are used, which allow the model parameters to be jointly estimated under both the real-world probability measure (necessary for risk assessment) and the risk-neutral probability measure (necessary for pricing). Specifically, an appropriate set of time series of credit spread term structures, differentiated by economic sector and rating class, is used.
The proposed model, in its final version, returns excellent results in terms of goodness of fit to historical data, and the projected data are consistent with historical data and the Solvency II framework.
The filtering techniques, in the different configurations used in this work (particle filtering with Gauss-Legendre quadrature techniques, particle filtering with
Sequential Importance Resampling algorithm, Kalman filter), were found to be an effective and flexible tool for estimating the models proposed, able to handle the high computational complexity of the problem addressed
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