Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by a finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months, and is a significant cost in practice. We have developed a Bayesian optimization system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing a generalized inverse of a high-dimensional non-linear function that does not require e.g. gradient information, which is often unavailable from discipline models. We furthermore develop a two-tier convergence criterion based on (i) convergence to a solution optimally satisfying all specified design criteria, or (ii) convergence to a minimum-norm solution. We demonstrate the proposed approach on a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient, and that the novel convergence criteria can be implemented straightforwardly based on existing concepts and subroutines in popular Bayesian optimization software packages.

Extracting information about hadron resonances requires fitting theoretical models to experimental data. However, this data often comes from different experiments of different physics quantities in varying kinematic regions; studying coupled channels with different kinematic coverages and binning can make direct comparison challenging. The consistency of these datasets directly impacts the quality of the fit, thus making it difficult to accurately constrain the theoretical models. Sparse datasets in key kinematic regions further complicates the quantification of uncertainties, often requiring arbitrary weighting that may introduce bias. A robust approach to solving these problems involves utilising Gaussian Processes (GPs), a Bayesian inference machine learning technique that provides probabilistic predictions for unknown datapoints. Unlike traditional machine learning methods, GPs do not require any training; instead, they operate on three fundamental assumptions: 1. Some kernel function can be defined to measure the covariance between known datapoints; 2. This same kernel function can be used to predict the covariance between unknown datapoints; 3. Some idea of the form of the posterior distribution is known (e.g.

Existing LiDAR-Inertial Odometry (LIO) frameworks typically utilize prior state trajectories derived from IMU integration to compensate for the motion distortion within LiDAR frames, and demonstrate outstanding accuracy and stability in regular low-speed and smooth scenes. However, in high-speed or intense motion scenarios, the residual distortion may increase due to the limitation of IMU's accuracy and frequency, which will degrade the consistency between the LiDAR frame with its represented geometric environment, leading pointcloud registration to fall into local optima and consequently increasing the drift in long-time and large-scale localization. To address the issue, we propose a novel asymptotically and consistently converging LIO framework called AC-LIO. First, during the iterative state estimation, we backwards propagate the update term based on the prior state chain, and asymptotically compensate the residual distortion before next iteration. Second, considering the weak correlation between the initial error and motion distortion of current frame, we propose a convergence criteria based on pointcloud constraints to control the back propagation. The approach of guiding the asymptotic distortion compensation based on convergence criteria can promote the consistent convergence of pointcloud registration and increase the accuracy and robustness of LIO. Experiments show that our AC-LIO framework, compared to other state-of-the-art frameworks, effectively promotes consistent convergence in state estimation and further improves the accuracy of long-time and large-scale localization and mapping.

Measuring Efficiency in neural network system development is an open research problem. This paper presents an experimental framework to measure the training efficiency of a neural architecture. To demonstrate our approach, we analyze the training efficiency of Convolutional Neural Networks and Bayesian equivalents on the MNIST and CIFAR-10 tasks. Our results show that training efficiency decays as training progresses and varies across different stopping criteria for a given neural model and learning task. We also find a non-linear relationship between training stopping criteria, training Efficiency, model size, and training Efficiency. Furthermore, we illustrate the potential confounding effects of overtraining on measuring the training efficiency of a neural architecture. Regarding relative training efficiency across different architectures, our results indicate that CNNs are more efficient than BCNNs on both datasets. More generally, as a learning task becomes more complex, the relative difference in training efficiency between different architectures becomes more pronounced.

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as safety-critical requirements using discrete-time control barrier functions within a model predictive control (MPC) framework. Existing work usually focus on the feasibility or the safety for the optimization problem, and the majority of the existing work restrict the discussions to relative-degree one control barrier functions. Additionally, the real-time computation is challenging when a large horizon is considered in the MPC problem for relative-degree one or high-order control barrier functions. In this paper, we propose a framework that solves the safety-critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high-order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results.

Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. However, the most common algorithm for fitting finite mixture models, the EM algorithm, falls victim to a number of issues. We address these issues that plague clustering using finite mixture models, including convergence to solutions corresponding to local maxima and algorithm speed concerns in high dimensional cases. This is done by developing two novel algorithms that incorporate a spectral decomposition of the data matrix and a non-parametric bootstrap sampling scheme. Simulations show the validity of our algorithms and demonstrate not only their flexibility but also their ability to avoid solutions corresponding to local-maxima, when compared to other (bootstrapped) clustering algorithms for estimating finite mixture models. Our novel algorithms have a typically more consistent convergence criteria as well as a significant increase in speed over other bootstrapped algorithms that fit finite mixture models.

In the field, robots often need to operate in unknown and unstructured environments, where accurate sensing and state estimation (SE) becomes a major challenge. Cameras have been used to great success in mapping and planning in such environments, as well as complex but quasi-static tasks such as grasping, but are rarely integrated into the control loop for unstable systems. Learning pixel-to-torque control promises to allow robots to flexibly handle a wider variety of tasks. Although they do not present additional theoretical obstacles, learning pixel-to-torque control for unstable systems that that require precise and high bandwidth control still poses a significant practical challenge, and best practices have not yet been established. To help drive reproducible research on the practical aspects of learning pixel-to-torque control, we propose a platform that can flexibly represent the entire process, from lab to deployment, for learning pixel-to-torque control on a robot with fast, unstable dynamics: the vision-based Furuta pendulum. The platform can be reproduced with either off-the-shelf or custom-built hardware. We expect that this platform will allow researchers to quickly and systematically test different approaches, as well as reproduce and benchmark case studies from other labs. We also present a first case study on this system using DNNs which, to the best of our knowledge, is the first demonstration of learning pixel-to-torque control on an unstable system with update rates faster than 100 Hz. A video synopsis can be found online at https://youtu.be/S2llScfG-8E, and in the supplementary material.

Reinforcement learning (RL) is a promising tool to solve robust optimal well control problems where the model parameters are highly uncertain, and the system is partially observable in practice. However, RL of robust control policies often relies on performing a large number of simulations. This could easily become computationally intractable for cases with computationally intensive simulations. To address this bottleneck, an adaptive multi-grid RL framework is introduced which is inspired by principles of geometric multi-grid methods used in iterative numerical algorithms. RL control policies are initially learned using computationally efficient low fidelity simulations using coarse grid discretization of the underlying partial differential equations (PDEs). Subsequently, the simulation fidelity is increased in an adaptive manner towards the highest fidelity simulation that correspond to finest discretization of the model domain. The proposed framework is demonstrated using a state-of-the-art, model-free policy-based RL algorithm, namely the Proximal Policy Optimisation (PPO) algorithm. Results are shown for two case studies of robust optimal well control problems which are inspired from SPE-10 model 2 benchmark case studies. Prominent gains in the computational efficiency is observed using the proposed framework saving around 60-70% of computational cost of its single fine-grid counterpart.

The PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has proven useful for applications in different domains such as chemometrics, and neuroscience. However, the evolving mode of the PARAFAC2 model is traditionally modelled implicitly, which makes it challenging to regularise it. Currently, the only way to apply regularisation on that mode is with a flexible coupling approach, which finds the solution through regularised least-squares subproblems. In this work, we instead propose an alternating direction method of multipliers (ADMM)-based algorithm for fitting PARAFAC2 and widen the possible regularisation penalties to any proximable function. Our numerical experiments demonstrate that the proposed ADMM-based approach for PARAFAC2 can accurately recover the underlying components from simulated data while being both computationally efficient and flexible in terms of imposing constraints.

Machine learning (ML) training algorithms often possess an inherent self-correcting behavior due to their iterative-convergent nature. Recent systems exploit this property to achieve adaptability and efficiency in unreliable computing environments by relaxing the consistency of execution and allowing calculation errors to be self-corrected during training. However, the behavior of such systems are only well understood for specific types of calculation errors, such as those caused by staleness, reduced precision, or asynchronicity, and for specific types of training algorithms, such as stochastic gradient descent. In this paper, we develop a general framework to quantify the effects of calculation errors on iterative-convergent algorithms and use this framework to design new strategies for checkpoint-based fault tolerance. Our framework yields a worst-case upper bound on the iteration cost of arbitrary perturbations to model parameters during training. Our system, SCAR, employs strategies which reduce the iteration cost upper bound due to perturbations incurred when recovering from checkpoints. We show that SCAR can reduce the iteration cost of partial failures by 78% - 95% when compared with traditional checkpoint-based fault tolerance across a variety of ML models and training algorithms.