For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). The companion paper proposed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. T o address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cram er-Rao lower bound as a benchmark. Index T erms--Bayesian filtering, counter-adversarial systems, extended Kalman filter, inverse filtering, non-linear processes.

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. We demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

Neural networks (NN) have become almost ubiquitous with image classification, but in their standard form produce point estimates, with no measure of confidence. Bayesian neural networks (BNN) provide uncertainty quantification (UQ) for NN predictions and estimates through the posterior distribution. As NN are applied in more high-consequence applications, UQ is becoming a requirement. BNN provide a solution to this problem by not only giving accurate predictions and estimates, but also an interval that includes reasonable values within a desired probability. Despite their positive attributes, BNN are notoriously difficult and time consuming to train. Traditional Bayesian methods use Markov Chain Monte Carlo (MCMC), but this is often brushed aside as being too slow. The most common method is variational inference (VI) due to its fast computation, but there are multiple concerns with its efficacy. We apply and compare MCMC- and VI-trained BNN in the context of target detection in hyperspectral imagery (HSI), where materials of interest can be identified by their unique spectral signature. This is a challenging field, due to the numerous permuting effects practical collection of HSI has on measured spectra. Both models are trained using out-of-the-box tools on a high fidelity HSI target detection scene. Both MCMC- and VI-trained BNN perform well overall at target detection on a simulated HSI scene. This paper provides an example of how to utilize the benefits of UQ, but also to increase awareness that different training methods can give different results for the same model. If sufficient computational resources are available, the best approach rather than the fastest or most efficient should be used, especially for high consequence problems.

Establishing a human settlement on Mars is an incredibly complex engineering problem. The inhospitable nature of the Martian environment requires any habitat to be largely self-sustaining. Beyond mining a few basic minerals and water, the colonizers will be dependent on Earth resupply and replenishment of necessities via technological means, i.e., splitting Martian water into oxygen for breathing and hydrogen for fuel. Beyond the technical and engineering challenges, future colonists will also face psychological and human behavior challenges. Our goal is to better understand the behavioral and psychological interactions of future Martian colonists through an Agent-Based Modeling (ABM simulation) approach. We seek to identify areas of consideration for planning a colony as well as propose a minimum initial population size required to create a stable colony. Accounting for engineering and technological limitations, we draw on research regarding high performing teams in isolated and high stress environments (ex: submarines, Arctic exploration, ISS, war) to include the 4 basic personality types within the ABM. Interactions between agents with different psychological profiles are modeled at the individual level, while global events such as accidents or delays in Earth resupply affect the colony as a whole. From our multiple simulations and scenarios (up to 28 Earth years), we found that an initial population of 22 was the minimum required to maintain a viable colony size over the long run. We also found that the agreeable personality type was the one more likely to survive. We find, contrary to other literature, that the minimum number of people with all personality types that can lead to a sustainable settlement is in the tens and not hundreds.

Decision-focused learning (DFL) has recently emerged as a powerful approach for predict-then-optimize problems by customizing a predictive model to a downstream optimization task. However, existing end-to-end DFL methods are hindered by three significant bottlenecks: model mismatch error, sample average approximation error, and gradient approximation error. Model mismatch error stems from the misalignment between the model's parameterized predictive distribution and the true probability distribution. Sample average approximation error arises when using finite samples to approximate the expected optimization objective. Gradient approximation error occurs as DFL relies on the KKT condition for exact gradient computation, while most methods approximate the gradient for backpropagation in non-convex objectives. In this paper, we present DF2 -- the first \textit{distribution-free} decision-focused learning method explicitly designed to address these three bottlenecks. Rather than depending on a task-specific forecaster that requires precise model assumptions, our method directly learns the expected optimization function during training. To efficiently learn the function in a data-driven manner, we devise an attention-based model architecture inspired by the distribution-based parameterization of the expected objective. Our method is, to the best of our knowledge, the first to address all three bottlenecks within a single model. We evaluate DF2 on a synthetic problem, a wind power bidding problem, and a non-convex vaccine distribution problem, demonstrating the effectiveness of DF2.

We introduce AutoGluon-TimeSeries - an open-source AutoML library for probabilistic time series forecasting. Focused on ease of use and robustness, AutoGluon-TimeSeries enables users to generate accurate point and quantile forecasts with just 3 lines of Python code. Built on the design philosophy of AutoGluon, AutoGluon-TimeSeries leverages ensembles of diverse forecasting models to deliver high accuracy within a short training time. AutoGluon-TimeSeries combines both conventional statistical models, machine-learning based forecasting approaches, and ensembling techniques. In our evaluation on 29 benchmark datasets, AutoGluon-TimeSeries demonstrates strong empirical performance, outperforming a range of forecasting methods in terms of both point and quantile forecast accuracy, and often even improving upon the best-in-hindsight combination of prior methods.

Autonomous underwater vehicles (AUVs) play a crucial role in surveying marine environments, carrying out underwater inspection tasks, and ocean exploration. However, in order to ensure that the AUV is able to carry out its mission successfully, a control system capable of adapting to changing environmental conditions is required. Furthermore, to ensure the robotic platform's safe operation, the onboard controller should be able to operate under certain constraints. In this work, we investigate the feasibility of Model Predictive Path Integral Control (MPPI) for the control of an AUV. We utilise a non-linear model of the AUV to propagate the samples of the MPPI, which allow us to compute the control action in real time. We provide a detailed evaluation of the effect of the main hyperparameters on the performance of the MPPI controller. Furthermore, we compared the performance of the proposed method with a classical PID and Cascade PID approach, demonstrating the superiority of our proposed controller. Finally, we present results where environmental constraints are added and show how MPPI can handle them by simply incorporating those constraints in the cost function.

The efficient utilization of wind power by wind turbines relies on the ability of their pitch systems to adjust blade pitch angles in response to varying wind speeds. However, the presence of multiple health conditions in the pitch system due to the long-term wear and tear poses challenges in accurately classifying them, thus increasing the maintenance cost of wind turbines or even damaging them. This paper proposes a novel method based on hard sample mining-enabled supervised contrastive learning (HSMSCL) to address this problem. The proposed method employs cosine similarity to identify hard samples and subsequently, leverages supervised contrastive learning to learn more discriminative representations by constructing hard sample pairs. Furthermore, the hard sample mining framework in the proposed method also constructs hard samples with learned representations to make the training process of the multilayer perceptron (MLP) more challenging and make it a more effective classifier. The proposed approach progressively improves the fault diagnosis model by introducing hard samples in the SCL and MLP phases, thus enhancing its performance in complex multi-class fault diagnosis tasks. To evaluate the effectiveness of the proposed method, two real datasets comprising wind turbine pitch system cog belt fracture data are utilized. The fault diagnosis performance of the proposed method is compared against existing methods, and the results demonstrate its superior performance. The proposed approach exhibits significant improvements in fault diagnosis performance, providing promising prospects for enhancing the reliability and efficiency of wind turbine pitch system fault diagnosis.

This paper presents a safety-critical locomotion control framework for quadrupedal robots. Our goal is to enable quadrupedal robots to safely navigate in cluttered environments. To tackle this, we introduce exponential Discrete Control Barrier Functions (exponential DCBFs) with duality-based obstacle avoidance constraints into a Nonlinear Model Predictive Control (NMPC) with Whole-Body Control (WBC) framework for quadrupedal locomotion control. This enables us to use polytopes to describe the shapes of the robot and obstacles for collision avoidance while doing locomotion control of quadrupedal robots. Compared to most prior work, especially using CBFs, that utilize spherical and conservative approximation for obstacle avoidance, this work demonstrates a quadrupedal robot autonomously and safely navigating through very tight spaces in the real world. (Our open-source code is available at github.com/HybridRobotics/quadruped_nmpc_dcbf_duality, and the video is available at youtu.be/p1gSQjwXm1Q.)

Developing extended hydrodynamics equations valid for both dense and rarefied gases remains a great challenge. A systematical solution for this challenge is the moment method describing both dense and rarefied gas behaviors with moments of gas molecule velocity distributions. Among moment methods, the maximal entropy moment method (MEM) stands out for its well-posedness and stability, which utilizes velocity distributions with maximized entropy. However, finding such distributions requires solving an ill-conditioned and computation-demanding optimization problem. This problem causes numerical overflow and breakdown when the numerical precision is insufficient, especially for flows like high-speed shock waves. It also prevents modern GPUs from accelerating optimization with their enormous single floating-point precision computation power. This paper aims to stabilize MEM, making it practical for simulating very strong normal shock waves on modern GPUs at single precision. We propose the gauge transformations for MEM, making the optimization less ill-conditioned. We also tackle numerical overflow and breakdown by adopting the canonical form of distribution and Newton's modified optimization method. With these techniques, we achieved a single-precision GPU simulation of a Mach 10 shock wave with 35 moments MEM, surpassing the previous double-precision results of Mach 4. Moreover, we argued that over-refined spatial mesh degrades both the accuracy and stability of MEM. Overall, this paper makes the maximal entropy moment method practical for simulating very strong normal shock waves on modern GPUs at single-precision, with significant stability improvement compared to previous methods.