Bb-Simplex is centered around the Simplex control architecture, which consists of a high-performance advanced controller that is not guaranteed to maintain safety of the plant, a verified-safe baseline controller, and a decision module that switches control of the plant between the two controllers to ensure safety without sacrificing performance. In Bb-Simplex, Barrier certificates are used to prove that the baseline controller ensures safety. Furthermore, Bb-Simplex features a new automated method for deriving, from the barrier certificate, the conditions for switching between the controllers. Our method is based on the Taylor expansion of the barrier certificate and yields computationally inexpensive switching conditions. We also propose extensions to Bb-Simplex to enable its use in hybrid systems, which have multiple modes each with its own dynamics, and to support its use when only approximate dynamics (not exact dynamics) are available, for both continuous-time and hybrid dynamical systems. We consider significant applications of Bb-Simplex to microgrids featuring advanced controllers in the form of neural networks trained using reinforcement learning. These microgrids are modeled in RTDS, an industry-standard high-fidelity, real-time power systems simulator. Our results demonstrate that Bb-Simplex can automatically derive switching conditions for complex continuous-time and hybrid systems, the switching conditions are not overly conservative, and Bb-Simplex ensures safety even in the presence of adversarial attacks on the neural controller when only approximate dynamics (with an error bound) are available.

Domain decomposition is a technique used to reduce memory overhead on large neutron transport problems. Currently, the optimal load-balanced processor allocation for these domains is typically determined through small-scale simulations of the problem, which can be time-consuming for researchers and must be repeated anytime a problem input is changed. We propose a Transformer model with a unique 3D input embedding, and input representations designed for domain-decomposed neutron transport problems, which can predict the subdomain computation loads generated by small-scale simulations. We demonstrate that such a model trained on domain-decomposed Small Modular Reactor (SMR) simulations achieves 98.2% accuracy while being able to skip the small-scale simulation step entirely. Tests of the model's robustness on variant fuel assemblies, other problem geometries, and changes in simulation parameters are also discussed.

An important challenge for enabling the deployment of reinforcement learning (RL) algorithms in the real world is safety. This has resulted in the recent research field of Safe RL, which aims to learn optimal policies that are safe. One successful approach in that direction is probabilistic logic shields (PLS), a model-based Safe RL technique that uses formal specifications based on probabilistic logic programming, constraining an agent's policy to comply with those specifications in a probabilistic sense. However, safety is inherently a multi-agent concept, since real-world environments often involve multiple agents interacting simultaneously, leading to a complex system which is hard to control. Moreover, safe multi-agent RL (Safe MARL) is still underexplored. In order to address this gap, in this paper we ($i$) introduce Shielded MARL (SMARL) by extending PLS to MARL -- in particular, we introduce Probabilistic Logic Temporal Difference Learning (PLTD) to enable shielded independent Q-learning (SIQL), and introduce shielded independent PPO (SIPPO) using probabilistic logic policy gradients; ($ii$) show its positive effect and use as an equilibrium selection mechanism in various game-theoretic environments including two-player simultaneous games, extensive-form games, stochastic games, and some grid-world extensions in terms of safety, cooperation, and alignment with normative behaviors; and ($iii$) look into the asymmetric case where only one agent is shielded, and show that the shielded agent has a significant influence on the unshielded one, providing further evidence of SMARL's ability to enhance safety and cooperation in diverse multi-agent environments.

Abstract: Neuromorphic computing with crossbar arrays has emerged as a promising alternative to improve computing efficiency for machine learning. Previous work has focused on implementing crossbar arrays to perform basic mathematical operations. However, in this paper, we explore the impact of mapping the layers of an artificial neural network onto physical cross-bar arrays arranged in tiles across a chip. We have developed a simplified mapping algorithm to determine the number of physical tiles, with fixed optimal array dimensions, and to estimate the minimum area occupied by these tiles for a given design objective. This simplified algorithm is compared with conventional binary linear optimization, which solves the equivalent bin-packing problem. We have found that the optimum solution is not necessarily related to the minimum number of tiles; rather, it is shown to be an interaction between tile array capacity and the scaling properties of its peripheral circuits. Additionally, we have discovered that square arrays are not always the best choice for optimal mapping, and that performance optimization comes at the cost of total tile area. 1 Introduction The dream of emulating the operations of the brain is the driving force behind neuromorphic computing [1] [2] [3]. Coming even close to the capabilities of the brain, however, has been elusive. The use of artificial neural networks (ANN) for machine learning is a rapidly advancing step in this direction [4] [5]. ANNs allow domain-specific learning without knowledge of the intricate details of a specific domain. Instead, they connect numerical representations of domainspecific inputs with domain-specific outputs [6] [7] [8]. A neural network, in general, has several layers represented by a weight matrix.

Fully autonomous racing demands not only high-speed driving but also fair and courteous maneuvers. In this paper, we propose an autonomous racing framework that learns complex racing behaviors from expert demonstrations using hierarchical policy abstractions. At the trajectory level, our policy model predicts a dense distribution map indicating the likelihood of trajectories learned from offline demonstrations. The maximum likelihood trajectory is then passed to the control-level policy, which generates control inputs in a residual fashion, considering vehicle dynamics at the limits of performance. We evaluate our framework in a high-fidelity racing simulator and compare it against competing baselines in challenging multi-agent adversarial scenarios. Quantitative and qualitative results show that our trajectory planning policy significantly outperforms the baselines, and the residual control policy improves lap time and tracking accuracy. Moreover, challenging closed-loop experiments with ten opponents show that our framework can overtake other vehicles by understanding nuanced interactions, effectively balancing performance and courtesy like professional drivers.

For the retrieval of large-scale vegetation biophysical parameters, the inversion of radiative transfer models (RTMs) is the most commonly used approach. In recent years, Artificial Neural Network (ANN)-based methods have become the mainstream for inverting RTMs due to their high accuracy and computational efficiency. It has been widely used in the retrieval of biophysical variables (BV). However, due to the lack of the Bayesian inversion theory interpretation, it faces challenges in quantifying the retrieval uncertainty, a crucial metric for product quality validation and downstream applications such as data assimilation or ecosystem carbon cycling modeling. This study proved that the ANN trained with squared loss outputs the posterior mean, providing a rigorous foundation for its uncertainty quantification, regularization, and incorporation of prior information. A Bayesian theoretical framework was subsequently proposed for ANN-based methods. Using this framework, we derived a new algorithm called Uncertainty Prediction Neural Network (UpNet), which enables the simultaneous training of two ANNs to retrieve BV and provide retrieval uncertainty. To validate our method, we compared UpNet with the standard Bayesian inference method, i.e., Markov Chain Monte Carlo (MCMC), in the inversion of a widely used RTM called ProSAIL for retrieving BVs and estimating uncertainty. The results demonstrated that the BVs retrieved and the uncertainties estimated by UpNet were highly consistent with those from MCMC, achieving over a million-fold acceleration. These results indicated that UpNet has significant potential for fast retrieval and uncertainty quantification of BVs or other parameters with medium and high-resolution remote sensing data. Our Python implementation is available at: https://github.com/Dash-RSer/UpNet.

Earth Observation (EO) data analysis has been significantly revolutionized by deep learning (DL), with applications typically limited to grid-like data structures. Graph Neural Networks (GNNs) emerge as an important innovation, propelling DL into the non-Euclidean domain. Naturally, GNNs can effectively tackle the challenges posed by diverse modalities, multiple sensors, and the heterogeneous nature of EO data. To introduce GNNs in the related domains, our review begins by offering fundamental knowledge on GNNs. Then, we summarize the generic problems in EO, to which GNNs can offer potential solutions. Following this, we explore a broad spectrum of GNNs' applications to scientific problems in Earth systems, covering areas such as weather and climate analysis, disaster management, air quality monitoring, agriculture, land cover classification, hydrological process modeling, and urban modeling. The rationale behind adopting GNNs in these fields is explained, alongside methodologies for organizing graphs and designing favorable architectures for various tasks. Furthermore, we highlight methodological challenges of implementing GNNs in these domains and possible solutions that could guide future research. While acknowledging that GNNs are not a universal solution, we conclude the paper by comparing them with other popular architectures like transformers and analyzing their potential synergies.

Cooperatively Localizing robots should seek optimal control strategies to maximize precision of position estimation and ensure safety in flight. Observability-Aware Trajectory Optimization has strong potential to address this issue, but no concrete link between observability and precision has been proven yet. In this paper, we prove that improvement in positioning precision inherently follows from optimizing observability. Based on this finding, we develop an Observability-Aware Control principle to generate observability-optimal control strategies. We implement this principle in a Model Predictive Control framework, and we verify it on a team of quadrotor Unmanned Aerial Vehicles comprising a follower vehicle localizing itself by tracking a leader vehicle in both simulations and real-world flight tests. Our results demonstrate that maximizing observability contributed to improving global positioning precision for the quadrotor team.

Continuously adapting pre-trained models to local data on resource constrained edge devices is the $\emph{last mile}$ for model deployment. However, as models increase in size and depth, backpropagation requires a large amount of memory, which becomes prohibitive for edge devices. In addition, most existing low power neural processing engines (e.g., NPUs, DSPs, MCUs, etc.) are designed as fixed-point inference accelerators, without training capabilities. Forward gradients, solely based on directional derivatives computed from two forward calls, have been recently used for model training, with substantial savings in computation and memory. However, the performance of quantized training with fixed-point forward gradients remains unclear. In this paper, we investigate the feasibility of on-device training using fixed-point forward gradients, by conducting comprehensive experiments across a variety of deep learning benchmark tasks in both vision and audio domains. We propose a series of algorithm enhancements that further reduce the memory footprint, and the accuracy gap compared to backpropagation. An empirical study on how training with forward gradients navigates in the loss landscape is further explored. Our results demonstrate that on the last mile of model customization on edge devices, training with fixed-point forward gradients is a feasible and practical approach.

Feedback control for complex physical systems is essential in many fields of Engineering and Applied Sciences, which are typically governed by Partial Differential Equations (PDEs). In these cases, the state of the systems is often challenging or even impossible to observe completely, the systems exhibit nonlinear dynamics, and require low-latency feedback control [BNK20]; [PK20]; [KJ20]. Consequently, effectively controlling these systems is a computationally intensive task. For instance, significant efforts have been devoted in the last decade to the investigation of optimal control problems governed by PDEs [Hin+08]; [MQS22]; however, classical feedback control strategies face limitations with such highly complex dynamical systems. For instance, (nonlinear) model predictive control (MPC) [GP17] has emerged as an effective and important control paradigm. MPC utilizes an internal model of the dynamics to create a feedback loop and provide optimal controls, resulting in a difficult trade-off between model accuracy and computational performance. Despite its impressive success in disciplines such as robotics [Wil+18] and controlling PDEs [Alt14], MPC struggles with real-time applicability in providing low-latency actuation, due to the need for solving complex optimization problems. In recent years, reinforcement learning (RL), particularly deep reinforcement learning (DRL) [SB18], an extension of RL relying on deep neural networks (DNN), has gained popularity as a powerful and real-time applicable control paradigm. Especially in the context of solving PDEs, DRL has demonstrated outstanding capabilities in controlling complex and high-dimensional dynamical systems at low latency [You+23]; [Pei+23]; [BF24]; [Vin24].