With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned representation. As one example, in many applications that involve a signal propagating through physical media (e.g., optics, acoustics, fluid dynamics, etc), it is known that the dynamics of the signal must satisfy constraints imposed by the wave equation. Here we propose a matrix factorization technique that decomposes such signals into a sum of components, where each component is regularized to ensure that it {nearly} satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality. Through this line of work we establish theoretical connections between wave-informed learning and filtering theory in signal processing. We further demonstrate the application of this work on modal analysis problems commonly arising in structural diagnostics and prognostics.

Evaluating the performance of autonomous vehicle planning algorithms necessitates simulating long-tail traffic scenarios. Traditional methods for generating safety-critical scenarios often fall short in realism and controllability. Furthermore, these techniques generally neglect the dynamics of agent interactions. To mitigate these limitations, we introduce a novel closed-loop simulation framework rooted in guided diffusion models. Our approach yields two distinct advantages: 1) the generation of realistic long-tail scenarios that closely emulate real-world conditions, and 2) enhanced controllability, enabling more comprehensive and interactive evaluations. We achieve this through novel guidance objectives that enhance road progress while lowering collision and off-road rates. We develop a novel approach to simulate safety-critical scenarios through an adversarial term in the denoising process, which allows the adversarial agent to challenge a planner with plausible maneuvers, while all agents in the scene exhibit reactive and realistic behaviors. We validate our framework empirically using the NuScenes dataset, demonstrating improvements in both realism and controllability. These findings affirm that guided diffusion models provide a robust and versatile foundation for safety-critical, interactive traffic simulation, extending their utility across the broader landscape of autonomous driving. For additional resources and demonstrations, visit our project page at https://safe-sim.github.io.

The networked nature of multi-robot systems presents challenges in the context of multi-agent reinforcement learning. Centralized control policies do not scale with increasing numbers of robots, whereas independent control policies do not exploit the information provided by other robots, exhibiting poor performance in cooperative-competitive tasks. In this work we propose a physics-informed reinforcement learning approach able to learn distributed multi-robot control policies that are both scalable and make use of all the available information to each robot. Our approach has three key characteristics. First, it imposes a port-Hamiltonian structure on the policy representation, respecting energy conservation properties of physical robot systems and the networked nature of robot team interactions. Second, it uses self-attention to ensure a sparse policy representation able to handle time-varying information at each robot from the interaction graph. Third, we present a soft actor-critic reinforcement learning algorithm parameterized by our self-attention port-Hamiltonian control policy, which accounts for the correlation among robots during training while overcoming the need of value function factorization. Extensive simulations in different multi-robot scenarios demonstrate the success of the proposed approach, surpassing previous multi-robot reinforcement learning solutions in scalability, while achieving similar or superior performance (with averaged cumulative reward up to x2 greater than the state-of-the-art with robot teams x6 larger than the number of robots at training time).

Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical Artificial Intelligence. SMC searches for policy interventions to control probabilistic outcomes. Solving SMC is challenging because of its highly intractable nature($\text{NP}^{\text{PP}}$-complete), incorporating statistical inference and symbolic reasoning. Previous research on SMC solving lacks provable guarantees and/or suffers from sub-optimal empirical performance, especially when combinatorial constraints are present. We propose XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly intractable SMC problems with constant approximation guarantees. XOR-SMC transforms the highly intractable SMC into satisfiability problems, by replacing the model counting in SMC with SAT formulae subject to randomized XOR constraints. Experiments on solving important SMC problems in AI for social good demonstrate that XOR-SMC finds solutions close to the true optimum, outperforming several baselines which struggle to find good approximations for the intractable model counting in SMC.

But these systems have limitations. There are false positives and false negatives. What's more, they react only to an earthquake that has already begun--we can't predict an earthquake the way we can forecast the weather. And so many earthquake-prone regions are left in a state of constant suspense. A proper forecast could let us do a lot more to manage risk, from shutting down the power grid to evacuating residents.

Dyna-style model-based reinforcement learning contains two phases: model rollouts to generate sample for policy learning and real environment exploration using current policy for dynamics model learning. However, due to the complex real-world environment, it is inevitable to learn an imperfect dynamics model with model prediction error, which can further mislead policy learning and result in sub-optimal solutions. In this paper, we propose $\texttt{COPlanner}$, a planning-driven framework for model-based methods to address the inaccurately learned dynamics model problem with conservative model rollouts and optimistic environment exploration. $\texttt{COPlanner}$ leverages an uncertainty-aware policy-guided model predictive control (UP-MPC) component to plan for multi-step uncertainty estimation. This estimated uncertainty then serves as a penalty during model rollouts and as a bonus during real environment exploration respectively, to choose actions. Consequently, $\texttt{COPlanner}$ can avoid model uncertain regions through conservative model rollouts, thereby alleviating the influence of model error. Simultaneously, it explores high-reward model uncertain regions to reduce model error actively through optimistic real environment exploration. $\texttt{COPlanner}$ is a plug-and-play framework that can be applied to any dyna-style model-based methods. Experimental results on a series of proprioceptive and visual continuous control tasks demonstrate that both sample efficiency and asymptotic performance of strong model-based methods are significantly improved combined with $\texttt{COPlanner}$.

The advancement of Large Language Models (LLMs) has led to their widespread use across a broad spectrum of tasks including decision making. Prior studies have compared the decision making abilities of LLMs with those of humans from a psychological perspective. However, these studies have not always properly accounted for the sensitivity of LLMs' behavior to hyperparameters and variations in the prompt. In this study, we examine LLMs' performance on the Horizon decision making task studied by Binz and Schulz (2023) analyzing how LLMs respond to variations in prompts and hyperparameters. By experimenting on three OpenAI language models possessing different capabilities, we observe that the decision making abilities fluctuate based on the input prompts and temperature settings. Contrary to previous findings language models display a human-like exploration exploitation tradeoff after simple adjustments to the prompt.

Complex dynamical systems are notoriously difficult to model because some degrees of freedom (e.g., small scales) may be computationally unresolvable or are incompletely understood, yet they are dynamically important. For example, the small scales of cloud dynamics and droplet formation are crucial for controlling climate, yet are unresolvable in global climate models. Semi-empirical closure models for the effects of unresolved degrees of freedom often exist and encode important domain-specific knowledge. Building on such closure models and correcting them through learning the structural errors can be an effective way of fusing data with domain knowledge. Here we describe a general approach, principles, and algorithms for learning about structural errors. Key to our approach is to include structural error models inside the models of complex systems, for example, in closure models for unresolved scales. The structural errors then map, usually nonlinearly, to observable data. As a result, however, mismatches between model output and data are only indirectly informative about structural errors, due to a lack of labeled pairs of inputs and outputs of structural error models. Additionally, derivatives of the model may not exist or be readily available. We discuss how structural error models can be learned from indirect data with derivative-free Kalman inversion algorithms and variants, how sparsity constraints enforce a "do no harm" principle, and various ways of modeling structural errors. We also discuss the merits of using non-local and/or stochastic error models. In addition, we demonstrate how data assimilation techniques can assist the learning about structural errors in non-ergodic systems. The concepts and algorithms are illustrated in two numerical examples based on the Lorenz-96 system and a human glucose-insulin model.

The integration of sensorized vessels, enabling real-time data collection and machine learning-driven data analysis marks a pivotal advancement in the maritime industry. This transformative technology not only can enhance safety, efficiency, and sustainability but also usher in a new era of cost-effective and smart maritime transportation in our increasingly interconnected world. This study presents a deep learning-driven anomaly detection system augmented with interpretable machine learning models for identifying performance anomalies in an industrial sensorized vessel, called TUCANA. We Leverage a human-in-the-loop unsupervised process that involves utilizing standard and Long Short-Term Memory (LSTM) autoencoders augmented with interpretable surrogate models, i.e., random forest and decision tree, to add transparency and interpretability to the results provided by the deep learning models. The interpretable models also enable automated rule generation for translating the inference into human-readable rules. Additionally, the process also includes providing a projection of the results using t-distributed stochastic neighbor embedding (t-SNE), which helps with a better understanding of the structure and relationships within the data and assessment of the identified anomalies. We empirically evaluate the system using real data acquired from the vessel TUCANA and the results involve achieving over 80% precision and 90% recall with the LSTM model used in the process. The interpretable models also provide logical rules aligned with expert thinking, and the t-SNE-based projection enhances interpretability. Our system demonstrates that the proposed approach can be used effectively in real-world scenarios, offering transparency and precision in performance anomaly detection. ARITIME industry plays a crucial role in global mobility, providing cost-effective and efficient transportation for people and goods around the world [1]. From container ships to cruise liners, the industry offers a wide range of vessel types that are designed to meet the diverse needs of modern transportation. As the world becomes more interconnected, the demand for maritime transportation continues to grow, and the industry is constantly evolving to meet these changing needs.

We develop a new efficient sequential approximate leverage score algorithm, SALSA, using methods from randomized numerical linear algebra (RandNLA) for large matrices. We demonstrate that, with high probability, the accuracy of SALSA's approximations is within $(1 + O({\varepsilon}))$ of the true leverage scores. In addition, we show that the theoretical computational complexity and numerical accuracy of SALSA surpass existing approximations. These theoretical results are subsequently utilized to develop an efficient algorithm, named LSARMA, for fitting an appropriate ARMA model to large-scale time series data. Our proposed algorithm is, with high probability, guaranteed to find the maximum likelihood estimates of the parameters for the true underlying ARMA model. Furthermore, it has a worst-case running time that significantly improves those of the state-of-the-art alternatives in big data regimes. Empirical results on large-scale data strongly support these theoretical results and underscore the efficacy of our new approach.