In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system. We use rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold. This EDMD model leads to accurate prediction and can be generalized to several validation sets. Further, we design a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories. Simulation results show that the proposed MPC controller can run as fast as 100 Hz and is able to track arbitrary reference trajectories with good accuracy. Implementation details can be found in \url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}.

This work proposes a geometric insight into equivariant message passing on Riemannian manifolds. As previously proposed, numerical features on Riemannian manifolds are represented as coordinate-independent feature fields on the manifold. To any coordinate-independent feature field on a manifold comes attached an equivariant embedding of the principal bundle to the space of numerical features. We argue that the metric this embedding induces on the numerical feature space should optimally preserve the principal bundle's original metric. This optimality criterion leads to the minimization of a twisted form of the Polyakov action with respect to the graph of this embedding, yielding an equivariant diffusion process on the associated vector bundle. We obtain a message passing scheme on the manifold by discretizing the diffusion equation flow for a fixed time step. We propose a higher-order equivariant diffusion process equivalent to diffusion on the cartesian product of the base manifold. The discretization of the higher-order diffusion process on a graph yields a new general class of equivariant GNN, generalizing the ACE and MACE formalism to data on Riemannian manifolds.

Large indoor spaces have complex layouts making them difficult to navigate. Indoor spaces in hospitals, universities, shopping complexes, etc., carry multi-modal information in the form of text and symbols. Hence, it is difficult for Blind and Visually Impaired (BVI) people to independently navigate such spaces. Indoor environments are usually GPS-denied; therefore, Bluetooth-based, WiFi-based, or Range-based methods are used for localization. These methods have high setup costs, lesser accuracy, and sometimes need special sensing equipment. We propose a Visual Assist (VA) system for the indoor navigation of BVI individuals using visual Fiducial markers for localization. State-of-the-art (SOTA) approaches for visual localization using Fiducial markers use fixed cameras having a narrow field of view. These approaches stop tracking the markers when they are out of sight. We employ a Pan-Tilt turret-mounted camera which enhances the field of view to 360{\deg} for enhanced marker tracking. We, therefore, need fewer markers for mapping and navigation. The efficacy of the proposed VA system is measured on three metrics, i.e., RMSE (Root Mean Square Error), ADNN (Average Distance to Nearest Neighbours), and ATE (Absolute Trajectory Error). Our system outperforms Hector-SLAM, ORB-SLAM3, and UcoSLAM. The proposed system achieves localization accuracy within $\pm8cm$ compared to $\pm12cm$ and $\pm10cm$ for ORB-SLAM3 and UcoSLAM, respectively.

Quantum Computing (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is applied to Machine Learning (ML) applications, it forms a Quantum Machine Learning (QML) system. After discussing the basic concepts of QC and its advantages over classical computing, this paper reviews the key aspects of QML in a comprehensive manner. We discuss different QML algorithms and their domain applicability, quantum datasets, hardware technologies, software tools, simulators, and applications. In this survey, we provide valuable information and resources for readers to jumpstart into the current state-of-the-art techniques in the QML field.

Metal-organic frameworks (MOFs) are of immense interest in applications such as gas storage and carbon capture due to their exceptional porosity and tunable chemistry. Their modular nature has enabled the use of template-based methods to generate hypothetical MOFs by combining molecular building blocks in accordance with known network topologies. However, the ability of these methods to identify top-performing MOFs is often hindered by the limited diversity of the resulting chemical space. In this work, we propose MOFDiff: a coarse-grained (CG) diffusion model that generates CG MOF structures through a denoising diffusion process over the coordinates and identities of the building blocks. The all-atom MOF structure is then determined through a novel assembly algorithm. Equivariant graph neural networks are used for the diffusion model to respect the permutational and roto-translational symmetries. We comprehensively evaluate our model's capability to generate valid and novel MOF structures and its effectiveness in designing outstanding MOF materials for carbon capture applications with molecular simulations.

As LLMs have become increasingly popular, they have been used in almost every field. But as the application for LLMs expands from generic fields to narrow, focused science domains, there exists an ever-increasing gap in ways to evaluate their efficacy in those fields. For the benchmarks that do exist, a lot of them focus on questions that don't require proper understanding of the subject in question. In this paper, we present NuclearQA, a human-made benchmark of 100 questions to evaluate language models in the nuclear domain, consisting of a varying collection of questions that have been specifically designed by experts to test the abilities of language models. We detail our approach and show how the mix of several types of questions makes our benchmark uniquely capable of evaluating models in the nuclear domain. We also present our own evaluation metric for assessing LLM's performances due to the limitations of existing ones. Our experiments on state-of-the-art models suggest that even the best LLMs perform less than satisfactorily on our benchmark, demonstrating the scientific knowledge gap of existing LLMs.

Connected and autonomous vehicles have the potential to minimize energy consumption by optimizing the vehicle velocity and powertrain dynamics with Vehicle-to-Everything info en route. Existing deterministic and stochastic methods created to solve the eco-driving problem generally suffer from high computational and memory requirements, which makes online implementation challenging. This work proposes a hierarchical multi-horizon optimization framework implemented via a neural network. The neural network learns a full-route value function to account for the variability in route information and is then used to approximate the terminal cost in a receding horizon optimization. Simulations over real-world routes demonstrate that the proposed approach achieves comparable performance to a stochastic optimization solution obtained via reinforcement learning, while requiring no sophisticated training paradigm and negligible on-board memory.

We are interested in enabling visual planning for complex long-horizon tasks in the space of generated videos and language, leveraging recent advances in large generative models pretrained on Internet-scale data. To this end, we present video language planning (VLP), an algorithm that consists of a tree search procedure, where we train (i) vision-language models to serve as both policies and value functions, and (ii) text-to-video models as dynamics models. VLP takes as input a long-horizon task instruction and current image observation, and outputs a long video plan that provides detailed multimodal (video and language) specifications that describe how to complete the final task. VLP scales with increasing computation budget where more computation time results in improved video plans, and is able to synthesize long-horizon video plans across different robotics domains: from multi-object rearrangement, to multi-camera bi-arm dexterous manipulation. Generated video plans can be translated into real robot actions via goal-conditioned policies, conditioned on each intermediate frame of the generated video. Experiments show that VLP substantially improves long-horizon task success rates compared to prior methods on both simulated and real robots (across 3 hardware platforms).

High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov limit. Mathematically, underlying phenomenon can be captured via a stable $n$-dimensional linear transformation `$A$' and additive randomness. System identification aims at extracting useful information about underlying dynamical system, given a length $N$ trajectory from it (corresponds to an $n \times N$ dimensional data matrix). We use spectral theorem for non-Hermitian operators to show that spatio-temperal correlations are dictated by the discrepancy between algebraic and geometric multiplicity of distinct eigenvalues corresponding to state transition matrix. Small discrepancies imply that original trajectory essentially comprises of multiple lower dimensional random dynamical systems living on $A$ invariant subspaces and are statistically independent of each other. In the process, we provide first quantitative handle on decay rate of finite powers of state transition matrix $\|A^{k}\|$ . It is shown that when a stable dynamical system has only one distinct eigenvalue and discrepancy of $n-1$: $\|A\|$ has a dependence on $n$, resulting dynamics are spatially inseparable and consequently there exist at least one row with covariates of typical size $\Theta\big(\sqrt{N-n+1}$ $e^{n}\big)$ i.e., even under stability assumption, covariates can suffer from curse of dimensionality. In the light of these findings we set the stage for non-asymptotic error analysis in estimation of state transition matrix $A$ via least squares regression on observed trajectory by showing that element-wise error is essentially a variant of well-know Littlewood-Offord problem.

This paper aims to explore the potential of combining Deep Reinforcement Learning (DRL) with Knowledge Distillation (KD) by distilling various DRL algorithms and studying their distillation effects. By doing so, the computational burden of deep models could be reduced while maintaining the performance. The primary objective is to provide a benchmark for evaluating the performance of different DRL algorithms that have been refined using KD techniques. By distilling these algorithms, the goal is to develop efficient and fast DRL models. This research is expected to provide valuable insights that can facilitate further advancements in this promising direction. By exploring the combination of DRL and KD, this work aims to promote the development of models that require fewer GPU resources, learn more quickly, and make faster decisions in complex environments. The results of this research have the capacity to significantly advance the field of DRL and pave the way for the future deployment of resource-efficient, decision-making intelligent systems.