Multi-agent Path Finding for Mixed Autonomy Traffic Coordination

In the evolving landscape of urban mobility, the prospective integration of Connected and Automated Vehicles (CAVs) with Human-Driven Vehicles (HDVs) presents a complex array of challenges and opportunities for autonomous driving systems. While recent advancements in robotics have yielded Multi-Agent Path Finding (MAPF) algorithms tailored for agent coordination task characterized by simplified kinematics and complete control over agent behaviors, these solutions are inapplicable in mixed-traffic environments where uncontrollable HDVs must coexist and interact with CAVs. Addressing this gap, we propose the Behavior Prediction Kinematic Priority Based Search (BK-PBS), which leverages an offline-trained conditional prediction model to forecast HDV responses to CAV maneuvers, integrating these insights into a Priority Based Search (PBS) where the A* search proceeds over motion primitives to accommodate kinematic constraints. We compare BK-PBS with CAV planning algorithms derived by rule-based car-following models, and reinforcement learning. Through comprehensive simulation on a highway merging scenario across diverse scenarios of CAV penetration rate and traffic density, BK-PBS outperforms these baselines in reducing collision rates and enhancing system-level travel delay. Our work is directly applicable to many scenarios of multi-human multi-robot coordination.

Multi-agent Path Finding for Cooperative Autonomous Driving

Anticipating possible future deployment of connected and automated vehicles (CAVs), cooperative autonomous driving at intersections has been studied by many works in control theory and intelligent transportation across decades. Simultaneously, recent parallel works in robotics have devised efficient algorithms for multi-agent path finding (MAPF), though often in environments with simplified kinematics. In this work, we hybridize insights and algorithms from MAPF with the structure and heuristics of optimizing the crossing order of CAVs at signal-free intersections. We devise an optimal and complete algorithm, Order-based Search with Kinematics Arrival Time Scheduling (OBS-KATS), which significantly outperforms existing algorithms, fixed heuristics, and prioritized planning with KATS. The performance is maintained under different vehicle arrival rates, lane lengths, crossing speeds, and control horizon. Through ablations and dissections, we offer insight on the contributing factors to OBS-KATS's performance. Our work is directly applicable to many similarly scaled traffic and multi-robot scenarios with directed lanes.

Adaptive Policy Learning for Offline-to-Online Reinforcement Learning

Conventional reinforcement learning (RL) needs an environment to collect fresh data, which is impractical when online interactions are costly. Offline RL provides an alternative solution by directly learning from the previously collected dataset. However, it will yield unsatisfactory performance if the quality of the offline datasets is poor. In this paper, we consider an offline-to-online setting where the agent is first learned from the offline dataset and then trained online, and propose a framework called Adaptive Policy Learning for effectively taking advantage of offline and online data. Specifically, we explicitly consider the difference between the online and offline data and apply an adaptive update scheme accordingly, that is, a pessimistic update strategy for the offline dataset and an optimistic/greedy update scheme for the online dataset. Such a simple and effective method provides a way to mix the offline and online RL and achieve the best of both worlds. We further provide two detailed algorithms for implementing the framework through embedding value or policy-based RL algorithms into it. Finally, we conduct extensive experiments on popular continuous control tasks, and results show that our algorithm can learn the expert policy with high sample efficiency even when the quality of offline dataset is poor, e.g., random dataset.

DAMS-LIO: A Degeneration-Aware and Modular Sensor-Fusion LiDAR-inertial Odometry

The fusion scheme is crucial to the multi-sensor fusion method that is the promising solution to the state estimation in complex and extreme environments like underground mines and planetary surfaces. In this work, a light-weight iEKF-based LiDAR-inertial odometry system is presented, which utilizes a degeneration-aware and modular sensor-fusion pipeline that takes both LiDAR points and relative pose from another odometry as the measurement in the update process only when degeneration is detected. Both the CRLB theory and simulation test are used to demonstrate the higher accuracy of our method compared to methods using a single observation. Furthermore, the proposed system is evaluated in perceptually challenging datasets against various state-of-the-art sensor-fusion methods. The results show that the proposed system achieves real-time and high estimation accuracy performance despite the challenging environment and poor observations.

Benchmarking variational quantum circuits with permutation symmetry

We propose SnCQA, a set of hardware-efficient variational circuits of equivariant quantum convolutional circuits respective to permutation symmetries and spatial lattice symmetries with the number of qubits $n$. By exploiting permutation symmetries of the system, such as lattice Hamiltonians common to many quantum many-body and quantum chemistry problems, Our quantum neural networks are suitable for solving machine learning problems where permutation symmetries are present, which could lead to significant savings of computational costs. Aside from its theoretical novelty, we find our simulations perform well in practical instances of learning ground states in quantum computational chemistry, where we could achieve comparable performances to traditional methods with few tens of parameters. Compared to other traditional variational quantum circuits, such as the pure hardware-efficient ansatz (pHEA), we show that SnCQA is more scalable, accurate, and noise resilient (with $20\times$ better performance on $3 \times 4$ square lattice and $200\% - 1000\%$ resource savings in various lattice sizes and key criterions such as the number of layers, parameters, and times to converge in our cases), suggesting a potentially favorable experiment on near-time quantum devices.

Group-Equivariant Neural Networks with Fusion Diagrams

Many learning tasks in physics and chemistry involve global spatial symmetries as well as permutational symmetry between particles. The standard approach to such problems is equivariant neural networks, which employ tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increases, the bookkeeping associated with ensuring parsimony as well as equivariance quickly becomes nontrivial. In this paper, we propose to use fusion diagrams, a technique widely used in simulating SU($2$)-symmetric quantum many-body problems, to design new equivariant components for use in equivariant neural networks. This yields a diagrammatic approach to constructing new neural network architectures. We show that when applied to particles in a given local neighborhood, the resulting components, which we call fusion blocks, are universal approximators of any continuous equivariant function defined on the neighborhood. As a practical demonstration, we incorporate a fusion block into a pre-existing equivariant architecture (Cormorant) and show that it improves performance on benchmark molecular learning tasks.

Quantum Power Flows: From Theory to Practice

Climate change is becoming one of the greatest challenges to the sustainable development of modern society. Renewable energies with low density greatly complicate the online optimization and control processes, where modern advanced computational technologies, specifically quantum computing, have significant potential to help. In this paper, we discuss applications of quantum computing algorithms toward state-of-the-art smart grid problems. We suggest potential, exponential quantum speedup by the use of the Harrow-Hassidim-Lloyd (HHL) algorithms for sparse matrix inversions in power-flow problems. However, practical implementations of the algorithm are limited by the noise of quantum circuits, the hardness of realizations of quantum random access memories (QRAM), and the depth of the required quantum circuits. We benchmark the hardware and software requirements from the state-of-the-art power-flow algorithms, including QRAM requirements from hybrid phonon-transmon systems, and explicit gate counting used in HHL for explicit realizations. We also develop near-term algorithms of power flow by variational quantum circuits and implement real experiments for 6 qubits with a truncated version of power flows.

On the Super-exponential Quantum Speedup of Equivariant Quantum Machine Learning Algorithms with SU Symmetry

We introduce a framework of the equivariant convolutional algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU($d$) symmetries. It allows us to enhance a natural model of quantum computation--permutational quantum computing (PQC) [Quantum Inf. Comput., 10, 470-497 (2010)] --and defines a more powerful model: PQC+. While PQC was shown to be effectively classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas the best known classical algorithms runs in $O(n!n^2)$ time, thus providing strong evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.

Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans{ä}tze

We develop a theoretical framework for $S_n$-equivariant quantum convolutional circuits, building on and significantly generalizing Jordan's Permutational Quantum Computing (PQC) formalism. We show that quantum circuits are a natural choice for Fourier space neural architectures affording a super-exponential speedup in computing the matrix elements of $S_n$-Fourier coefficients compared to the best known classical Fast Fourier Transform (FFT) over the symmetric group. In particular, we utilize the Okounkov-Vershik approach to prove Harrow's statement (Ph.D. Thesis 2005 p.160) on the equivalence between $\operatorname{SU}(d)$- and $S_n$-irrep bases and to establish the $S_n$-equivariant Convolutional Quantum Alternating Ans{\"a}tze ($S_n$-CQA) using Young-Jucys-Murphy (YJM) elements. We prove that $S_n$-CQA are dense, thus expressible within each $S_n$-irrep block, which may serve as a universal model for potential future quantum machine learning and optimization applications. Our method provides another way to prove the universality of Quantum Approximate Optimization Algorithm (QAOA), from the representation-theoretical point of view. Our framework can be naturally applied to a wide array of problems with global $\operatorname{SU}(d)$ symmetry. We present numerical simulations to showcase the effectiveness of the ans{\"a}tze to find the sign structure of the ground state of the $J_1$--$J_2$ antiferromagnetic Heisenberg model on the rectangular and Kagome lattices. Our work identifies quantum advantage for a specific machine learning problem, and provides the first application of the celebrated Okounkov-Vershik's representation theory to machine learning and quantum physics.

An Extendible, Graph-Neural-Network-Based Approach for Accurate Force Field Development of Large Flexible Organic Molecules

An accurate force field is the key to the success of all molecular mechanics simulations on organic polymers and biomolecules. Accuracy beyond density functional theory is often needed to describe the intermolecular interactions, while most correlated wavefunction (CW) methods are prohibitively expensive for large molecules. Therefore, it posts a great challenge to develop an extendible ab initio force field for large flexible organic molecules at CW level of accuracy. In this work, we face this challenge by combining the physics-driven nonbonding potential with a data-driven subgraph neural network bonding model (named sGNN). Tests on polyethylene glycol polymer chains show that our strategy is highly accurate and robust for molecules of different sizes. Therefore, we can develop the force field from small molecular fragments (with sizes easily accessible to CW methods) and safely transfer it to large polymers, thus opening a new path to the next-generation organic force fields.