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Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. Traditional time series approaches for prediction often focus on either autoregressive modeling, which relies solely on past observations of the target ``endogenous variables'', or forward modeling, which considers only current covariate drivers ``exogenous variables''. However, effectively integrating past endogenous and past exogenous with current exogenous variables remains a significant challenge. In this paper, we propose ExoTST, a novel transformer-based framework that effectively incorporates current exogenous variables alongside past context for improved time series prediction. To integrate exogenous information efficiently, ExoTST leverages the strengths of attention mechanisms and introduces a novel cross-temporal modality fusion module. This module enables the model to jointly learn from both past and current exogenous series, treating them as distinct modalities. By considering these series separately, ExoTST provides robustness and flexibility in handling data uncertainties that arise from the inherent distribution shift between historical and current exogenous variables. Extensive experiments on real-world carbon flux datasets and time series benchmarks demonstrate ExoTST's superior performance compared to state-of-the-art baselines, with improvements of up to 10\% in prediction accuracy. Moreover, ExoTST exhibits strong robustness against missing values and noise in exogenous drivers, maintaining consistent performance in real-world situations where these imperfections are common., Comment: Accepted at ICDM 2024

In modern robotics, addressing the lack of accurate state space information in real-world scenarios has led to a significant focus on utilizing visuomotor observation to provide safety assurances. Although supervised learning methods, such as imitation learning, have demonstrated potential in synthesizing control policies based on visuomotor observations, they require ground truth safety labels for the complete dataset and do not provide formal safety assurances. On the other hand, traditional control-theoretic methods like Control Barrier Functions (CBFs) and Hamilton-Jacobi (HJ) Reachability provide formal safety guarantees but depend on accurate knowledge of system dynamics, which is often unavailable for high-dimensional visuomotor data. To overcome these limitations, we propose a novel approach to synthesize a semi-supervised safe visuomotor policy using barrier certificates that integrate the strengths of model-free supervised learning and model-based control methods. This framework synthesizes a provably safe controller without requiring safety labels for the complete dataset and ensures completeness guarantees for both the barrier certificate and the policy. We validate our approach through distinct case studies: an inverted pendulum system and the obstacle avoidance of an autonomous mobile robot., Comment: First two authors have contributed equally. 8 Pages, 3 figures

Fixed-wing UAVs have transformed the transportation system with their high flight speed and long endurance, yet their safe operation in increasingly cluttered environments depends heavily on effective collision avoidance techniques. This paper presents a novel method for safely navigating an aircraft along a desired route while avoiding moving obstacles. We utilize a class of control barrier functions (CBFs) based on collision cones to ensure the relative velocity between the aircraft and the obstacle consistently avoids a cone of vectors that might lead to a collision. By demonstrating that the proposed constraint is a valid CBF for the aircraft, we can leverage its real-time implementation via Quadratic Programs (QPs), termed the CBF-QPs. Validation includes simulating control law along trajectories, showing effectiveness in both static and moving obstacle scenarios., Comment: 4 Pages, 3 figures. Presented at CyPhySS, 2024, Bangalore. arXiv admin note: text overlap with arXiv:2303.15871

Locomotion on unknown terrains is essential for bipedal robots to handle novel real-world challenges, thus expanding their utility in disaster response and exploration. In this work, we introduce a lightweight framework that learns a single walking controller that yields locomotion on multiple terrains. We have designed a real-time robot controller based on diffusion models, which not only captures multiple behaviours with different velocities in a single policy but also generalizes well for unseen terrains. Our controller learns with offline data, which is better than online learning in aspects like scalability, simplicity in training scheme etc. We have designed and implemented a diffusion model-based policy controller in simulation on our custom-made Bipedal Robot model named Stoch BiRo. We have demonstrated its generalization capability and high frequency control step generation relative to typical generative models, which require huge onboarding compute., Comment: 6 pages, 5 figures

We propose a dialogue system that enables heart failure patients to inquire about salt content in foods and help them monitor and reduce salt intake. Addressing the lack of specific datasets for food-based salt content inquiries, we develop a template-based conversational dataset. The dataset is structured to ask clarification questions to identify food items and their salt content. Our findings indicate that while fine-tuning transformer-based models on the dataset yields limited performance, the integration of Neuro-Symbolic Rules significantly enhances the system's performance. Our experiments show that by integrating neuro-symbolic rules, our system achieves an improvement in joint goal accuracy of over 20% across different data sizes compared to naively fine-tuning transformer-based models., Comment: Accepted in CL4Health workshop in LREC-COLING'24

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee and performance of safe controllers rely on the construction of valid CBFs. Inspired by universal approximatability, CBFs are represented by neural networks, known as neural CBFs (NCBFs). This paper presents an algorithm for synthesizing formally verified continuous-time neural Control Barrier Functions in stochastic environments in a single step. The proposed training process ensures efficacy across the entire state space with only a finite number of data points by constructing a sample-based learning framework for Stochastic Neural CBFs (SNCBFs). Our methodology eliminates the need for post hoc verification by enforcing Lipschitz bounds on the neural network, its Jacobian, and Hessian terms. We demonstrate the effectiveness of our approach through case studies on the inverted pendulum system and obstacle avoidance in autonomous driving, showcasing larger safe regions compared to baseline methods., Comment: 8 pages, 3 figures

When interacting with Retrieval-Augmented Generation (RAG)-based conversational agents, the users must carefully craft their queries to be understood correctly. Yet, understanding the system's capabilities can be challenging for the users, leading to ambiguous questions that necessitate further clarification. This work aims to bridge the gap by developing a suggestion question generator. To generate suggestion questions, our approach involves utilizing dynamic context, which includes both dynamic few-shot examples and dynamically retrieved contexts. Through experiments, we show that the dynamic contexts approach can generate better suggestion questions as compared to other prompting approaches., Comment: 4 pages , 1 figure, accepted at WWW'24 workshop PromptEng

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the TurtleBot, Stoch-Jeep, and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (CBF-QPs). Comparative analysis with the state-of-the-art CBFs highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers., Comment: 13 pages, 16 pages. arXiv admin note: substantial text overlap with arXiv:2209.11524, arXiv:2303.15871, arXiv:2310.10839

This paper introduces the Stoch BiRo, a cost-effective bipedal robot designed with a modular mechanical structure having point feet to navigate uneven and unfamiliar terrains. The robot employs proprioceptive actuation in abduction, hips, and knees, leveraging a Raspberry Pi4 for control. Overcoming computational limitations, a Learning-based Linear Policy controller manages balance and locomotion with only 3 degrees of freedom (DoF) per leg, distinct from the typical 5DoF in bipedal systems. Integrated within a modular control architecture, these controllers enable autonomous handling of unforeseen terrain disturbances without external sensors or prior environment knowledge. The robot's policies are trained and simulated using MuJoCo, transferring learned behaviors to the Stoch BiRo hardware for initial walking validations. This work highlights the Stoch BiRo's adaptability and cost-effectiveness in mechanical design, control strategies, and autonomous navigation, promising diverse applications in real-world robotics scenarios., Comment: 7 Pages, 6 figures

In fields such as mining, search and rescue, and archaeological exploration, ensuring real-time, collision-free navigation of robots in confined, cluttered environments is imperative. Despite the value of established path planning algorithms, they often face challenges in convergence rates and handling dynamic infeasibilities. Alternative techniques like collision cones struggle to accurately represent complex obstacle geometries. This paper introduces a novel category of control barrier functions, known as Polygonal Cone Control Barrier Function (PolyC2BF), which addresses overestimation and computational complexity issues. The proposed PolyC2BF, formulated as a Quadratic Programming (QP) problem, proves effective in facilitating collision-free movement of multiple robots in complex environments. The efficacy of this approach is further demonstrated through PyBullet simulations on quadruped (unicycle model), and crazyflie 2.1 (quadrotor model) in cluttered environments., Comment: 6 Pages, 6 Figures. Accepted at European Control Conference (ECC) 2024. arXiv admin note: text overlap with arXiv:2303.15871

Autonomy advances have enabled robots in diverse environments and close human interaction, necessitating controllers with formal safety guarantees. This paper introduces an experimental platform designed for the validation and demonstration of a novel class of Control Barrier Functions (CBFs) tailored for Unmanned Ground Vehicles (UGVs) to proactively prevent collisions with kinematic obstacles by integrating the concept of collision cones. While existing CBF formulations excel with static obstacles, extensions to torque/acceleration-controlled unicycle and bicycle models have seen limited success. Conventional CBF applications in nonholonomic UGV models have demonstrated control conservatism, particularly in scenarios where steering/thrust control was deemed infeasible. Drawing inspiration from collision cones in path planning, we present a pioneering CBF formulation ensuring theoretical safety guarantees for both unicycle and bicycle models. The core premise revolves around aligning the obstacle's velocity away from the vehicle, establishing a constraint to perpetually avoid vectors directed towards it. This control methodology is rigorously validated through simulations and experimental verification on the Copernicus mobile robot (Unicycle Model) and FOCAS-Car (Bicycle Model)., Comment: 8 pages, 11 figures, Submitted at American Control Conference (ACC), 2024. arXiv admin note: substantial text overlap with arXiv:2209.11524

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal models like recurrent neural networks (RNNs), as they capture only the statistical connections in the training data and may fail to learn the underlying dynamics of the target system. To tackle this challenge, we propose a novel machine learning model based on Koopman operator theory, which we call Koopman Invertible Autoencoders (KIA), that captures the inherent characteristic of the system by modeling both forward and backward dynamics in the infinite-dimensional Hilbert space. This enables us to efficiently learn low-dimensional representations, resulting in more accurate predictions of long-term system behavior. Moreover, our method's invertibility design guarantees reversibility and consistency in both forward and inverse operations. We illustrate the utility of KIA on pendulum and climate datasets, demonstrating 300% improvements in long-term prediction capability for pendulum while maintaining robustness against noise. Additionally, our method excels in long-term climate prediction, further validating our method's effectiveness., Comment: Accepted at IEEE International Conference on Data Mining (ICDM) 2023

In neural network training, RMSProp and Adam remain widely favoured optimisation algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. Additionally, questions about their theoretical convergence properties continue to be a subject of interest. In this paper, we theoretically analyse a constant step size version of Adam in the non-convex setting and discuss why it is important for the convergence of Adam to use a fixed step size. This work demonstrates the derivation and effective implementation of a constant step size for Adam, offering insights into its performance and efficiency in non convex optimisation scenarios. (i) First, we provide proof that these adaptive gradient algorithms are guaranteed to reach criticality for smooth non-convex objectives with constant step size, and we give bounds on the running time. Both deterministic and stochastic versions of Adam are analysed in this paper. We show sufficient conditions for the derived constant step size to achieve asymptotic convergence of the gradients to zero with minimal assumptions. Next, (ii) we design experiments to empirically study Adam's convergence with our proposed constant step size against stateof the art step size schedulers on classification tasks. Lastly, (iii) we also demonstrate that our derived constant step size has better abilities in reducing the gradient norms, and empirically, we show that despite the accumulation of a few past gradients, the key driver for convergence in Adam is the non-increasing step sizes., Comment: 48 pages including proofs and extended experiments

Legged robots exhibit significant potential across diverse applications, including but not limited to hazardous environment search and rescue missions and the exploration of unexplored regions both on Earth and in outer space. However, the successful navigation of these robots in dynamic environments heavily hinges on the implementation of efficient collision avoidance techniques. In this research paper, we employ Collision Cone Control Barrier Functions (C3BF) to ensure the secure movement of legged robots within environments featuring a wide array of static and dynamic obstacles. We introduce the Quadratic Program (QP) formulation of C3BF, referred to as C3BF-QP, which serves as a protective filter layer atop a reference controller to ensure the robots' safety during operation. The effectiveness of this approach is illustrated through simulations conducted on PyBullet., Comment: 5 Pages, 5 Figures. Updated the baseline controller. arXiv admin note: text overlap with arXiv:2303.15871

Retirement prediction helps individuals and institutions make informed financial, lifestyle, and workforce decisions based on estimated retirement portfolios. This paper attempts to predict retirement using Monte Carlo simulations, allowing one to probabilistically account for a range of possibilities. The authors propose a model to predict the values of the investment accounts IRA and 401(k) through the simulation of inflation rates, interest rates, and other pertinent factors. They provide a user case study to discuss the implications of the proposed model., Comment: Conference Proceedings require that all preprints be withdrawn before the paper is indexed

Unmanned aerial vehicles (UAVs), specifically quadrotors, have revolutionized various industries with their maneuverability and versatility, but their safe operation in dynamic environments heavily relies on effective collision avoidance techniques. This paper introduces a novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles. We propose a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision. By showing that the proposed constraint is a valid CBF for quadrotors, we are able to leverage its real-time implementation via Quadratic Programs (QPs), called the CBF-QPs. Validation includes PyBullet simulations and hardware experiments on Crazyflie 2.1, demonstrating effectiveness in static and moving obstacle scenarios. Comparative analysis with literature, especially higher order CBF-QPs, highlights the proposed approach's less conservative nature. Simulation and Hardware videos are available here: https://tayalmanan28.github.io/C3BF-UAV/, Comment: Accepted at American Control Conference(ACC) 2024. 6 pages, 8 figures

In this paper, we propose a new class of Control Barrier Functions (CBFs) for Unmanned Ground Vehicles (UGVs) that help avoid collisions with kinematic (non-zero velocity) obstacles. While the current forms of CBFs have been successful in guaranteeing safety/collision avoidance with static obstacles, extensions for the dynamic case have seen limited success. Moreover, with the UGV models like the unicycle or the bicycle, applications of existing CBFs have been conservative in terms of control, i.e., steering/thrust control has not been possible under certain scenarios. Drawing inspiration from the classical use of collision cones for obstacle avoidance in trajectory planning, we introduce its novel CBF formulation with theoretical guarantees on safety for both the unicycle and bicycle models. The main idea is to ensure that the velocity of the obstacle w.r.t. the vehicle is always pointing away from the vehicle. Accordingly, we construct a constraint that ensures that the velocity vector always avoids a cone of vectors pointing at the vehicle. The efficacy of this new control methodology is later verified by Pybullet simulations on TurtleBot3 and F1Tenth., Comment: 6 pages, 4 figures, For supplement video follow https://youtu.be/Dme7Wm9y6es. *The first and second authors have contributed equally

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips; and can be slightly modified to appear as a sub-problem in many areas, such as DNA sequencing. In this paper, a study on parallelization of the Brute Force approach (under several paradigms) of the Travelling Salesman Problem is presented. Detailed timing studies for the serial and various parallel implementations of the Travelling Salesman Problem have also been illustrated.