arXiv subjects

Kaustav Chakraborty

Publications and source records attributed to Kaustav Chakraborty.

At least 19 recordsLinked to original sources

arXiv2025

Safety Evaluation of Motion Plans Using Trajectory Predictors as Forward Reachable Set Estimators

The advent of end-to-end autonomy stacks - often lacking interpretable intermediate modules - has placed an increased burden on ensuring that the final output, i.e., the motion plan, is safe in order to validate the safety of the entire stack. This requires a safety monitor that is both complete (able to detect all unsafe plans) and sound (does not flag safe plans). In this work, we propose a principled safety monitor that leverages modern multi-modal trajectory predictors to approximate forward reachable sets (FRS) of surrounding agents. By formulating a convex program, we efficiently extract these data-driven FRSs directly from the predicted state distributions, conditioned on scene context such as lane topology and agent history. To ensure completeness, we leverage conformal prediction to calibrate the FRS and guarantee coverage of ground-truth trajectories with high probability. To preserve soundness in out-of-distribution (OOD) scenarios or under predictor failure, we introduce a Bayesian filter that dynamically adjusts the FRS conservativeness based on the predictor's observed performance. We then assess the safety of the ego vehicle's motion plan by checking for intersections with these calibrated FRSs, ensuring the plan remains collision-free under plausible future behaviors of others. Extensive experiments on the nuScenes dataset show our approach significantly improves soundness while maintaining completeness, offering a practical and reliable safety monitor for learned autonomy stacks.

cs.RO↗

arXiv2025

Algorithmic detection of crystal structures from computer simulation data

Detection of crystal structures from particle positions of crystalline assemblies formed in computer simulations is an unsolved problem. The standard protocol, formulated in the reciprocal space, for structure determination from experimental diffraction data is not suitable for analysis of computer simulation data, after converting them to the Fourier space. There is a long history of attempts to tackle this problem by analyzing the system in the real space by using ideas of local neighbors and broken symmetries of the crystalline state. In this paper, we propose a heuristic solution to this problem by detecting all possible unit cells directly from particle coordinates obtained in a typical computer simulation. The method is based on well known facts about crystal structures, some of which are underutilized in the context of the current problem. These include, the symmetry of the coordination polyhedron and its empirical relationship with directions of lattice vectors for a simple Bravais lattice, and the fact that any complex crystal can be systematically decomposed into multiple Bravais lattices. By using these ideas, along with standard computational techniques like search, clustering and convex hull construction, we were able to handle complex basis and construct all crystallographically viable unit cells from the coordinates. The method is capable of handling statistical noise by employing certain cutoffs and deals with multicomponent systems in a transparent manner. We validated it on real Monte Carlo simulation data and variety of test systems, including crystals with tens of particles in the basis. Our heuristic algorithm, which requires minimal human intervention and computational resources, provides a solution to the long standing problem and would be beneficial to the wider communities of condensed matter physics and computational materials science.

cond-mat.mtrl-sci↗

arXiv2025

A Bootstrap-based Method for Testing Network Similarity

This paper studies the matched network inference problem, where the goal is to determine if two networks, defined on a common set of nodes, exhibit a specific form of stochastic similarity. Two notions of similarity are considered: (i) equality, i.e., testing whether the networks arise from the same random graph model, and (ii) scaling, i.e., testing whether their probability matrices are proportional for some unknown scaling constant. We develop a testing framework based on a parametric bootstrap approach and a Frobenius norm-based test statistic. The proposed approach is highly versatile as it covers both the equality and scaling problems, and ensures adaptability under various model settings, including stochastic blockmodels, Chung-Lu models, and random dot product graph models. We establish theoretical consistency of the proposed tests and demonstrate their empirical performance through extensive simulations under a wide range of model classes. Our results establish the flexibility and computational efficiency of the proposed method compared to existing approaches. We also report a real-world application involving the Aarhus network dataset, which reveals meaningful sociological patterns across different communication layers.

stat.ME↗

arXiv2024

Phase behavior of hard sheared cube family

A sheared cube is made out of a cube by giving a shear to the body in one direction keeping one of the faces fixed. We investigate here the thermodynamic phase behavior of a family of such regular hard sheared cubes, each of the members of the family having a distinct angle made by the faces with the perpendicular on the fixed face. Hard particle Monte Carlo (HPMC) has been performed with these anisotropic building blocks resulting entropy-driven self assembly. Thereby computational evidence of discrete plastic crystal phase has been found in crystal. The discrete plastic crystal phase is known to form through the spontaneous self-assembly of certain polyhedra. Throughout the entire solid regime particle orientations exhibit strong specific correlations before melting into a liquid, without any evidence of freely rotating plastic crystal at lower density solid. It has been thoroughly observed that geometrical attributes of the shapes don't determine any of the properties that designate this orientational disorder phase reported here. We also find that particle's rotational symmetric axes and one of the rotational symmetric axes of the unit cell of the crystal have a strong relationship in their alignment in space. These results, achieved with shapes having crystallographic point group symmetry, are investigated as being consistent with the phenomenology of discrete plastic crystal phase established in earlier works with hard particles having non-crystallographic point group symmetry.

cond-mat.soft↗

arXiv2024

Predictive orientational phase behavior in convex polyhedral entropic crystals

Hard convex polyhedra, idealized models for anisotropic colloids and nanoparticles, are known to form variety of orientational phases despite the regular arrangement of particles in the crystalline assemblies. Based on the orientational behavior of the constituents particles, such phases could be categorized into freely rotating plastic crystals (PC), discrete plastic crystals (DPC) and orientationally ordered crystals (OC). In this article, we report an extensive Monte Carlo computer simulation study of sixty hard convex polyhedral shape indicating a direct predictive relationship between the nature of orientational phases in the crystalline assemblies and single-particle shape attributes. The influence of three attributes namely; (i) Isoperimetric Quotient (IQ) i.e., the extent of asphericity; (ii) isotropy of the moment of inertia tensor in the principal frame and (iii) number of symmetry operations in the point group of the particle and self-assembled crystal structure, were observed to control the orientational phase behavior of the entire solid region in many-body system. The translational order in the crystal appeared to play significant role only in the DPC phase, where as, other two phases were completely governed by the combination of two attributes. In this study, the role of shape attributes were characterized by sequential appearance of one or two of the aforementioned rotational phases across the phase diagram in a pressure dependent manner which could be regarded as an important stepping stone towards fully predictive self-assembly behavior of hard particle systems.

cond-mat.soft↗

arXiv2024

Understanding orientational disorder in crystalline assemblies of hard convex polyhedra

Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of orientational phase with discrete rotational mobility has been reported in hard particle systems. In this paper, we present a new analysis method for characterizing orientational phase of a crystal, which is based on algorithmic detection of unique orientations. Using this method we collected complete statistics of discrete orientations along the Monte Carlo simulation trajectories and observed that particles were equally partitioned among them, with specific values of pairwise orientational differences. These features remained constant across the pressure range and did not depend on rotational mobility. The discrete mobility was characteristic of a distinct equilibrium thermodynamic phase, qualitatively different from the freely rotating plastic phase with continuous orientations. The high pressure behavior with frozen particle orientations was part of that the same description and not a non-equilibrium arrested state. We introduced a precise notion of orientational order and demonstrated that the system was maximally disordered at the level of unit cell, even though individual particles could only take few discrete orientations. We report the existence of this phase in five polyhedral shapes and in systematically curated shape families constructed around two of them. The symmetry mismatch between the particle and the crystallographic point groups was found to be a predictive indicator for the occurrence of this phase.

cond-mat.soft↗

arXiv2024

Role of symmetry in the orientationally disordered crystals of hard convex polyhedra

The crystalline solids with lack of orientational ordering of anisotropic particles serve the purpose of studying the disordered systems with many fundamental applications in contemporary research. Despite the orientational disorder, multiple unique orientations with fixed angular differences exist in the crystal structures giving rise of "discrete plastic crystal" phase where the particles jump discretely within the unique orientations. We report the computational evidence of the role of symmetries between polyhedral particles and respective crystalline structures in controlling the existence of such phase at comparatively higher range of packing fractions beyond the freely rotating plastic crystals. The point groups of the particle and crystal structure were found to be directly connected in terms of the parallel alignment between the highest order rotational symmetry axes of the particle point group and any rotational axes of crystallographic point group, as a characteristic feature of this phase giving rise of discrete orientations. Based on our previous research [Kundu \textit{et al.}, arXiv:2311.06799, 2023] and new findings reported here, this symmetry relationship appeared to occur at the unit cells of the crystal structures which acted as the source of correlation, where as, all previously reported conserved orientational attributes i.e., number of unique orientations with fixed angular differences, equal population densities within the unique orientations, could be thought as the signatures of correlation present in the entire system. This relationship appeared to control all the aspects of phase which might be useful to draw fundamental insights about the disordered phases with orientational correlation as well as designing the disorder in the crystals.

cond-mat.soft↗

arXiv2024

Enhancing Safety and Robustness of Vision-Based Controllers via Reachability Analysis

Autonomous systems, such as self-driving cars and drones, have made significant strides in recent years by leveraging visual inputs and machine learning for decision-making and control. Despite their impressive performance, these vision-based controllers can make erroneous predictions when faced with novel or out-of-distribution inputs. Such errors can cascade into catastrophic system failures and compromise system safety. In this work, we compute Neural Reachable Tubes, which act as parameterized approximations of Backward Reachable Tubes to stress-test the vision-based controllers and mine their failure modes. The identified failures are then used to enhance the system safety through both offline and online methods. The online approach involves training a classifier as a run-time failure monitor to detect closed-loop, system-level failures, subsequently triggering a fallback controller that robustly handles these detected failures to preserve system safety. For the offline approach, we improve the original controller via incremental training using a carefully augmented failure dataset, resulting in a more robust controller that is resistant to the known failure modes. In either approach, the system is safeguarded against shortcomings that transcend the vision-based controller and pertain to the closed-loop safety of the overall system. We validate the proposed approaches on an autonomous aircraft taxiing task that involves using a vision-based controller to guide the aircraft towards the centerline of the runway. Our results show the efficacy of the proposed algorithms in identifying and handling system-level failures, outperforming methods that rely on controller prediction error or uncertainty quantification for identifying system failures.

cs.RO↗

arXiv2024

System-Level Safety Monitoring and Recovery for Perception Failures in Autonomous Vehicles

The safety-critical nature of autonomous vehicle (AV) operation necessitates development of task-relevant algorithms that can reason about safety at the system level and not just at the component level. To reason about the impact of a perception failure on the entire system performance, such task-relevant algorithms must contend with various challenges: complexity of AV stacks, high uncertainty in the operating environments, and the need for real-time performance. To overcome these challenges, in this work, we introduce a Q-network called SPARQ (abbreviation for Safety evaluation for Perception And Recovery Q-network) that evaluates the safety of a plan generated by a planning algorithm, accounting for perception failures that the planning process may have overlooked. This Q-network can be queried during system runtime to assess whether a proposed plan is safe for execution or poses potential safety risks. If a violation is detected, the network can then recommend a corrective plan while accounting for the perceptual failure. We validate our algorithm using the NuPlan-Vegas dataset, demonstrating its ability to handle cases where a perception failure compromises a proposed plan while the corrective plan remains safe. We observe an overall accuracy and recall of 90% while sustaining a frequency of 42Hz on the unseen testing dataset. We compare our performance to a popular reachability-based baseline and analyze some interesting properties of our approach in improving the safety properties of an AV pipeline.

cs.RO↗

arXiv2024

Detecting and Mitigating System-Level Anomalies of Vision-Based Controllers

Autonomous systems, such as self-driving cars and drones, have made significant strides in recent years by leveraging visual inputs and machine learning for decision-making and control. Despite their impressive performance, these vision-based controllers can make erroneous predictions when faced with novel or out-of-distribution inputs. Such errors can cascade to catastrophic system failures and compromise system safety. In this work, we introduce a run-time anomaly monitor to detect and mitigate such closed-loop, system-level failures. Specifically, we leverage a reachability-based framework to stress-test the vision-based controller offline and mine its system-level failures. This data is then used to train a classifier that is leveraged online to flag inputs that might cause system breakdowns. The anomaly detector highlights issues that transcend individual modules and pertain to the safety of the overall system. We also design a fallback controller that robustly handles these detected anomalies to preserve system safety. We validate the proposed approach on an autonomous aircraft taxiing system that uses a vision-based controller for taxiing. Our results show the efficacy of the proposed approach in identifying and handling system-level anomalies, outperforming methods such as prediction error-based detection, and ensembling, thereby enhancing the overall safety and robustness of autonomous systems.

cs.RO↗

arXiv2024

On Safety and Liveness Filtering Using Hamilton-Jacobi Reachability Analysis

Hamilton-Jacobi (HJ) reachability-based filtering provides a powerful framework to co-optimize performance and safety (or liveness) for autonomous systems. Under this filtering scheme, a nominal controller is minimally modified to ensure system safety or liveness. However, the resulting controllers can exhibit abrupt switching and bang-bang behavior, which is not suitable for applications of autonomous systems in the real world. This work presents a novel, unifying framework to design safety and liveness filters through reachability analysis. We explicitly characterize the maximal set of control inputs that ensures safety (or liveness) at a given state. Different safety filters can then be constructed using different subsets of this maximal set along with a projection operator to modify the nominal controller. We use the proposed framework to design three safety filters, each balancing performance, computation time, and smoothness differently. We highlight their relative strengths and limitations by applying these filters to autonomous navigation and rocket landing scenarios and on a physical robot testbed. We also discuss practical aspects associated with implementing these filters on real-world autonomous systems. Our research advances the understanding and potential application of reachability-based controllers on real-world autonomous systems.

cs.RO↗

arXiv2024

Discovering Closed-Loop Failures of Vision-Based Controllers via Reachability Analysis

Machine learning driven image-based controllers allow robotic systems to take intelligent actions based on the visual feedback from their environment. Understanding when these controllers might lead to system safety violations is important for their integration in safety-critical applications and engineering corrective safety measures for the system. Existing methods leverage simulation-based testing (or falsification) to find the failures of vision-based controllers, i.e., the visual inputs that lead to closed-loop safety violations. However, these techniques do not scale well to the scenarios involving high-dimensional and complex visual inputs, such as RGB images. In this work, we cast the problem of finding closed-loop vision failures as a Hamilton-Jacobi (HJ) reachability problem. Our approach blends simulation-based analysis with HJ reachability methods to compute an approximation of the backward reachable tube (BRT) of the system, i.e., the set of unsafe states for the system under vision-based controllers. Utilizing the BRT, we can tractably and systematically find the system states and corresponding visual inputs that lead to closed-loop failures. These visual inputs can be subsequently analyzed to find the input characteristics that might have caused the failure. Besides its scalability to high-dimensional visual inputs, an explicit computation of BRT allows the proposed approach to capture non-trivial system failures that are difficult to expose via random simulations. We demonstrate our framework on two case studies involving an RGB image-based neural network controller for (a) autonomous indoor navigation, and (b) autonomous aircraft taxiing.

cs.RO↗

arXiv2023

Sensitivity to CP Discovery in the Presence of Lorentz Invariance Violating Potential at T2HK/T2HKK

Investigation of conservation/violation of CP symmetry in the leptonic sector is very essential in understanding the evolution of the universe. Lorentz invariance and CPT are fundamental symmetries of nature. The violation of Lorentz invariance can also lead to CPT violations. The standard three flavour neutrino oscillation framework presents a scenario to observe the signature of Lorentz invariance and CP violations. This work focuses on the effect of Lorentz invariance violating (LIV) parameters on the sensitivity to CP violation. We investigate the sensitivity in two proposed configurations of the upcoming T2HK experiment: (i) one detector each placed at 295 km and 1100 km, and (ii) two identical detectors at 295 km. This study probes the effect of CPT violating parameters $a_{eμ},a_{eτ},a_{μτ}$.

hep-ph↗

arXiv2022

Analytic treatment of 3-flavor neutrino oscillation and decay in matter

We present compact analytic expressions for 3-flavor neutrino oscillation probabilities with invisible neutrino decay, where matter effects have been explicitly included. We take into account the possibility that the oscillation and decay components of the effective Hamiltonian do not commute. This is achieved by employing the techniques of inverse Baker-Campbell-Hausdorff (BCH) expansion and the Cayley-Hamilton theorem applied in the 3-flavor framework. If only the vacuum mass eigenstate $ν_3$ decays, we show that the treatment of neutrino propagation may be reduced to an effective 2-flavor analysis in the One Mass Scale Dominance (OMSD) approximation. The oscillation probabilities for $P_{μμ}$, $P_{ee}$, $P_{eμ}$ and $P_{μe}$ -- relevant for reactor, long baseline and atmospheric neutrino experiments -- are obtained as perturbative expansions for the case of only $ν_3$ decay, as well as for the more general scenario where all components of the decay matrix are non-zero. The analytic results thus obtained match the exact numerical results for constant density matter to a high precision and provide physical insights into possible effects of the decay of neutrinos as they propagate through Earth matter. We find that the effects of neutrino decay are most likely to be observable in $P_{μμ}$. We also point out that at any long baseline, the oscillation dips in $P_{μμ}$ can show higher survival probabilities in the case with decay than without decay, and explain this feature using our analytic approximations.

hep-ph↗

arXiv2022

Constraining general U(1) interactions from neutrino-electron scattering measurements at DUNE near detector

The neutrino-electron scattering process is a powerful tool to explore new physics beyond the standard model. Recently the possibility of DUNE Near Detector (ND) to constrain various new physics scenarios using this process have been highlighted in the literature. In this work, we consider the most general U(1) model and probe the constraints on the mass and coupling strength of the additional $Z'$ from $ν-e$ scattering at DUNE ND. The presence of the $Z^\prime$ gives rise to extra interference effects. In the context of the general U(1) model, the destructive interference can occur in either neutrino or anti-neutrino channel or for both or none. This opens up the possibilities of getting four different type of signal in the neutrino and ant-neutrino runs of DUNE. We perform the analysis using both the total rate and binned events spectrum. Our results show that in a bin by bin analysis the effect of destructive interference is less compared to the analysis using total rate. We present the bounds on the $ m_{Z^\prime} - g_X$ plane from $ν-e$ scattering measurements at DUNE ND and compare these with those obtained from other $ν-e$ scattering, COHERENT, and beam dump experiments. We show that the DUNE ND can give the best bound for certain mass ranges of $Z^\prime$.

hep-ph↗

arXiv2021

Neutrino propagation when mass eigenstates and decay eigenstates mismatch

We point out that the Hermitian and anti-Hermitian components of the effective Hamiltonian for decaying neutrinos cannot be simultaneously diagonalized by unitary transformations for all matter densities. We develop a formalism for the two-flavor neutrino propagation through matter of uniform density, for neutrino decay to invisible states. Employing a resummation of the Zassenhaus expansion, we obtain compact analytic expressions for neutrino survival and conversion probabilities, to first and second order in the "mismatch parameter" $\barγ$.

hep-ph↗

arXiv2021

New physics at nuSTORM

In this work we investigate the usefulness of nuSTORM as a probe of two new-physics scenarios which are sterile neutrinos and non-unitarity of the neutrino mixing matrix. For the sterile neutrino we show the importance of the neutral current events when combined with the charged current events to constrain the effective mixing angle, $θ_{μμ}$, and the sterile mixing angles $θ_{14}$ and $θ_{24}$. We also study the role nuSTORM will play in the study of neutrino oscillation physics if the three generation neutrino mixing matrix is non-unitary. In this context we elucidate the role of nuSTORM, considering both charged current and neutral current events, in constraining the various non-unitarity parameters such as $α_{11}$, $|α_{21}|$ and $α_{22}$.

hep-ph↗

arXiv2020

Invisible neutrino decay : First vs second oscillation maximum

We study the physics potential of the long-baseline experiments T2HK, T2HKK and ESS$ν$SB in the context of invisible neutrino decay. We consider normal mass ordering and assume that the state $ν_{3}$ as unstable, decaying into sterile states during the flight and obtain constraints on the neutrino decay lifetime ($τ_3$). We find that T2HK, T2HKK and ESS$ν$SB are sensitive to the decay-rate of $ν_{3}$ for $τ_{3}/m_{3} \leq 2.72\times10^{-11}$s/eV, $τ_{3}/m_{3} \leq 4.36\times10^{-11}$s/eV and $τ_{3}/m_{3} \leq 2.43\times10^{-11}$s/eV respectively at 3$σ$ C.L. We compare and contrast the sensitivities of the three experiments and specially investigate the role played by the mixing angle $θ_{23}$. It is seen that for experiments with flux peak near the second oscillation maxima, the poorer sensitivity to $θ_{23}$ results in weaker constraints on the decay lifetime. Although, T2HKK has one detector close to the second oscillation maxima, having another detector at the first oscillation maxima results in superior sensitivity to decay. In addition, we find a synergy between the two baselines of the T2HKK experiment which helps in giving a better sensitivity for $θ_{23}$ in the higher octant. We discuss the octant sensitivity in presence of decay and show that there is an enhancement in sensitivity which occurs due to the contribution from the survival probability $P_{μμ}$ which is more pronounced for the experiments at the second oscillation maxima. We also obtain the combined sensitivity of T2HK+ESS$ν$SB and T2HKK+ESS$ν$SB as $τ_{3}/m_{3} \leq 4.36\times10^{-11}$s/eV and $τ_{3}/m_{3} \leq 5.53\times10^{-11}$s/eV respectively at 3$σ$ C.L.

hep-ph↗