arXiv subjects

Soumyendu Raha

Publications and source records attributed to Soumyendu Raha.

At least 19 recordsLinked to original sources

arXiv2026

Transient Stability of Nonlinear Stochastic Dynamics: A Finite-Amplitude Logarithmic Measure Framework

Spacecraft guidance, navigation, and control systems operating during mission-critical phases such as atmospheric entry, powered descent, and planetary landing require reliable assessment of finite-time transient behavior under stochastic uncertainty. Existing stochastic stability frameworks primarily characterize asymptotic or infinitesimal behavior and therefore provide limited insight into finite-amplitude transient amplification over operationally relevant time horizons. This paper develops a finite-amplitude logarithmic measure for nonlinear Itô stochastic differential equations, extending classical matrix measures from infinitesimal to finite-amplitude perturbation evolution. The proposed framework establishes finite-time mean and variance bounds for logarithmic perturbation growth, derives Chernoff-type probabilistic bounds on transient amplification, and shows that mean transient stability does not necessarily guarantee finite-time pathwise safety. The theory is further extended to projected stochastic dynamics, leading to a transient-risk index that quantitatively balances deterministic contraction and diffusion-induced variability for transient-risk-aware system design. The proposed framework is validated through Monte Carlo simulations and flight-like lunar descent telemetry. The results demonstrate substantially improved prediction of nonlinear transient growth compared with classical Jacobian-based approaches and successfully distinguish trajectories exhibiting similar nominal behavior but significantly different transient-risk characteristics. The proposed framework provides a unified methodology for finite-time transient stability analysis, probabilistic transient-risk assessment, and transient-risk-aware guidance, navigation, and control of nonlinear stochastic aerospace systems.

math.DS↗

arXiv2026

Geometry-Consistent Bayesian Filtering under Structural Model Uncertainty: A Geometric Projection Particle Filter

Nonlinear state estimation under structural model uncertainty remains a fundamental challenge in autonomous Guidance, Navigation, and Control (GNC) systems. Conventional Bayesian filtering separates state propagation from measurement correction, allowing model mismatch to accumulate during propagation, resulting in proposal--likelihood inconsistency, particle degeneracy, and degraded estimation accuracy. Existing approaches primarily improve proposal distributions or weighting strategies without explicitly incorporating measurement geometry into state propagation. This paper introduces a geometry-consistent Bayesian filtering framework that incorporates measurement geometry directly into the propagation process. The nominal drift is projected onto the measurement-consistent subspace, yielding a geometry-consistent proposal while preserving the Bayesian posterior through a rigorous change-of-measure formulation. A Geometric Projection Particle Filter (GPF) is developed together with a geometric co-state that quantifies instantaneous dynamics--measurement inconsistency. Theoretical analysis establishes existence and uniqueness of the projected dynamics, posterior preservation, standard Monte Carlo convergence of the particle approximation, and robustness under structural model uncertainty. The framework is validated using lunar descent navigation under partial observability and persistent model uncertainty. Compared with the bootstrap particle filter and conventional Gaussian filtering methods, GPF consistently achieves higher effective sample size and lower estimation error. These results demonstrate that geometry-consistent propagation provides a principled, computationally efficient, and theoretically grounded framework for robust nonlinear Bayesian filtering.

math.DS↗

arXiv2026

Effective Resistance-Based Graph Sparsification and Community Detection

Community detection is a key task in network analysis, providing insight into the structural organization of complex systems. Effective resistance, a graph-theoretic metric derived from electrical network theory, has emerged as a powerful tool for evaluating connectivity and influence within networks. This paper proposes an effective resistance-based community detection algorithm that calculates the similarity between nodes using effective resistance values and produces a weighted graph. The sparse graph used in the algorithm is generated after computing the minimum spanning tree (MST) of the weighted graph and adopting a threshold sparsification strategy on non-MST edges. A maximum modularity approach is adopted using the Clauset-Newman-Moore algorithm on the resultant sparse graph. This algorithm is evaluated for both synthetic and real-world networks, demonstrating its effectiveness compared to popular existing methods. The result shows that the effective resistance-based approach accurately captures the structures of the community while maintaining computational efficiency.

cs.SI↗

arXiv2026

Low Latency Stand Alone Compute-Efficient Forecasting of Marine Engine Time Series Data

The operational reliability of a high performance marine vessel depends critically on the health of its marine propulsion systems, which are increasingly subjected to diverse operational loads and environmental stressors. This paper proposes a robust mathematical framework for non-linear state-space forecasting of marine engine parameters using adaptive-window multi-particle stochastic differential equations. Traditional time-series models such as Vector Autoregressive Integrated Moving Average, often fail to capture the inherent stochasticity and transient dynamics of complex systems due to their reliance on fixed-window linear assumptions. To address this, we develop a dual-layered estimation approach: first, an adaptive lookback mechanism dynamically adjusts the learning window size based on the instantaneous drift magnitude, ensuring responsiveness during non-stationary regimes. Second, a Multi-Particle ensemble is evolved via Euler-Maruyama discretization, where each particle trajectory represents a stochastic realization of the system state. To refine the ensemble mean and mitigate the "noise-chasing" behavior of raw estimators, a Girsanov transform induced change of probability measure is implemented, assigning higher probabilistic weights to particles that align with the physical drift. Theoretical evaluation and empirical benchmarking demonstrate that the proposed adaptive SDE framework significantly outperforms classical statistical baselines in multi-step prediction stability and computational efficiency. The model provides a scalable, "grey-box" solution for real-time risk quantification in systems characterized by high-frequency volatility and non-linear transitions.

eess.SY↗

arXiv2026

Co-State Based Data Fusion and Risk Aware Filtering for Spacecraft Navigation and Hazard Prediction

This paper develops a co-state based fusion frame work for spacecraft navigation, consistency monitoring, and hazard forecasting. A differential algebraic co-state is introduced as an instantaneous Lagrange multiplier that enforces measurement dynamics compatibility at the differential level and provides a physically interpretable signal of geometric inconsistency. On a longer time scale, co-state and innovation trajectories are used to learn a continuous time Markov generator governing transitions between coarse behavioural regimes, enabling intrinsic probabilistic risk forecasting through mode probabilities and mean first-passage time (MFPT). The resulting architecture unifies geometric projection, stochastic inference, and probabilistic risk assessment in a single online pipeline without requiring predefined fault models, labelled failure data, or heuristic thresholds. The framework is demonstrated on real lunar powered-descent telemetry, where it detects structural internal model inconsistency significantly earlier than physical divergence or statistical inconsistency in an Extended Kalman Filter (EKF). The results show that geometric inconsistency, stochastic drift, and probabilistic risk rise coherently prior to failure, yielding interpretable and operationally meaningful early-warning capability for autonomous landing systems.

math.DS↗

arXiv2026

A graph based advection framework for climate-driven species distribution

Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based reaction-diffusion-advection framework explicitly incorporating directional movement induced by environmental gradients. Our results show while diffusion promotes overall population persistence across the network, advective movement induces asymmetric flows. It create population hotspots by directing individuals toward optimal niches, often associated with nodes of high in-degree. We demonstrate the interplay between advection strength and network topology in determining species persistence. Strong advection increase local extinction risk by accumulating populations toward favorable nodes. Additionally, loss of ecological corridors can disrupt directed flow within the network, thereby restricting species from favorable patches. We found that this disruption might not cause immediate extinction, rather forcing species to spread to the suboptimal patches. Our advection framework therefore efficiently captures how directional movement interacting with network topology governs species redistribution, hotspot formation, and predict extinction risk under environmental change.

math.DS↗

arXiv2025

SGRDN-Data learned sparsification of graph reaction-diffusion networks

Graph sparsification is an area of interest in computer science and applied mathematics. Sparsification of a graph, in general, aims to reduce the number of edges in the network while preserving specific properties of the graph, like cuts and subgraph counts. Computing the sparsest cuts of a graph is known to be NP-hard, and sparsification routines exist for generating linear-sized sparsifiers in almost quadratic running time $O(n^{2 + ε})$. Consequently, obtaining a sparsifier can be a computationally demanding task, and the complexity varies based on the level of sparsity required. We propose SGRDN to extend sparsification to complex reaction-diffusion systems. This approach seeks to sparsify the graph such that the inherent reaction-diffusion dynamics are strictly preserved on the resulting structure. By selectively considering a subset of trajectories, we frame the network sparsification issue as a data assimilation problem within a Reduced Order Model (ROM) space, imposing constraints to conserve the eigenmodes of the Laplacian matrix ($L = D - A$), the difference between the degree matrix ($D$) and the adjacency matrix ($A$) despite perturbations. We derive computationally efficient eigenvalue and eigenvector approximations for perturbed Laplacian matrices and integrate these as spectral preservation constraints in the optimization problem. To further validate the method's broad applicability, we conducted an additional experiment on Neural Ordinary Differential Equations (neural ODEs), where SGRDN successfully achieved parameter sparsity.

cs.SI↗

arXiv2025

Improving Surrogate Model Robustness to Perturbations for Dynamical Systems Through Machine Learning and Data Assimilation

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal Decomposition (POD) can be used in such cases. However, these reduced order models are susceptible to perturbations in the input. We propose a novel framework that combines machine learning and data assimilation techniques to improving surrogate models to handle perturbations in input data effectively. Through rigorous experiments on dynamical systems modelled on graphs, we demonstrate that our framework substantially improves the accuracy of surrogate models under input perturbations. Furthermore, we evaluate the framework's efficacy on alternative surrogate models, including neural ODEs, and the empirical results consistently show enhanced performance.

cs.CE↗

arXiv2023

Intrinsic Stochastic Differential Equations and Extended Ito Formula on Manifolds

A general way of representing Stochastic Differential Equations (SDEs) on smooth manifold is based on Schwartz morphism. In this manuscript we are interested in SDEs on a smooth manifold $M$ that are driven by p-dimensional Wiener process $W_t \in \mathbb{R}^p$. In terms of Schwartz morphism, such SDEs are represented by Schwartz morphism that morphs the semi-martingale $(t,W_t)\in\mathbb{R}^{p+1}$ into a semi-martingale on the manifold $M$. We show that it is possible to construct such Schwartz morphisms using special maps that we call as diffusion generators. We show that one of the ways of constructing diffusion generator is by using regular Lagrangian. Using this diffusion generator approach, we also give extended Ito formula (also known as generalized Ito formula or Ito-Wentzell's formula) for SDEs on manifold.

math.DG↗

arXiv2023

Explicitly Constrained Stochastic Differential Equations on Manifolds

In this manuscript we consider Intrinsic Stochastic Differential Equations on manifolds and constrain it to a level set of a smooth function. Such type of constraints are known as explicit algebraic constraints. The system of differential equation and the algebraic constraints is, in combination, called the Stochastic Differential Algebraic Equations (SDAEs). We consider these equations on manifolds and present methods for computing the solution of SDAEs on manifolds.

math.PR↗

arXiv2023

On Explicit Stochastic Differential Algebraic Equations

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the category of Stochastic Differential-Algebraic Equations (SDAEs). In this article, the focus is on combining ideas from the local theory of Differential-Algebraic Equations with that of Stochastic Differential Equations. The question of existence and uniqueness of the solution for SDAEs is addressed by using contraction mapping theorem in an appropriate Banach space to arrive at a sufficient condition. From the geometric point of view, a necessary condition is derived for the existence of the solution. It is observed that there exists a class of completely high index SDAEs for which there is no solution. Hence, techniques to find approximate solution of completely high index equations are presented. The techniques are illustrated with examples and numerical computations.

math.OC↗

arXiv2022

Progression, Detection and Remission: Evolution of Chronic Myeloid Leukemia using a three-stage probabilistic model

We present a three-stage probabilistic model for the progression of Chronic Myeloid Leukemia (CML), as manifested by the leukemic stem cells, progenitor cells and mature leukemic cells. This progression is captured through the process of cell division and cell mutation, with probabilities of occurrence being assigned to both of them. The key contributions of this study include, the determination of the expected number of the leukemic stem cells, progenitor cells, mature leukemic cells, as well as total number of these cells (in terms of probabilities, and contingent on the initial cell count), expected time to reach a threshold level of total and injurious leukemic cells, as well as the critical time when the disease changes its phases, the probability of extinction of CML, and the dynamics of CML evolution consequent to primary therapy. Finally, the results obtained are demonstrated with numerical illustrations.

q-bio.PE↗

arXiv2021

Metapopulation dynamics of a respiratory disease with infection during travel

We formulate a compartmental model for the propagation of a respiratory disease in a patchy environment. The patches are connected through the mobility of individuals, and we assume that disease transmission and recovery are possible during travel. Moreover, the migration terms are assumed to depend on the distance between patches and the perceived severity of the disease. The positivity and boundedness of the model solutions are discussed. We analytically show the existence and global asymptotic stability of the disease-free equilibrium. We study three different network topologies numerically and find that underlying network structure is crucial for disease transmission. Further numerical simulations reveal that infection during travel has the potential to change the stability of disease-free equilibrium from stable to unstable. The coupling strength and transmission coefficients are also very crucial in disease propagation. Different exit screening scenarios indicate that the patch with the highest prevalence may have adverse effects but other patches will be benefited from exit screening. Furthermore, while studying the multi-strain dynamics, it is observed that two co-circulating strains will not persist simultaneously in the community but only one of the strains may persist in the long run. Transmission coefficients corresponding to the second strain are very crucial and show threshold like behavior with respect to the equilibrium density of the second strain.

q-bio.PE↗

arXiv2021

Prediction of dynamical systems using geometric constraints imposed by observations

Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this article, an approach for data-based model improvement is described which exploits the geometric constraints imposed by the system observations to estimate these unmodeled terms. The nominal model is augmented using these extra forcing terms to make predictions. This approach is applied to navigational satellite orbit prediction to bring down the error to approximately 12% of the error when using the nominal force model for a 2-hour prediction. In another example improved temperature predictions over the nominal heat equation are obtained for one-dimensional conduction.

cs.CE↗

arXiv2020

Modeling Control, Lockdown \& Exit Strategies for COVID-19 Pandemic in India

COVID-19--a viral infectious disease--has quickly emerged as a global pandemic infecting millions of people with a significant number of deaths across the globe. The symptoms of this disease vary widely. Depending on the symptoms an infected person is broadly classified into two categories namely, asymptomatic and symptomatic. Asymptomatic individuals display mild or no symptoms but continue to transmit the infection to otherwise healthy individuals. This particular aspect of asymptomatic infection poses a major obstacle in managing and controlling the transmission of the infectious disease. In this paper, we attempt to mathematically model the spread of COVID-19 in India under various intervention strategies. We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population. Impact of various factors such as presence of asymptotic individuals, lockdown strategies, social distancing practices, quarantine, and hospitalization on the disease transmission is extensively studied. Numerical simulation of our model is matched with the real COVID-19 data of India till May 15, 2020 for the purpose of estimating the model parameters. Our model with zone-wise lockdown is seen to give a decent prediction for July 20, 2020.

q-bio.PE↗

arXiv2019

Stabilized Partitioning of Metapopulations Networks

A metapopulations network is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to the other via dispersal connections. The loss of dispersal connections among the habitat patches can impact the stability of the system. In this work, we determine if there exist(s) set(s) of dispersal connections removal of which causes partitioning(s) of the metapopulations network into dynamically stable sub-networks. Our study finds that there exists a lower bound threshold Fiedler value which guarantees the dynamical stability of the network dynamics. Necessary and sufficient mathematical conditions for finding partitions that result in sub-networks with the desired threshold Fiedler values have been derived and illustrated with examples. Although posed and discussed in the ecological context, it may be pointed out that such partitioning problems exist across any spatially discrete but connected dynamical systems with reaction-diffusion. Non-ecological examples are power distribution grids, intra-cellular reaction pathway networks and high density nano-fluidic lab-on-chip applications.

math.DS↗

arXiv2019

A quantitative study on the role of TKI combined with Wnt/$β$-catenin signaling and IFN-$α$ in the treatment of CML through deterministic and stochastic approaches

We propose deterministic and stochastic models for studying the pharmacokinetics of chronic myeloid leukemia (CML), upon administration of IFN-$α$ (the traditional treatment for CML), TKI (the current frontline medication for CML) and Wnt/$β$-catenin signaling (the state-of-the art therapeutic breakthrough for CML). To the best of our knowledge, no mathematical model incorporating all these three therapeutic protocols are available in literature. Further, this work introduces a stochastic approach in the study of CML dynamics. The key contributions of this work are: (1) Determination of the patient condition, contingent upon the patient specific model parameters, which leads to prediction of the appropriate patient specific therapeutic dosage. (2) Addressing the question of how the dual therapy of TKI and Wnt/$β$-catenin signaling or triple combination of all three, offers potentially improved therapeutic responses, particularly in terms of reduced side effects of TKI or IFN-$α$. (3) Prediction of the likelihood of CML extinction/remission based on the level of CML stem cells at detection.

q-bio.TO↗

arXiv2018

Ecologically Sustainable Partitioning of a Metapopulations Network

A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut passing through metapopulations habitat such that populations remain stable. We combine the dynamical system stability analysis with graph partitioning algorithms in our approach to the problem. It finds such a safe construction, when one exists, provided the algebraic connectivity of the graph components is stronger than all the spatially local instabilities in the respective components. The dynamics of the populations on the spatially discrete patches (graph nodes) and their spatial communication with other patches is modeled as a reaction-diffusion system. By reversing the Turing-instability idea the stability conditions of the partitioned system are found to depend on local dynamics of the metapopulations and the Fiedler value of the Laplacian matrix of the graph. This leads to the necessary and sufficient conditions for removal of the graph edges subject to the stability of the partitioned graph networks. An heuristic bisection graph partitioning algorithm has been proposed and examples illustrate the theoretical result.

math.DS↗