arXiv subjects

Pinaki Pal

Publications and source records attributed to Pinaki Pal.

At least 19 recordsLinked to original sources

arXiv2026

Double explosive transitions in adaptive multilayer networks with higher-order interactions

Can asymmetry between two interacting networks fundamentally change how they synchronize? We identify double explosive transitions in the forward direction, backward direction, or a combination thereof, with single or double hysteresis loops in an adaptive bilayer multiplex network of Kuramoto oscillators with pairwise and three-body interactions and asymmetric phase lags. Using the Ott-Antonsen reduction, we derive a low-dimensional system and perform a stability analysis. The reduced model accurately captures the full microscopic dynamics and enables analytical expressions for the bifurcation points. Systematic mapping across multiple parameter planes reveals eight distinct synchronization regimes. The relative ordering of saddle-node and pitchfork bifurcation points---controlled by phase-lag asymmetry, cross-layer adaptation, and the higher-order interaction strength---creates two distinct coherent branches (weak and strong), giving rise to double explosive transitions. Crucially, phase-lag asymmetry acts as a robust control knob: while symmetric phase lags suppress explosive transitions, layer-specific differences promote multistability and double explosive transitions. The higher-order interaction strength $K_2$ and adaptation strengths $q$, $p$, and $h$ further modulate these transitions in a complex, parameter-dependent manner. Excellent agreement between analytical predictions and numerical simulations confirms the robustness of our reduced description.

nlin.AO↗

arXiv2026

A Reinforcement-Learning-Augmented Liquid-Fueled Reactor Network Model for Predicting Lean Blowout in Gas Turbine Combustors

This study introduces a reinforcement learning (RL) framework for generating optimal liquid-fueled reactors to improve lean blowout (LBO) predictions in gas turbine combustors. Existing approaches for determining cluster boundaries rely on manual heuristics or distance-based metrics in the input space. In contrast, the proposed method is goal-oriented, explicitly accounting for the target metric (e.g., LBO prediction accuracy) during cluster formation. The framework employs a multi-stage clustering--classification strategy: an initial clustering step (e.g., $k$-means clustering) generates a large set of homogeneous micro-clusters, followed by an actor-critic RL agent that merges them into optimal reactor zones. The validation study, performed using a Jet-A mechanism (119 species, 841 reactions), shows the RL framework offers improved predictive fidelity compared to $k$-means and captures the correct LBO trends, while achieving substantial speedups relative to the high-fidelity computational model. Overall, the RL-driven approach demonstrates strong potential as a computationally efficient reduced-order modeling technique that can complement high-fidelity simulations for rapid design-space exploration.

cs.LG↗

arXiv2026

A unified framework for synchronization optimization in directed multiplex networks

The multiplex network paradigm has been instrumental in revealing many unexpected phenomena and dynamical regimes in complex interacting systems. Nevertheless, most of the current research focuses on undirected multiplex structures, whereas real-world systems predominantly involve directed interactions. Here, we present an analytical framework for attaining optimal synchronization in directed multiplex networks composed of phase oscillators, considering both frustrated and non-frustrated regimes. A multiplex synchrony alignment function (MSAF) is introduced for this purpose, whose formulation integrates structural properties and dynamical characteristics of the individual directed layers. Using this function, we derive two classes of frequency distributions: one that yields perfect synchronization at a prescribed coupling strength in the presence of phase-lag, and another that optimizes synchronization over a broad range of coupling strengths. Numerical simulations on various directed duplex topologies demonstrate that both frequency sets substantially outperform conventional distributions. We also explore network optimization through a directed link rewiring strategy aimed at minimizing the MSAF, along with a swapping algorithm for optimally assigning fixed frequencies on both layers of a given directed duplex network. Examination of synchrony-optimized directed networks uncovers three notable correlations: a positive relationship between frequency and out-degree, a negative correlation between neighboring frequencies, and an anti-correlation between mirror node frequencies across directed layers.

nlin.AO↗

arXiv2026

A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems

Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling framework for prediction of fluid flows, and demonstrate it for high-pressure gas injection phenomena relevant to reciprocating engines. The approach employs a hierarchical Vision Transformer (SwinV2-UNet) architecture that processes multimodal flow datasets from multi-fidelity simulations. The model architecture is conditioned on auxiliary tokens explicitly encoding the data modality and time increment. Model performance is assessed on two different tasks: (1) spatiotemporal rollouts, where the model autoregressively predicts the flow state at future times; and (2) feature transformation, where the model infers unobserved fields/views from observed fields/views. We train separate models on multimodal datasets generated from in-house CFD simulations of argon jet injection into a nitrogen environment, encompassing multiple grid resolutions, turbulence models, and equations of state. The resulting data-driven models learn to generalize across resolutions and modalities, accurately forecasting the flow evolution and reconstructing missing flow-field information from limited views. This work demonstrates how large vision transformer-based models can be adapted to advance predictive modeling of complex fluid flow systems.

physics.flu-dyn↗

arXiv2025

Mesh-based Super-resolution of Detonation Flows with Multiscale Graph Transformers

Super-resolution flow reconstruction using state-of-the-art data-driven techniques is valuable for a variety of applications, such as subgrid/subfilter closure modeling, accelerating spatiotemporal forecasting, data compression, and serving as an upscaling tool for sparse experimental measurements. In the present work, a first-of-its-kind multiscale graph transformer approach is developed for mesh-based super-resolution (SR-GT) of reacting flows. The novel data-driven modeling paradigm leverages a graph-based flow-field representation compatible with complex geometries and non-uniform/unstructured grids. Further, the transformer backbone captures long-range dependencies between different parts of the low-resolution flow-field, identifies important features, and then generates the super-resolved flow-field that preserves those features at a higher resolution. The performance of SR-GT is demonstrated in the context of spectral-element-discretized meshes for a challenging test problem of 2D detonation propagation within a premixed hydrogen-air mixture exhibiting highly complex multiscale reacting flow behavior. The SR-GT framework utilizes a unique element + neighborhood graph representation for the coarse input, which is then tokenized before being processed by the transformer component to produce the fine output. It is demonstrated that SR-GT provides high super-resolution accuracy for reacting flow-field features and superior performance compared to traditional interpolation-based SR schemes.

cs.LG↗

arXiv2025

Enhancing cluster synchronization in phase-lagged multilayer networks

Cluster synchronization in multilayer networks of phase oscillators with phase-lag poses significant challenges due to the destabilizing effects of delayed interactions. Leveraging the Sakaguchi-Kuramoto model, this study addresses these challenges by systematically exploring the role of natural frequency distributions in sustaining cluster synchronization under high phase-lag conditions. We focus on four distributions: uniform (uni-uni), partially degree-correlated (deg-uni, uni-deg), and fully degree-correlated (deg-deg), where oscillators' intrinsic frequencies align with their network connectivity. Through numerical and analytical investigations, we demonstrate that the deg-deg distribution, where both layers employ degree-matched frequencies, remarkably enhances synchronization stability, outperforming other configurations. We analyze two distinct network architectures: one composed entirely of nontrivial clusters and another combining trivial and nontrivial clusters. Results reveal that structural heterogeneity encoded in the deg-deg coupling counteracts phase-lag-induced desynchronization, enabling robust cluster synchronization even at large phase-lag values. Stability is rigorously validated via transverse Lyapunov exponents (TLEs), which confirm that deg-deg networks exhibit broader synchronization regimes compared to uniform or partially correlated systems. These findings provide critical insights into the interplay between topological heterogeneity and dynamical resilience, offering a framework for designing robust multilayer systems from delay-tolerant power grids to adaptive biological networks, where synchronization under phase-lag is paramount.

nlin.CD↗

arXiv2025

Generalized Adaptation-Induced Non-universal Synchronization Transitions in Random Hypergraphs

We investigate the effect of partial order parameter adaptation in form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are considered as pairwise and triangular. Using the Ott-Antonsen ansatz, we obtain a set of self-consistent equations of the order parameter that describe the synchronization diagrams. A broad diversity of synchronization transitions are observed as a result of the interaction between the partial adaptation approach, generalized adaptation functions, and coupling strengths. The system specifically shows a double-jump transition under a power-law form of the adaptation function. A polynomial form of the adaptation function leads to the emergence of an intermediate synchronization state for specific combinations of one negative and one positive coefficient. Moreover, the synchronization transition may become continuous or explosive when the pairwise coupling strength varies. The generality of this synchronization behavior is further supported by results obtained using a Gaussian adaptation function.

nlin.AO↗

arXiv2025

Effect of phase-lag on synchronization in adaptive multilayer networks with higher-order interactions

We investigate the transition to synchronization in adaptive multilayer networks with higher-order interactions both analytically and numerically in the presence of phase frustration ($\beta$). The higher order topology consists of pairwise and triadic couplings. The analytical framework for the investigation is based on the Ott-Antonsen ansatz which leads to a convenient low-dimensional model. Extensive bifurcation analysis of the low-dimensional model and the numerical simulation of the full networks are performed to explore the paths to synchronization. The combined analysis shows a complex dependence of the transition to synchronization on adaptation exponents, coupling strengths, phase lag parameter, and multilayer configuration. Various types of transitions to synchronization, namely continuous, tiered, and explosive, are exhibited by the system in different regions of the parameter space. In all the cases, a satisfactory match between the low-dimensional model and the numerical simulation results is observed. The origin of different transitions to synchronization is clearly understood using the low-dimensional model. Exploration of a wide region of the parameter space suggests that the phase frustration parameter inhibits tired as well as explosive synchronization transitions for fixed triadic coupling strength ($K_2$). On the other hand, discontinuous transition is promoted by the phase frustration parameter for fixed pairwise coupling strength ($K_1$). Moreover, the exponent of the adaptation function with the pairwise coupling decreases the width of the hysteresis, despite the dominance of the higher-order coupling for fixed $\beta$ and $K_2$. While, the exponent of the function adapted with higher-order coupling shows the opposite effect, it promotes bistability in spite of dominance of pairwise coupling strength for fixed $\beta$, and $K_1$.

nlin.AO↗

arXiv2025

A Generative Deep Learning Workflow for Inverse Molecular Design of Fuels

In the present work, a generative deep learning framework combining a Co-optimized Variational Autoencoder (Co-VAE) with quantitative structure-property relationship (QSPR) techniques is developed to enable inverse molecular design of fuels. The Co-VAE approach integrates an auxiliary fuel property prediction regression head with the VAE latent space, enhancing molecular reconstruction and accurate property estimation (Research Octane Number (RON) chosen as the fuel property of interest for demonstration studies). A subset of the GDB-13 database, combined with a curated RON database, is used for the Co-VAE training. Hyperparameter tuning is further utilized to optimize the balance among reconstruction fidelity, chemical validity, and RON prediction. Subsequently, an independent regression model is trained to further improve RON prediction accuracy, and a differential evolution algorithm is employed to efficiently navigate the Co-VAE latent space and identify promising fuel molecule candidates with RON greater than a chosen threshold. The overall generative deep learning framework captures complex structure-property relationships within a latent representation, and can be readily extended to different or multiple fuel properties, allowing exploration of large chemical spaces relevant to fuel design. Furthermore, the framework can be further augmented by incorporating additional synthesizability criteria to improve applicability and reliability for de novo design of novel high-performance fuels.

cs.LG↗

arXiv2025

Effect of oblique horizontal magnetic field on convection rolls

We investigate the effect of external horizontal magnetic field applied on the convection rolls obliquely (at an angle $\phi$ with the $x$-axis) in electrically conducting low Prandtl number fluids under the paradigm of the Rayleigh-B\'{e}nard convection by performing three-dimensional direct numerical simulations. The control parameters, namely, the Chandrasekhar number ($\mathrm{Q}$) and the reduced Rayleigh number $r$ (ratio of Rayleigh number to critical Rayleigh number), are varied in the ranges $0 \leq \mathrm{Q} \leq 1000$ and $1 \leq r \leq 20$ for the Prandtl numbers $\mathrm{Pr} = 0.1$ and $0.2$ by considering three horizontal aspect ratios ($\Gamma$): $\frac{1}{2}$, $1$ and $2$. In the absence of the magnetic field, the convection starts in the form of steady rolls including the one parallel to the $x$-axis. As the oblique horizontal magnetic field is switched on at an angle $\phi \in (0^\circ, ~90^\circ]$ with the $x$-axis, it is observed that the Lorentz force generated by the component of the magnetic field transverse to the axis of the convection rolls inhibits convection in the form of steady rolls. Thus, with the application of the magnetic field, the convection is suppressed and restarts for a higher Rayleigh number in the form of steady convection rolls. The rolls can either be oriented along the $x$-axis (steady parallel rolls, SPR) or oriented at an angle $45^\circ$ (steady oblique rolls, SOR$^+$) with the $x$-axis depending on the choices of the parameters. A rich bifurcation structure with standing and traveling patterns emerges at higher $r$. The oscillatory instability of steady rolls scales as $ \mathrm{Q}^\alpha $ with distinct exponents for weak and strong magnetic fields. Additionally, heat transfer decreases with increasing $ \phi $ for given $ \mathrm{Q} $ and $ \mathrm{Pr} $.

physics.flu-dyn↗

arXiv2024

A double explosive Kuramoto transition in hypergraphs

This study aims to develop a generalised concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. We found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the triadic coupling. A compromise between the two factors may result in a double explosive transition. To reinforce numerical observations, we employed the Ott--Antonsen ansatz. We observed that for a wide class of hypergraphs, combining two elements can result in a double explosive transition.

nlin.AO↗

arXiv2024

Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modeling

This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer. As the name implies, the focus is on enabling scalable operations that satisfy physical consistency via halo nodes at sub-graph boundaries. Here, consistency refers to the fact that a GNN trained and evaluated on one rank (one large graph) is arithmetically equivalent to evaluations on multiple ranks (a partitioned graph). This concept is demonstrated by interfacing GNNs with NekRS, a GPU-capable exascale CFD solver developed at Argonne National Laboratory. It is shown how the NekRS mesh partitioning can be linked to the distributed GNN training and inference routines, resulting in a scalable mesh-based data-driven modeling workflow. We study the impact of consistency on the scalability of mesh-based GNNs, demonstrating efficient scaling in consistent GNNs for up to O(1B) graph nodes on the Frontier exascale supercomputer.

cs.DC↗

arXiv2024

Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. The architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor-Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.

physics.flu-dyn↗

arXiv2024

Transition to synchronization in adaptive Sakaguchi-Kuramoto model with higher-order interactions

We investigate the phenomenon of transition to synchronization in Sakaguchi-Kuramoto model in the presence of higher-order interactions and global order parameter adaptation. The investigation is done by performing extensive numerical simulations and low dimensional modeling of the system. Numerical simulations of the full system show both continuous (second order) as well as discontinuous transitions. The discontinuous transitions can either be associated with explosive (first order) or with tiered synchronization states depending on the choice of parameters. To develop an in depth understanding of the transition scenario in the parameter space we derive a reduced order model (ROM) using the Ott-Antonsen ansatz, the results of which closely matches with that of the numerical simulations of the full system. The simplicity and analytical accessibility of the ROM helps to conveniently unfold the transition scenario in the system having complex dependence on the parameters. Simultaneous analysis of the full system and the ROM clearly identifies the regions of the parameter space exhibiting different types of transitions. It is observed that the second order continuous transition is connected with a supercritical pitchfork bifurcation (PB) of the ROM. On the other hand, the discontinuous teired transition is associated with multiple saddle-node (SN) bifurcations along with a supercritical PB and the first order explosive transition involves a subcritical PB alongside a SN bifurcation.

nlin.AO↗

arXiv2024

Transitions near the onset of stationary rotating magnetoconvection: role of magnetic Prandtl number

We investigate the instabilities and associated bifurcation structure near the onset of rotating magnetoconvection of low Prandtl number fluids by performing three dimensional direct numerical simulations. Previous studies considered zero magnetic Prandtl number ($\mathrm{Pm}$) limit for the investigation of bifurcation structure near the onset of convection. Here we numerically investigate the effect of $\mathrm{Pm}$ on the bifurcation structure. The classical Rayleigh-B\'{e}nard convection setup in the presence of horizontal magnetic field and rotation about the vertical axis are considered for the study. The control parameters, including the Taylor number ($\mathrm{Ta}$), Chandrasekhar number ($\mathrm{Q}$), reduced Rayleigh number ($\mathrm{r}$), and magnetic Prandtl number ($\mathrm{Pm}$) are varied in the ranges $0 < \mathrm{Ta}\leq 500$, $0 < \mathrm{Q}\leq 1000$, $0.8\leq \mathrm{r} \leq 2$ and $0 < \mathrm{Pm} < 1$ by considering Prandtl numbers $\mathrm{Pr}= 0.025$ and $0.1$. The investigation reveals the presence of supercritical, subcritical and hybrid transitions to convection. These transitions leads to infinitesimal and finite amplitude fluid patterns at the onset of convection. The finite amplitude solutions can be both stationary and time dependent. The bifurcation structures associated with these flow patterns at the onset are studied in detail. For very small $\mathrm{Pm}$, the bifurcation structure is found to be qualitatively similar to the ones observed in the $\mathrm{Pm}\rightarrow 0$ limit. However, as $\mathrm{Pm}$ is increased, several new solutions appear at the onset and the resulting bifurcation structures are greatly modified.

physics.flu-dyn↗

arXiv2024

One dimensional models for supercritical and subcritical transitions in rotating convection

Numerous study on natural and man made systems including rotating convection report the phenomena of supercritical and subcritical transitions from one state to another with the variation of relevant control parameters. However, the complexity of the rotating convection system even under the idealized Rayleigh-B\'enard geometry, hindered the simplest possible description of these transitions to convection. Here we present an one dimensional description of the stationary subcritical and supercritical transitions to rotating Rayleigh-B\'enard convection both for rigid and free-slip boundary conditions. The analysis of the one dimensional models and performance of three dimensional direct numerical simulations of the system show qualitatively similar results in a wide region of the parameter space. A brief discussion on time dependent convection of overstable origin is also presented.

physics.flu-dyn↗

arXiv2024

Computational Study on the Impact of Gasoline-Ethanol Blending on Autoignition and Soot/NOx Emissions under Gasoline Compression Ignition Conditions

Computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition engine are performed to investigate the impact of gasoline-ethanol blending on autoignition, nitrogen oxide (NOx), and soot emissions under low-load conditions. A four-component toluene primary reference fuel (TPRF) + ethanol (ETPRF) surrogate (with 10% ethanol by volume; E10) is employed to represent the test gasoline (RD5-87). A 3D engine CFD model employing finite-rate chemistry with a skeletal kinetic mechanism, adaptive mesh refinement (AMR), and hybrid method of moments (HMOM) is adopted to capture in-cylinder combustion and soot/NOx emissions. The engine CFD model is validated against experimental data for three gasoline-ethanol blends: E10, E30 and E100, with varying ethanol content by volume. Model validation is carried out for multiple start-of-injection (SOI) timings (-21, -27, -36, and -45 crank angle degrees after top-dead-center (aTDC)) with respect to in-cylinder pressure, heat release rate, combustion phasing, NOx and soot emissions. For late injection timings (-21 and -27oaTDC), E30 yields higher soot than E10; while the trend reverses for early injection cases (-36 and -45oaTDC). E100 yields the lowest amount of soot among all fuels irrespective of SOI timing. Further, E10 shows a non-monotonic trend in soot emissions with SOI timing: SOI-36>SOI-45>SOI-21>SOI-27, while soot emissions from E30 exhibit monotonic decrease with advancing SOI timing. NOx emissions from various fuels follow a trend of E10>E30>E100. NOx emissions increase as SOI timing is advanced for all fuels, with an anomaly for E10 and E100 where NOx decreases when SOI is advanced beyond -36oaTDC. Detailed analysis of the numerical results is performed to investigate the emission trends and elucidate the impact of chemical composition and physical properties on autoignition and emissions characteristics.

math.NA↗

arXiv2024

A Spectral Element Enrichment Wall-Model

We develop an enrichment wall-model within the spectral element method (SEM) framework for large-eddy simulations of wall-bounded flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical law-of-the-wall enrichment function representing the mean velocity near the wall. In the solution representation, this enrichment function captures the large gradients in the boundary layer, which allows the polynomial modes to represent the turbulent fluctuations. The enriched solution is able to resolve the shear stress at the wall without any modification to the no-slip wall boundary conditions. The performance of the SEM enrichment wall-modeling approach is assessed in turbulent channel flow LES for a range of Reynolds numbers. The results show that the proposed method improves solution accuracy on under-resolved near-wall grids as compared to the traditional shear stress wall-models.

physics.flu-dyn↗