arXiv subjects

Souvik Chakraborty

Publications and source records attributed to Souvik Chakraborty.

At least 55 records · Page 3Linked to original sources

arXiv2025

Distribution-Free Uncertainty-Aware Virtual Sensing via Conformalized Neural Operators

Robust uncertainty quantification (UQ) remains a critical barrier to the safe deployment of deep learning in real-time virtual sensing, particularly in high-stakes domains where sparse, noisy, or non-collocated sensor data are the norm. We introduce the Conformalized Monte Carlo Operator (CMCO), a framework that transforms neural operator-based virtual sensing with calibrated, distribution-free prediction intervals. By unifying Monte Carlo dropout with split conformal prediction in a single DeepONet architecture, CMCO achieves spatially resolved uncertainty estimates without retraining, ensembling, or custom loss design. Our method addresses a longstanding challenge: how to endow operator learning with efficient and reliable UQ across heterogeneous domains. Through rigorous evaluation on three distinct applications: turbulent flow, elastoplastic deformation, and global cosmic radiation dose estimation-CMCO consistently attains near-nominal empirical coverage, even in settings with strong spatial gradients and proxy-based sensing. This breakthrough offers a general-purpose, plug-and-play UQ solution for neural operators, unlocking real-time, trustworthy inference in digital twins, sensor fusion, and safety-critical monitoring. By bridging theory and deployment with minimal computational overhead, CMCO establishes a new foundation for scalable, generalizable, and uncertainty-aware scientific machine learning.

cs.LG↗

arXiv2025

Half-integer thermal conductance in the absence of Majorana mode

Considering a range of candidate quantum phases of matter, half-integer thermal conductance ($κ_{\text{th}}$) is believed to be an unambiguous evidence of non-Abelian states. It has been long known that such half-integer values arise due to the presence of Majorana edge modes, representing a significant step towards topological quantum computing platforms. Here, we challenge this prevailing notion by presenting a comprehensive theoretical and experimental study where half-integer two-terminal thermal conductance plateau is realized employing Abelian phases. Our proposed setup features a confined geometry of bilayer graphene, interfacing distinct particle-like and hole-like integer quantum Hall states. Each segment of the device exhibits full charge and thermal equilibration. Our approach is amenable to generalization to other quantum Hall platforms, and may give rise to other values of fractional (electrical and thermal) quantized transport. Our study demonstrates that the observation of robust non-integer values of thermal conductance can arise as a manifestation of mundane equilibration dynamics as opposed to underlying non-trivial topology.

cond-mat.mes-hall↗

arXiv2025

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems

Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional, data-intensive regimes remains a significant challenge. In this work, we introduce a novel, scalable GPO, which capitalizes on sparsity, locality, and structural information through judicious kernel design. Addressing the fundamental limitation of cubic computational complexity, our method leverages nearest-neighbor-based local kernel approximations in the spatial domain, sparse kernel approximation in the parameter space, and structured Kronecker factorizations to enable tractable inference on large-scale datasets and high-dimensional input. While local approximations often introduce accuracy trade-offs due to limited kernel interactions, we overcome this by embedding operator-aware kernel structures and employing expressive, task-informed mean functions derived from neural operator architectures. Through extensive evaluations on a broad class of nonlinear PDEs - including Navier-Stokes, wave advection, Darcy flow, and Burgers' equations - we demonstrate that our framework consistently achieves high accuracy across varying discretization scales. These results underscore the potential of our approach to bridge the gap between scalability and fidelity in GPO, offering a compelling foundation for uncertainty-aware modeling in complex physical systems.

stat.ML↗

arXiv2025

MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation

We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the pointwise operator learning neural architecture nonlinear manifold decoder (NOMAD) with mixture density-based methods to estimate conditional probability distributions for stochastic output functions. MD-NOMAD harnesses the ability of probabilistic mixture models to estimate complex probability and the high-dimensional scalability of pointwise neural operator NOMAD. We conduct empirical assessments on a wide array of stochastic ordinary and partial differential equations and present the corresponding results, which highlight the performance of the proposed framework.

cs.LG↗

arXiv2025

Geometry adaptive waveformer for cardio-vascular modeling

Modeling cardiovascular anatomies poses a significant challenge due to their complex, irregular structures and inherent pathological conditions. Numerical simulations, while accurate, are often computationally expensive, limiting their practicality in clinical settings. Traditional machine learning methods, on the other hand, often struggle with some major hurdles, including high dimensionality of the inputs, inability to effectively work with irregular grids, and preserving the time dependencies of responses in dynamic problems. In response to these challenges, we propose a geometry adaptive waveformer model to predict blood flow dynamics in the cardiovascular system. The framework is primarily composed of three components: a geometry encoder, a geometry decoder, and a waveformer. The encoder transforms input defined on the irregular domain to a regular domain using a graph operator-based network and signed distance functions. The waveformer operates on the transformed field on the irregular grid. Finally, the decoder reverses this process, transforming the output from the regular grid back to the physical space. We evaluate the efficacy of the approach on different sets of cardiovascular data.

cs.LG↗

arXiv2025

Deep Muscle EMG construction using A Physics-Integrated Deep Learning approach

Electromyography (EMG)--based computational musculoskeletal modeling is a non-invasive method for studying musculotendon function, human movement, and neuromuscular control, providing estimates of internal variables like muscle forces and joint torques. However, EMG signals from deeper muscles are often challenging to measure by placing the surface EMG electrodes and unfeasible to measure directly using invasive methods. The restriction to the access of EMG data from deeper muscles poses a considerable obstacle to the broad adoption of EMG-driven modeling techniques. A strategic alternative is to use an estimation algorithm to approximate the missing EMG signals from deeper muscle. A similar strategy is used in physics-informed deep learning, where the features of physical systems are learned without labeled data. In this work, we propose a hybrid deep learning algorithm, namely the neural musculoskeletal model (NMM), that integrates physics-informed and data-driven deep learning to approximate the EMG signals from the deeper muscles. While data-driven modeling is used to predict the missing EMG signals, physics-based modeling engraves the subject-specific information into the predictions. Experimental verifications on five test subjects are carried out to investigate the performance of the proposed hybrid framework. The proposed NMM is validated against the joint torque computed from 'OpenSim' software. The predicted deep EMG signals are also compared against the state-of-the-art muscle synergy extrapolation (MSE) approach, where the proposed NMM completely outperforms the existing MSE framework by a significant margin.

cs.LG↗

arXiv2025

Thermopower probing emergent local moments in magic-angle twisted bilayer graphene

Recent experiments on magic-angle twisted bilayer graphene (MATBLG) have revealed the formation of flatbands, suggesting that correlation effects are likely to dominate in this system. Yet, a global transport measurement showing distinct signatures of strong correlations like local moments arising from the flatbands is missing. Utilizing thermopower as a sensitive global transport probe for measuring entropy, we unveil the presence of emergent local moments through their impact on entropy. Remarkably, in addition to sign changes at the Dirac point ($ν= 0$) and full band filling ($ν= \pm 4$), the thermopower of MATBLG demonstrates additional sign changes at the location, $ν_{cross} \sim \pm 1$, which do not vary with temperature from $5K$ to $\sim 60K$. This is in contrast to sensitive temperature-dependent crossing points seen in our study on twisted bilayer graphene devices with weaker correlations. Further, we have investigated the effect of magnetic field ($B$) on the thermopower, both $B_{\parallel}$ and $B_{\perp}$. Our results show a $30\%$ and $50\%$ reduction, respectively, that is consistent with suppression seen in the layered oxide due to the partial polarization of the spin entropy. The observed robust crossing points, together with suppression in a magnetic field, cannot be explained solely from the contributions of band fermions; instead, our data is consistent with the dominant contribution arising from the entropy of the emergent localized moments of a strongly correlated flatband.

cond-mat.mes-hall↗

arXiv2025

A Bayesian Approach for Discovering Time- Delayed Differential Equation from Data

Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem due to the inherent nonlinearity, uncertainty, and noise in real-world systems. Conventional equation discovery methods often exhibit limitations when dealing with large time delays, relying on deterministic techniques or optimization-based approaches that may struggle with scalability and robustness. In this paper, we present BayTiDe - Bayesian Approach for Discovering Time-Delayed Differential Equations from Data, that is capable of identifying arbitrarily large values of time delay to an accuracy that is directly proportional to the resolution of the data input to it. BayTiDe leverages Bayesian inference combined with a sparsity-promoting discontinuous spike-and-slab prior to accurately identify time-delayed differential equations. The approach accommodates arbitrarily large time delays with accuracy proportional to the input data resolution, while efficiently narrowing the search space to achieve significant computational savings. We demonstrate the efficiency and robustness of BayTiDe through a range of numerical examples, validating its ability to recover delayed differential equations from noisy data.

stat.ML↗

arXiv2024

FUsion-based ConstitutivE model (FuCe): Towards model-data augmentation in constitutive modelling

Constitutive modelling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying stress conditions due to their fixed forms and limited parameters. While recent advances in deep learning have addressed some limitations of classical models, purely data-driven methods tend to require large datasets, lack interpretability, and struggle to generalize beyond their training data. To tackle these issues, we introduce "Fusion-based Constitutive model (FuCe): Towards model-data augmentation in constitutive modelling". This approach combines established phenomenological models with an ICNN architecture, designed to train on the limited and noisy force-displacement data typically available in practical applications. The hybrid model inherently adheres to necessary constitutive conditions. During inference, Monte Carlo dropout is employed to generate Bayesian predictions, providing mean values and confidence intervals that quantify uncertainty. We demonstrate the model's effectiveness by learning two isotropic constitutive models and one anisotropic model with a single fibre direction, across six different stress states. The framework's applicability is also showcased in finite element simulations across three geometries of varying complexities. Our results highlight the framework's superior extrapolation capabilities, even when trained on limited and noisy data, delivering accurate and physically meaningful predictions across all numerical examples.

cs.CE↗

arXiv2024

Distribution free uncertainty quantification in neuroscience-inspired deep operators

Energy-efficient deep learning algorithms are essential for a sustainable future and feasible edge computing setups. Spiking neural networks (SNNs), inspired from neuroscience, are a positive step in the direction of achieving the required energy efficiency. However, in a bid to lower the energy requirements, accuracy is marginally sacrificed. Hence, predictions of such deep learning algorithms require an uncertainty measure that can inform users regarding the bounds of a certain output. In this paper, we introduce the Conformalized Randomized Prior Operator (CRP-O) framework that leverages Randomized Prior (RP) networks and Split Conformal Prediction (SCP) to quantify uncertainty in both conventional and spiking neural operators. To further enable zero-shot super-resolution in UQ, we propose an extension incorporating Gaussian Process Regression. This enhanced super-resolution-enabled CRP-O framework is integrated with the recently developed Variable Spiking Wavelet Neural Operator (VSWNO). To test the performance of the obtained calibrated uncertainty bounds, we discuss four different examples covering both one-dimensional and two-dimensional partial differential equations. Results demonstrate that the uncertainty bounds produced by the conformalized RP-VSWNO significantly enhance UQ estimates compared to vanilla RP-VSWNO, Quantile WNO (Q-WNO), and Conformalized Quantile WNO (CQ-WNO). These findings underscore the potential of the proposed approach for practical applications.

stat.ML↗

arXiv2024

Hybrid variable spiking graph neural networks for energy-efficient scientific machine learning

Graph-based representations for samples of computational mechanics-related datasets can prove instrumental when dealing with problems like irregular domains or molecular structures of materials, etc. To effectively analyze and process such datasets, deep learning offers Graph Neural Networks (GNNs) that utilize techniques like message-passing within their architecture. The issue, however, is that as the individual graph scales and/ or GNN architecture becomes increasingly complex, the increased energy budget of the overall deep learning model makes it unsustainable and restricts its applications in applications like edge computing. To overcome this, we propose in this paper Hybrid Variable Spiking Graph Neural Networks (HVS-GNNs) that utilize Variable Spiking Neurons (VSNs) within their architecture to promote sparse communication and hence reduce the overall energy budget. VSNs, while promoting sparse event-driven computations, also perform well for regression tasks, which are often encountered in computational mechanics applications and are the main target of this paper. Three examples dealing with prediction of mechanical properties of material based on microscale/ mesoscale structures are shown to test the performance of the proposed HVS-GNNs in regression tasks. We have also compared the performance of HVS-GNN architectures with the performance of vanilla GNNs and GNNs utilizing leaky integrate and fire neurons. The results produced show that HVS-GNNs perform well for regression tasks, all while promoting sparse communication and, hence, energy efficiency.

cs.LG↗

arXiv2024

A dual physics-informed neural network for topology optimization

We propose a novel dual physics-informed neural network for topology optimization (DPNN-TO), which merges physics-informed neural networks (PINNs) with the traditional SIMP-based topology optimization (TO) algorithm. This approach leverages two interlinked neural networks-a displacement network and an implicit density network-connected through an energy-minimization-based loss function derived from the variational principles of the governing equations. By embedding deep learning within the physical constraints of the problem, DPNN-TO eliminates the need for large-scale data and analytical sensitivity analysis, addressing key limitations of traditional methods. The framework efficiently minimizes compliance through energy-based objectives while enforcing volume fraction constraints, producing high-resolution designs for both 2D and 3D optimization problems. Extensive numerical validation demonstrates that DPNN-TO outperforms conventional methods, solving complex structural optimization scenarios with greater flexibility and computational efficiency, while addressing challenges such as multiple load cases and three-dimensional problems without compromising accuracy.

physics.comp-ph↗

arXiv2024

G$^{2}$TR: Generalized Grounded Temporal Reasoning for Robot Instruction Following by Combining Large Pre-trained Models

Consider the scenario where a human cleans a table and a robot observing the scene is instructed with the task "Remove the cloth using which I wiped the table". Instruction following with temporal reasoning requires the robot to identify the relevant past object interaction, ground the object of interest in the present scene, and execute the task according to the human's instruction. Directly grounding utterances referencing past interactions to grounded objects is challenging due to the multi-hop nature of references to past interactions and large space of object groundings in a video stream observing the robot's workspace. Our key insight is to factor the temporal reasoning task as (i) estimating the video interval associated with event reference, (ii) performing spatial reasoning over the interaction frames to infer the intended object (iii) semantically track the object's location till the current scene to enable future robot interactions. Our approach leverages existing large pre-trained models (which possess inherent generalization capabilities) and combines them appropriately for temporal grounding tasks. Evaluation on a video-language corpus acquired with a robot manipulator displaying rich temporal interactions in spatially-complex scenes displays an average accuracy of 70.10%. The dataset, code, and videos are available at https://reail-iitdelhi.github.io/temporalreasoning.github.io/ .

cs.RO↗

arXiv2024

Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanics

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty quantification. This paper introduces a novel Gaussian Process (GP) based neural operator for solving parametric differential equations. The approach proposed leverages the expressive capability of deterministic neural operators and the uncertainty awareness of conventional GP. In particular, we propose a ``neural operator-embedded kernel'' wherein the GP kernel is formulated in the latent space learned using a neural operator. Further, we exploit a stochastic dual descent (SDD) algorithm for simultaneously training the neural operator parameters and the GP hyperparameters. Our approach addresses the (a) resolution dependence and (b) cubic complexity of traditional GP models, allowing for input-resolution independence and scalability in high-dimensional and non-linear parametric systems, such as those encountered in computational mechanics. We apply our method to a range of non-linear parametric partial differential equations (PDEs) and demonstrate its superiority in both computational efficiency and accuracy compared to standard GP models and wavelet neural operators. Our experimental results highlight the efficacy of this framework in solving complex PDEs while maintaining robustness in uncertainty estimation, positioning it as a scalable and reliable operator-learning algorithm for computational mechanics.

stat.ML↗

arXiv2024

Harnessing physics-informed operators for high-dimensional reliability analysis problems

Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly and time-consuming, especially when dealing with systems governed by complex physical laws which necessitates computationally intensive numerical methods such as finite element or finite volume techniques. On the other hand, surrogate-based methods offer an efficient alternative for computing reliability by approximating the underlying model from limited data. Neural operators have recently emerged as effective surrogates for modelling physical systems governed by partial differential equations. These operators can learn solutions to PDEs for varying inputs and parameters. Here, we investigate the efficacy of the recently developed physics-informed wavelet neural operator in solving reliability analysis problems. In particular, we investigate the possibility of using physics-informed operator for solving high-dimensional reliability analysis problems, while bypassing the need for any simulation. Through four numerical examples, we illustrate that physics-informed operator can seamlessly solve high-dimensional reliability analysis problems with reasonable accuracy, while eliminating the need for running expensive simulations.

math.NA↗

arXiv2024

Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid

Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unstructured grids and irregular domains. Spatial graph neural networks utilize local convolution in a neighborhood to potentially address these challenges, yet they often suffer from issues such as over-smoothing and over-squashing in deep architectures. Conversely, spectral graph neural networks leverage global convolution to capture extensive features and long-range dependencies in domain graphs, albeit at a high computational cost due to Eigenvalue decomposition. In this paper, we introduce a novel approach, referred to as Spatio-Spectral Graph Neural Operator (Sp$^2$GNO) that integrates spatial and spectral GNNs effectively. This framework mitigates the limitations of individual methods and enables the learning of solution operators across arbitrary geometries, thus catering to a wide range of real-world problems. Sp$^2$GNO demonstrates exceptional performance in solving both time-dependent and time-independent partial differential equations on regular and irregular domains. Our approach is validated through comprehensive benchmarks and practical applications drawn from computational mechanics and scientific computing literature.

cs.LG↗

arXiv2024

Discovering governing equation in structural dynamics from acceleration-only measurements

Over the past few years, equation discovery has gained popularity in different fields of science and engineering. However, existing equation discovery algorithms rely on the availability of noisy measurements of the state variables (i.e., displacement {and velocity}). This is a major bottleneck in structural dynamics, where we often only have access to acceleration measurements. To that end, this paper introduces a novel equation discovery algorithm for discovering governing equations of dynamical systems from acceleration-only measurements. The proposed algorithm employs a library-based approach for equation discovery. To enable equation discovery from acceleration-only measurements, we propose a novel Approximate Bayesian Computation (ABC) model that prioritizes parsimonious models. The efficacy of the proposed algorithm is illustrated using {four} structural dynamics examples that include both linear and nonlinear dynamical systems. The case studies presented illustrate the possible application of the proposed approach for equation discovery of dynamical systems from acceleration-only measurements.

stat.ML↗

arXiv2024

Generative flow induced neural architecture search: Towards discovering optimal architecture in wavelet neural operator

We propose a generative flow-induced neural architecture search algorithm. The proposed approach devices simple feed-forward neural networks to learn stochastic policies to generate sequences of architecture hyperparameters such that the generated states are in proportion with the reward from the terminal state. We demonstrate the efficacy of the proposed search algorithm on the wavelet neural operator (WNO), where we learn a policy to generate a sequence of hyperparameters like wavelet basis and activation operators for wavelet integral blocks. While the trajectory of the generated wavelet basis and activation sequence is cast as flow, the policy is learned by minimizing the flow violation between each state in the trajectory and maximizing the reward from the terminal state. In the terminal state, we train WNO simultaneously to guide the search. We propose to use the exponent of the negative of the WNO loss on the validation dataset as the reward function. While the grid search-based neural architecture generation algorithms foresee every combination, the proposed framework generates the most probable sequence based on the positive reward from the terminal state, thereby reducing exploration time. Compared to reinforcement learning schemes, where complete episodic training is required to get the reward, the proposed algorithm generates the hyperparameter trajectory sequentially. Through four fluid mechanics-oriented problems, we illustrate that the learned policies can sample the best-performing architecture of the neural operator, thereby improving the performance of the vanilla wavelet neural operator.

cs.LG↗