arXiv subjects

Subhankar Sarkar

Publications and source records attributed to Subhankar Sarkar.

4 recordsLinked to original sources

arXiv2026

Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator

Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications. Existing neural operators achieve high accuracy but leave deployment to embedded edge platforms unaddressed. Here we introduce VIRSO (Virtual Irregular Real-Time Sparse Operator), the first neural operator with a unique spatial-spectral architecture that explicitly addresses edge-deployment hardware. VIRSO learns a nonlinear mapping from sparse, geometrically disjoint boundary inputs to spatially continuous interior multiphysics fields on irregular unstructured meshes through a spectral-spatial decomposition explicitly aligned with hardware execution: a compute-bound graph spectral pathway and a memory-bandwidth-bound spatial-aggregation pathway, each independently characterized on datacenter and embedded accelerators. The design reduces the inference energy-delay product by 29$\times$ relative to the vanilla graph-operator baseline (206 J$\cdot$ms $\to$ 7.0 J$\cdot$ms on an NVIDIA H200) and enables 17.0 samples/s embedded inference on an NVIDIA Jetson Orin Nano within 7.06 W board-level power, without modification. A mesh-density-adaptive graph construction strategy (V-KNN) simultaneously improves accuracy and reduces graph edge count by 34%. Across three benchmarks with reconstruction ratios from 47:1 to 156:1, VIRSO achieves mean relative $L_2$ errors below 1% with fewer parameters than operator baselines and delivers an inference speedup of $\approx 10^4$ times over the high-fidelity reference solver. To our knowledge, this is the first demonstration of a single-digit-watt neural operator, establishing hardware co-design as a missing ingredient in operator-based inference and a tractable path to real-time deployment.

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arXiv2025

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and Geometry- Aware Spatio-Spectral Graph Neural Operator ($\pi$G-Sp$^2$GNO) for learning the solution operators of time-independent and time-dependent PDEs. The proposed approach first improves upon the recently developed Sp$^2$GNO by enabling geometry awareness and subsequently exploits the governing physics to learn the underlying solution operator in a simulation-free setup. While the spatio-spectral structure present in the proposed architecture allows multiscale learning, two separate strategies for enabling geometry awareness is introduced in this paper. For time dependent problems, we also introduce a novel hybrid physics informed loss function that combines higher-order time-marching scheme with upscaled theory inspired stochastic projection scheme. This allows accurate integration of the physics-information into the loss function. The performance of the proposed approach is illustrated on number of benchmark examples involving regular and complex domains, variation in geometry during inference, and time-independent and time-dependent problems. The results obtained illustrate the efficacy of the proposed approach as compared to the state-of-the-art physics-informed neural operator algorithms in the literature.

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arXiv2024

Virtual Sensing to Enable Real-Time Monitoring of Inaccessible Locations & Unmeasurable Parameters

Real-time monitoring of safety-critical interior states is an open problem across energy, environmental and industrial systems where direct instrumentation is infeasible. Approaches based on governing equations, discrete state vectors or fixed sensor locations cannot deliver mesh-independent, field-level reconstruction at arbitrary interior coordinates in real time. Here we introduce neural operator-based virtual sensing, a framework for recovering inaccessible interior fields from sparse boundary measurements, instantiated with MIMONet, a multi-input, multi-output neural operator that fuses heterogeneous inputs and decodes coupled fields through a shared latent representation. Across three engineering-grade evaluations of escalating complexity - confined recirculating flow, pressurized water reactor subchannels and compact power-system heat exchangers - MIMONet attains relative reconstruction error below 5% with sub-millisecond inference, with calibrated uncertainty and noise resilience. We validate the framework on three independent real-world datasets spanning electrochemical energy, atmospheric science and physical oceanography: current-density mapping in a hydrogen fuel cell, wind-speed profiling on meteorological towers, and North Atlantic ocean state from a global reanalysis. MIMONet improves on classical virtual-sensing baselines by 72-84%, including 84% for fuel-cell internal fields recovered from 10% sensor coverage and 83% for hub-height wind speed recovered from lower-level tower sensors. Most notably, it recovers sea-surface height, a field with no direct sensors, from its learned coupling to observed temperature and salinity at 4.1x lower error than the best classical predictor. These results establish operator-based virtual sensing as a practical route to real-time field observability in systems where the states that matter most cannot be measured directly.

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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.

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