arXiv subjects

Dibakar Roy Sarkar

Publications and source records attributed to Dibakar Roy Sarkar.

6 recordsLinked to original sources

arXiv2026

Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates time-integrated deep operator networks (TI-DeepONet) as differentiable PDE surrogate models within differentiable predictive control (DPC), a self-supervised learning framework for constrained neural control policies. The TI-DeepONet architecture learns temporal derivatives and couples them with numerical integrators, while the DPC algorithm uses automatic differentiation to compute policy gradients by backpropagating the expectations of the optimal control loss through the learned TI-DeepONet. This approach enables efficient offline optimization of neural policies without the need for online optimization or supervisory controllers. We empirically demonstrate the proposed method across diverse PDE systems, including the heat, the nonlinear inviscid Burgers', and the reaction-diffusion equations. The learned policies achieve target tracking, constraint satisfaction, and curvature minimization objectives, while generalizing across distributions of initial conditions and parameters. Moreover, we demonstrate four to five orders of magnitude acceleration at inference time compared to nonlinear model predictive control benchmarks. These results highlight the promise of neural operator learning for scalable model-based control of PDEs.

cs.CE↗

arXiv2026

CINOC: Cardinality-Invariant Neural Operator Policies for Scalable PDE Control

Controlling partial differential equations (PDEs) with learning-based policies remains fundamentally limited by fixed-dimensional representations: policies trained for a specific sensor, actuator, or agent configuration typically fail when the configuration changes. This limitation is particularly severe in multi-agent PDE control, where policies do not scale across population sizes without retraining. We address this challenge by introducing Cardinality Invariant Neural Operator Control (CINOC), reformulating PDE control as an operator learning problem that maps state fields to continuous control functions and trains them end-to-end through differentiable PDE solvers, yielding policies that naturally adapt to varying sensor and actuator configurations. Remarkably, CINOC policies trained on small swarms exhibit cardinality invariance, allowing for zero-shot transfer to significantly larger populations as well as robustness to partial agent failure. This scalability arises from agents sharing a common policy and coordinating through their physical environment, which produces an emergent self-normalization effect. To explain this phenomenon, we provide a theorem grounded in mean-field theory demonstrating that policy gradients computed from finite-agent systems converge to those of a continuous control limit. Empirically, we validate CINOC on tracking, stabilization, and density transport across linear, nonlinear, chaotic, and turbulent PDEs.

eess.SY↗

arXiv2026

Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injury

Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computationally expensive for clinical settings. Neural operators offer much faster inference. Their ability to integrate volumetric imaging with scalar metadata remains underexplored for biomechanical predictions. Objective: This study evaluates multimodal neural operator architectures for brain biomechanics. We test strategies fusing volumetric anatomical imaging, demographic features, and acquisition parameters to predict full-field brain displacement from MRE data. Methods: We framed TBI modeling as a multimodal operator learning problem. Two fusion strategies were tested. Field projection was applied for Fourier Neural Operator (FNO) architectures. Branch decomposition was used for Deep Operator Networks (DeepONet). Four models (FNO, Factorized FNO, Multi-Grid FNO, DeepONet) were evaluated on 249 in vivo MRE datasets across frequencies from 20 to 90 Hz. Results: DeepONet achieved the highest accuracy on real displacement fields (MSE = 0.0039, 90.0% accuracy) with the fastest inference (3.83 it/s) and fewest parameters (2.09M). MG-FNO performed best on imaginary fields (MSE = 0.0058, 88.3% accuracy) requiring the lowest GPU memory among FNO variants (7.12 GB). No single architecture dominated all criteria. This reveals distinct trade-offs between accuracy, spatial fidelity, and computational cost. Conclusion: Neural operators augmented with multimodal fusion can accurately predict full-field brain displacement from heterogeneous inputs. They offer inference times orders of magnitude faster than finite element solvers. This comparison provides guidance for selecting operator learning approaches in biomedical settings.

cs.LG↗

arXiv2026

Learning Hidden Physics and System Parameters with Deep Operator Networks

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks (PINNs) and sparse regression, are limited by their need for extensive retraining, sensitivity to noise, or inability to generalize across families of partial differential equations (PDEs). In this work, we introduce two complementary frameworks based on deep operator networks (DeepONet) to address these limitations. The first, termed the Deep Hidden Physics Operator (DHPO), extends hidden-physics modeling into the operator-learning paradigm, enabling the discovery of unknown PDE terms across diverse equation families by identifying the mapping of unknown physical operators. The second is a parameter identification framework that combines pretrained DeepONet with physics-informed inverse modeling to infer system parameters directly from sparse sensor data. We demonstrate the effectiveness of these approaches on benchmark problems, including the Reaction-Diffusion system, Burgers' equation, the 2D Heat equation, and 2D Helmholtz equation. Across all cases, the proposed methods achieve high accuracy, with relative solution errors on the order of O(10^-2) and parameter estimation errors on the order of O(10^-3), even under limited and noisy observations. By uniting operator learning with physics-informed modeling, this work offers a unified and data-efficient framework for physics discovery and parameter identification, paving the way for robust inverse modeling in complex dynamical systems.

cs.LG↗

arXiv2026

ARIA: Adaptive Retrieval Intelligence Assistant -- A Multimodal RAG Framework for Domain-Specific Engineering Education

Developing effective, domain-specific educational support systems is central to advancing AI in education. Although large language models (LLMs) demonstrate remarkable capabilities, they face significant limitations in specialized educational applications, including hallucinations, limited knowledge updates, and lack of domain expertise. Fine-tuning requires complete model retraining, creating substantial computational overhead, while general-purpose LLMs often provide inaccurate responses in specialized contexts due to reliance on generalized training data. To address this, we propose ARIA (Adaptive Retrieval Intelligence Assistant), a Retrieval-Augmented Generation (RAG) framework for creating intelligent teaching assistants across university-level courses. ARIA leverages a multimodal content extraction pipeline combining Docling for structured document analysis, Nougat for mathematical formula recognition, and GPT-4 Vision API for diagram interpretation, with the e5-large-v2 embedding model for high semantic performance and low latency. This enables accurate processing of complex educational materials while maintaining pedagogical consistency through engineered prompts and response controls. We evaluate ARIA using lecture material from Statics and Mechanics of Materials, a sophomore-level civil engineering course at Johns Hopkins University, benchmarking against ChatGPT-5. Results demonstrate 97.5% accuracy in domain-specific question filtering and superior pedagogical performance. ARIA correctly answered all 20 relevant course questions while rejecting 58 of 60 non-relevant queries, achieving 90.9% precision, 100% recall, and 4.89/5.0 average response quality. These findings demonstrate that ARIA's course-agnostic architecture represents a scalable framework for domain-specific educational AI deployment.

cs.IR↗

arXiv2025

Learning Generalizable Neural Operators for Inverse Problems

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}$, an inverse basis-to-basis neural operator framework that addresses this limitation. Our key innovation is to decouple function representation from the inverse map. We learn neural basis functions for the input and output spaces, then train inverse models that operate on the resulting coefficient space. This structure allows us to learn deterministic, invertible, and probabilistic models within a single framework, and to choose models based on the degree of ill-posedness. We evaluate our approach on six inverse PDE benchmarks, including two novel datasets, and compare against existing invertible neural operator baselines. We learn probabilistic models that capture uncertainty and input variability, and remain robust to measurement noise due to implicit denoising in the coefficient calculation. Our results show consistent re-simulation performance across varying levels of ill-posedness. By separating representation from inversion, our framework enables scalable surrogate models for inverse problems that generalize across instances, domains, and degrees of ill-posedness.

cs.LG↗