arXiv subjects

Somdatta Goswami

Publications and source records attributed to Somdatta Goswami.

At least 19 recordsLinked to original sources

arXiv2026

Fracture-Bench: A Controlled Benchmark Suite for Machine Learning Surrogates in Phase-Field Fracture Mechanics

Machine-learning surrogates are increasingly proposed to replace phase-field fracture simulations in many-query tasks such as uncertainty quantification, inverse analysis and design. Little controlled evidence shows which architectures are reliable, for which fracture problems and how far beyond their training data. We introduce Fracture-Bench, an open benchmark of two phase-field datasets with fixed splits, common test metrics and a description of each dataset's physical regime. Dataset~1 contains 1,000 AT2 simulations of multiple cracks growing from a notched hole in a hyperelastic plate under random non-uniform biaxial boundary displacements (44 load steps, $128\times128$ grid). Dataset~2 contains 4,000 PF-CZM simulations of a pre-cracked plate with two inclusions, each ten times stiffer or more compliant than the matrix ($128\times256$ grid). We train a Fourier neural operator (FNO), DeepONet, Latent DeepONet, a UNet and a conditional diffusion model on identical splits and compare one test metric per dataset, training time, inference time and model size. On Dataset~1, FNO and Latent DeepONet attain mean test errors of order $10^{-6}$, about ten times lower than UNet and DeepONet. On Dataset~2, the diffusion model is most accurate, with about one sixth of the UNet error, but requires \SI{706}{s} per prediction versus \SI{6}{ms} for UNet. For all architectures, most of the error occurs in the final load steps, after crack localization. Dataset~2 contains initial cracks less than one grid cell apart that produce qualitatively different paths. Architecture rankings therefore depend on the task, and errors averaged over densely sampled inputs reveal little about near-bifurcation cases. Data, codes, splits, regime descriptors and generalization splits are public, with a protocol for adding under-represented regimes such as mixed-mode, three-dimensional and experimentally paired fracture.

physics.comp-ph↗

arXiv2026

Data-Efficient Time-Dependent PDE Surrogates: Graph Neural Simulators vs. Neural Operators

Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have gained popularity as surrogates for systems driven by partial differential equations (PDEs). However, their reliance on large datasets and limited ability to generalize in low-data regimes hinder their practical utility. We argue that these limitations arise from their global processing of data, which fails to exploit the local, discretized structure of physical systems. To address this, we propose Graph Neural Simulators (GNS) as a principled surrogate modeling paradigm for time-dependent PDEs. GNS leverages message-passing combined with numerical time-stepping schemes to learn PDE dynamics by modeling the instantaneous time derivatives. This design mimics traditional numerical solvers, enabling stable long-horizon rollouts and strong inductive biases that enhance generalization. We rigorously evaluate GNS on five canonical PDE systems: (1) 2D scalar Burgers', (2) 2D coupled Burgers', (3) 2D Allen-Cahn, (4) 2D nonlinear shallow water equations, and (5) 2D flow past a cylinder, comparing against SOTA NOs including DeepONet, FNO, and GINO. Results demonstrate that GNS is markedly more data-efficient, achieving less than 1% relative L2 error using only 3% of available trajectories, and exhibits dramatically reduced error accumulation over time (82.5% lower autoregressive error than FNO, 99.9% lower than DeepONet). To choose the training data, we introduce a PCA combined with KMeans trajectory selection strategy. These findings provide compelling evidence that GNS, with its graph-based locality and solver-inspired design, is the most suitable and scalable surrogate modeling framework for AI-driven scientific discovery.

cs.LG↗

arXiv2026

Learning Physics from an Imperfect Ancestor

Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed neural networks avoid dependence on labeled data, yet their optimization can be basin-fragile: when the governing residual admits multiple solutions, a PINN trained from scratch may converge to a physically incorrect state despite achieving a small residual. We show that these failure modes can be addressed jointly: an imperfect NO provides the structural prior needed to place a PINN in the correct solution basin, while the PDE residual refines the solution beyond the operator's accuracy. We introduce a three-stage framework that freezes the spatial basis of a physics-informed NO, extrapolates its solution branch to an out-of-distribution parameter using a polynomial continuation prior, and distills the resulting field into a fresh PINN. The NO need not be accurate at the target; it transfers solution-branch information, while PDE residual minimization in the PINN governs convergence. We evaluate the framework on three nonlinear PDEs: 1D viscous Burgers, 2D steady Allen-Cahn near a pitchfork bifurcation, and 2D steady lid-driven cavity flow. For Allen-Cahn, where the trivial solution satisfies the PDE residual exactly, a standard PINN collapses to the trivial zero branch, whereas distillation from the crude extrapolated operator recovers the non-trivial branch that matches the finite-difference reference. For the lid-driven cavity, extrapolating to a Reynolds number of Re = 3200 accelerates convergence to the correct physical state, achieving competitive accuracy using fewer parameters and optimization steps than recent literature baselines. These results establish a simple principle: an NO need not accurately predict the solution to be useful; it only needs to identify the correct basin from which PINN optimization can recover it.

cs.LG↗

arXiv2026

A Non-Overlapping Schwarz Hybrid Finite Element-Neural Operator Framework for Solid Mechanics on Irregular Domains

Finite element (FE) methods are the benchmark for solid mechanics simulations, yet their computational cost becomes prohibitive for problems with localised nonlinearities, fine-scale features, or long-time dynamic evolution. In our earlier FE-neural operator (FE-NO) hybrid framework [1], physics-informed deep operator networks were coupled with FE solvers through overlapping domain decomposition with Dirichlet-Dirichlet interface exchange, accelerating intensive subdomains while preserving FE fidelity elsewhere. Two limitations remained: the overlapping formulation required redundant interface computations that increased inner Schwarz iteration counts, and the convolutional feature extractor restricted the NO subdomain to structured grids, precluding irregular geometries. A non-overlapping Schwarz alternating method with Neumann-Dirichlet interface exchange replaces it, transmitting traction from the NO to FE rather than displacement. This eliminates the overlap layer and reduces inner Schwarz iterations while maintaining bounded error accumulation across all tested time horizons. For arbitrarily shaped subdomains, a Point-DeepONet operates on unstructured FE point clouds without interpolation, extending it to non-convex and irregular geometries. Strain and stress operators are derived analytically from the displacement operators via kinematic equations, rather than as independent networks, reducing trainable parameter sets while enforcing mechanical consistency by construction. The framework is validated on three benchmarks: static linear elasticity, quasi-static hyperelasticity, and elastodynamics with regular and irregular geometries. These results establish a non-overlapping FE-NO coupling paradigm that is geometry-flexible, parameter-efficient, and convergence-stable, providing a pathway for hybrid physics-based and operator-learning solvers in large-scale dynamic solid mechanics.

cs.CE↗

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

Can Coding Agents Reproduce Findings in Computational Materials Science?

Large language models are increasingly deployed as autonomous coding agents and have achieved remarkably strong performance on software engineering benchmarks. However, it is unclear whether such success transfers to computational scientific workflows, where tasks require not only strong coding ability, but also the ability to navigate complex, domain-specific procedures and to interpret results in the context of scientific claims. To address this question, we present AutoMat, a benchmark for evaluating LLM-based agents' ability to reproduce claims from computational materials science. AutoMat poses three interrelated challenges: recovering underspecified computational procedures, navigating specialized toolchains, and determining whether the resulting evidence supports a claim. By working closely with subject matter experts, we curate a set of claims from real materials science papers to test whether coding agents can recover and execute the end-to-end workflow needed to support (or undermine) such claims. We then evaluate multiple representative coding agent settings across several foundation models. Our results show that current LLM-based agents obtain low overall success rates on AutoMat, with the best-performing setting achieving a success rate of only 53%. Error analysis further reveals that agents perform worst when workflows must be reconstructed from paper text alone and that they fail primarily due to incomplete procedures, methodological deviations, and execution fragility. Taken together, these findings position AutoMat as both a benchmark for computational scientific reproducibility and a tool for diagnosing the current limitations of agentic systems in AI-for-science settings.

cs.CL↗

arXiv2026

ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching

Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings. Neural operator (NO) surrogates offer fast inference across parametric and functional inputs; however, most autoregressive NO frameworks remain vulnerable to compounding errors, and ensemble-averaged metrics provide limited guarantees for individual inference trajectories. In practice, error accumulation can become unacceptable beyond the training horizon, and existing methods lack mechanisms for online monitoring or correction. To address this gap, we propose ANCHOR (Adaptive Numerical Correction for High-fidelity Operator Rollouts), an online, instance-aware hybrid inference framework for stable long-horizon prediction of nonlinear, time-dependent PDEs. ANCHOR treats a pretrained NO as the primary inference engine and adaptively couples it with a classical numerical solver using a physics-informed, residual-based error estimator. Inspired by adaptive time-stepping in numerical analysis, ANCHOR monitors an exponential moving average (EMA) of the normalized PDE residual to detect accumulating error and trigger corrective solver interventions without requiring access to ground-truth solutions. We show that the EMA-based estimator correlates strongly with the true relative L2 error, enabling data-free, instance-aware error control during inference. Evaluations on six canonical PDEs: 1D and 2D Burgers', 2D Allen-Cahn, 2D Cahn-Hilliard, 2D Navier-Stokes, and 3D heat conduction, demonstrate that ANCHOR reliably bounds long-horizon error growth, stabilizes extrapolative rollouts, and significantly improves robustness over standalone neural operators, while remaining substantially more efficient than high-fidelity numerical solvers.

cs.LG↗

arXiv2026

Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation

Generating high-quality meshes for arbitrary geometries remains a fundamental bottleneck in computational engineering, often demanding heuristic tuning and semi-manual workflows. In this paper, we introduce Dmsh, a first fully automated reinforcement learning pipeline that unifies geometric decomposition and quadrilateral mesh generation within a single learning-based framework. Dmsh decomposes the problem through three coordinated agents handling topology simplification, geometric regularization, and mesh generation. The meshing process is formulated as a Markov Decision Process and solved using a parametric Soft Actor-Critic architecture with decoupled critics, enabling efficient exploration of a hybrid discrete-continuous action space. A curriculum learning strategy ensures scalability from simple domains to highly complex geometries, suppressing seed variance. By design, the recursive decomposition enables parallel meshing of subregions, yielding globally conforming all-quadrilateral meshes without post hoc correction. Across a wide range of benchmarks, Dmsh consistently outperforms existing methods in automation, robustness, and mesh quality, establishing a new paradigm for learning-based mesh generation.

math.NA↗

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

SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications

Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where repeated operator evaluations in dense networks incur substantial computational and energy costs. To address this challenge, we introduce the Separable Physics-informed Neuroscience-inspired Operator Network (SPINONet), a neuroscience-inspired framework that reduces redundant computation across repeated evaluations while remaining compatible with physics-informed training. SPINONet incorporates regression-friendly neuroscience-inspired spiking neurons through an architecture-aware design that enables sparse, event-driven computation, improving energy efficiency while preserving the continuous, coordinate-differentiable pathways required for computing spatio-temporal derivatives. We evaluate SPINONet on a range of partial differential equations representative of computational mechanics problems, with spatial, temporal, and parametric dependencies in both time-dependent and steady-state settings, and demonstrate predictive performance comparable to conventional physics-informed operator learning approaches despite the induced sparse communication. In addition, limited data supervision in a hybrid setup is shown to improve performance in challenging regimes where purely physics-informed training may converge to spurious solutions. Finally, we provide an analytical discussion linking architectural components and design choices of SPINONet to reductions in computational load and energy consumption.

physics.comp-ph↗

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

Towards Unified AI-Driven Fracture Mechanics: The Extended Deep Energy Method (XDEM)

Physics-Informed Neural Networks (PINNs) have recently emerged as powerful tools for solving partial differential equations (PDEs), with the Deep Energy Method (DEM) proving especially effective in fracture mechanics due to its energy-based formulation. Despite these advances, existing DEM approaches require dense collocation near cracks, face stability challenges, and typically treat discrete and continuous fracture models separately. To overcome these limitations, we introduce the Extended Deep Energy Method (XDEM), a unified deep learning framework that incorporates both displacement discontinuities and crack-tip asymptotics in the discrete setting, while flexibly coupling displacement and phase fields in the continuous setting. This integration enables accurate fracture predictions using uniformly distributed, relatively sparse collocation points. Validation across benchmark problems including stress intensity factor evaluation, straight and kinked crack growth, and complex crack initiation demonstrates that XDEM consistently outperforms standard DEM in accuracy and efficiency. By bridging discrete and phase-field models within a single framework, XDEM establishes a robust foundation for applying AI to fracture mechanics and opens new avenues for predictive modeling in engineering and materials science.

physics.comp-ph↗

arXiv2026

A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials

Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to oversmooth high-frequency gradients, while neural operators like DeepONet exhibit spectral bias and underpredict localized extremes. Diffusion models can recover fine-scale structure but often introduce low-frequency amplitude drift, degrading physical scaling. To address these limitations, we propose a hybrid surrogate framework, cDDPM-DeepONet, that decouples stress morphology from magnitude. A conditional denoising diffusion probabilistic model (cDDPM), built on a UNet backbone, generates normalized von Mises stress fields conditioned on geometry and loading. In parallel, a modified DeepONet predicts global scaling parameters (minimum and maximum stress), enabling reconstruction of full-resolution physical stress maps. This separation allows the diffusion model to focus on spatial structure while the operator network corrects global amplitude, mitigating spectral and scaling biases. We evaluate the framework on nonlinear hyperelastic datasets with single and multiple polygonal voids. The proposed model consistently outperforms UNet, DeepONet, and standalone cDDPM baselines by one to two orders of magnitude. Spectral analysis shows strong agreement with finite element solutions across all wavenumbers, preserving both global behavior and localized stress concentrations.

stat.ML↗

arXiv2026

TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation

Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms: fixed-horizon rollouts, which predict full spatiotemporal solutions while ignoring temporal causality, and autoregressive schemes, which accumulate errors through sequential prediction. We introduce TI-DeepONet, a framework that integrates neural operators with adaptive numerical time-stepping to preserve the Markovian structure of dynamical systems while mitigating long-term error growth. Our method shifts the learning objective from direct state prediction to approximating instantaneous time-derivative fields, which are then integrated using standard numerical solvers. This naturally enables continuous-time prediction and allows the use of higher-order integrators at inference than those used in training, improving both efficiency and accuracy. We further propose TI(L)-DeepONet, which incorporates learnable coefficients for intermediate stages in multi-stage integration, adapting to solution-specific dynamics and enhancing fidelity. Across six canonical PDEs featuring chaotic, dissipative, dispersive, and high-dimensional behavior, TI(L)-DeepONet maeginally outperforms TI-DeepONet, and both achieve major reductions in relative L2 extrapolation error: about 96.3% compared to autoregressive methods and 83.6% compared to fixed-horizon approaches. Notably, both models maintain stable predictions over temporal domains nearly twice the training interval. This work establishes a physics-aware operator learning framework that bridges neural approximation with numerical analysis principles, addressing a key gap in long-term forecasting of complex physical systems.

cs.LG↗

arXiv2026

Causality-Respecting Adaptive Refinement for PINNs: Enabling Precise Interface Evolution in Phase Field Modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. This study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen--Cahn equation, a widely used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an overshoot and relocate phenomenon in dynamic cases with complex morphologies, showcasing the method's adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR--causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

physics.comp-ph↗

arXiv2026

Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference

Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire trajectories in one pass, often fail to capture the causal dependencies and generalize poorly outside the training time horizon. Autoregressive (AR) approaches, evolving the system step by step, suffer from error accumulation, limiting long-term accuracy. These shortcomings limit the long-term accuracy and reliability of both strategies. To address these issues, we introduce the Physics-Informed Time-Integrated Deep Operator Network (PITI-DeepONet), a dual-output architecture trained via physics-informed or hybrid physics- and data-driven objectives to ensure stable, accurate long-term evolution well beyond the training horizon. Instead of forecasting future states, the network learns the time-derivative operator from the current state, integrating it using classical time-stepping schemes to advance the solution in time. Additionally, the framework can leverage residual monitoring during inference to estimate prediction quality and detect when the system transitions outside the training domain. Applied to benchmark problems, PITI-DeepONet demonstrates enhanced accuracy and stability over extended inference time horizons when compared to traditional methods. Mean relative $\mathcal{L}_2$ errors reduced by 84\% (versus FR) and 79\% (versus AR) for 1D heat equation; by 87\% (versus FR) and 98\% (versus AR) for the 1D Burgers equation; by 42\% (versus FR) and 89\% (versus AR) for the 2D Allen-Cahn equation; and by 58\% (vs. FR) and 61\% (vs. AR) for the 1D Kuramoto-Sivashinsky equation. By moving beyond classic FR and AR schemes, PITI-DeepONet paves the way for more reliable, long-term integration of complex, time-dependent PDEs.

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↗