Research in computational engineering increasingly treats modular composition and adaptive control as primary design principles, reflecting a shift from monolithic end-to-end learning toward interpretable, recomposable systems. Across PDE surrogate modeling, topology optimization, and multiphysics prediction, neural operators are being augmented with explicit physical constraints, symbolic compression, and hierarchical structure: HyCOP learns interpretable policies over modular PDE solvers with theoretical error decomposition; scale-autoregressive modeling factors fluid-flow generation coarse-to-fine to concentrate computation where uncertainty peaks; neural bundle maps decouple geometric complexity from physics to enable continuity across configurations; and Gaussian KANs are stabilized through partition-of-unity normalization and principled scale selection rather than hyperparameter search. Simultaneously, LLMs are entering the engineering workflow not as black-box surrogates but as adaptive orchestrators within structured pipelines: they serve as topology-optimization controllers responding to real-time solver diagnostics, as autonomous agents executing complete computational-mechanics workflows from perception through code-compliant reporting, and as solvers for combinatorial design problems where semantic alignment between LLM priors and structural objectives determines effectiveness. A third strand addresses inverse problems and discovery under data scarcity through physics-aware frameworks: bias-inheritance analysis reveals that symbolic compression cannot repair constitutive bias from poorly posed numerical inverses, shifting focus upstream; conditional flow matching recovers hidden granular-flow mechanics from sparse observations with uncertainty quantification; and weak-form PINNs with noise-robust objectives outperform direct residual minimization. Across these areas, evaluation has matured beyond accuracy metrics to emphasize reproducibility, constraint satisfaction, long-horizon stability, and explicit diagnostics, reflecting recognition that low loss or short-term prediction does not guarantee physical validity or engineering utility.
Cole Brennan
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We introduce HyCOP, a modular framework that learns parametric PDE solution operators by composing simple modules (advection, diffusion, learned closures, boundary handling) in a query-conditioned way. Rather than learning a monolithic map, HyCOP learns a policy over short programs - which module to apply and for how long - conditioned on regime features and state statistics. Modules may be numerical sub-solvers or learned components, enabling hybrid surrogates evaluated at arbitrary query times without autoregressive rollout. Across diverse PDE benchmarks, HyCOP produces interpretable programs, delivers order-of-magnitude OOD improvements over monolithic neural operators, and supports modular transfer through dictionary updates (e.g., boundary swaps, residual enrichment). Our theory characterizes expressivity and gives an error decomposition that separates composition error from module error and doubles as a process-level diagnostic.
Design Structure Matrix (DSM) modularization, the task of partitioning system elements into cohesive modules, is a fundamental combinatorial challenge in engineering design. Traditional methods treat modularization as a pure graph optimization, without access to the engineering context embedded in the system. Building on prior work on LLM-based combinatorial optimization for DSM sequencing, this paper extends the method to modularization across five cases and three backbone LLMs. Our method achieves near-reference quality within 30 iterations without requiring specialized optimization code. Counterintuitively, domain knowledge, beneficial in sequencing, consistently impairs performance on more complex DSMs. We attribute this to semantic misalignment between the LLM's functional priors and the purely structural optimization objective, and propose the semantic-alignment hypothesis as a testable condition governing knowledge effectiveness with LLMs. Ablation studies identify the most effective input representation, objective formulation, and solution pool design for practical deployment. These findings offer practical guidance for deploying LLMs in engineering design optimization.
Technology mapping is a critical yet challenging stage in logic synthesis. While Large Language Models (LLMs) have been applied to generate optimization scripts, their potential for core algorithm enhancement remains untapped. We introduce MappingEvolve, an open-source framework that pioneers the use of LLMs to directly evolve technology mapping code. Our method abstracts the mapping process into distinct optimization operators and employs a hierarchical agent-based architecture, comprising a Planner, Evolver, and Evaluator, to guide the evolutionary search. This structured approach enables strategic and effective code modifications. Experiments show our method significantly outperforms direct evolution and strong baselines, achieving 10.04\% area reduction versus ABC and 7.93\% versus mockturtle, with 46.6\%--96.0\% $S_{overall}$ improvement on EPFL benchmarks, while explicitly navigating the area--delay trade-off. Our code and data are available at https://github.com/Flians/MappingEvolve.
Gaussian basis functions provide an efficient and flexible alternative to spline activations in KANs. In this work, we introduce the partition-of-unity Gaussian KAN (PU-GKAN), a Shepard-type normalized Gaussian KAN in which the Gaussian basis values on each edge are divided by their local sum over fixed centers. This produces a partition-of-unity feature map with trainable coefficients, while preserving the standard edge-based KAN structure. The normalized construction gives exact constant reproduction at the edge level and admits an explicit finite-feature kernel interpretation. We formulate both the standard Gaussian KAN (GKAN) and PU-GKAN from a finite-feature and additive-kernel viewpoint, making the induced layer kernels and empirical feature matrices explicit. Using the first-layer feature matrix as the reference object, we adopt a practical scale-selection interval for \(ε\), with the lower endpoint determined by adjacent-center overlap and the upper endpoint determined by a conservative conditioning threshold. Numerical experiments show that PU-GKAN reduces sensitivity to \(ε\), improves validation accuracy for most smooth and moderately non-smooth targets, and gives more stable training behavior. The benefit persists across sample-size and center-number sweeps, higher-dimensional architectures, Matérn RBF bases, and physics-informed examples involving Helmholtz and wave equations. These results indicate that Shepard-type partition-of-unity normalization is a simple and effective stabilization mechanism for RBF-based KANs.
The Gaussian scale parameter \(ε\) is central to the behavior of Gaussian Kolmogorov--Arnold Networks (KANs), yet its role in deep edge-based architectures has not been studied systematically. In this paper, we investigate how \(ε\) affects Gaussian KANs through first-layer feature geometry, conditioning, and approximation behavior. Our central observation is that scale selection is governed primarily by the first layer, since it is the only layer constructed directly on the input domain and any loss of distinguishability introduced there cannot be recovered by later layers. From this viewpoint, we analyze the first-layer feature matrix and identify a practical operating interval, \[ ε\in \left[\frac{1}{G-1},\frac{2}{G-1}\right], \] where \(G\) denotes the number of Gaussian centers. For the standard shared-center Gaussian KAN used in current practice, we interpret this interval not as a universal optimality result, but as a stable and effective design rule, and validate it through brute-force sweeps over \(ε\) across function-approximation problems with different collocation densities, grid resolutions, network architectures, and input dimensions, as well as a physics-informed Helmholtz problem. We further show that this range is useful for fixed-scale selection, variable-scale constructions, constrained training of \(ε\), and efficient scale search using early training MSE. Finally, using a matched Chebyshev reference, we show that a properly scaled Gaussian KAN can already be competitive in accuracy relative to another standard KAN basis. In this way, the paper positions scale selection as a practical design principle for Gaussian KANs rather than as an ad hoc hyperparameter choice.
Financial institutions face tension between maximizing data utility and mitigating the re-identification risks inherent in traditional anonymization methods. This paper explores Differentially Private (DP) synthetic data as a robust "Privacy by Design" framework to resolve this conflict, ensuring output privacy while satisfying stringent regulatory obligations. We examine two distinct generative paradigms: Direct Tabular Synthesis, which reconstructs high-fidelity joint distributions from raw data, and DP-Seeded Agent-Based Modeling (ABM), which uses DP-protected aggregates to parameterize complex, stateful simulations. While tabular synthesis excels at reflecting static historical correlations for QA testing and business analytics, the DP-Seeded ABM offers a forward-looking "counterfactual laboratory" capable of modeling dynamic market behaviors and black swan events. By decoupling individual identities from data utility, these methodologies eliminate traditional data-clearing bottlenecks, enabling seamless cross-institutional research and compliant decision-making in an evolving regulatory landscape.
Brain digital twins aim to provide faithful, individualized computational representations of brains as dynamical systems, enabling mechanistic understanding and supporting prediction of clinical interventions. Yet current approaches remain fragmented across data pipelines, model classes, temporal scales, and computing platforms, which prevents the preservation of execution semantics across the end-toend workflow. This survey introduces physically constrained executability as a unifying perspective for comparing approaches at the level of execution: whether an execution state is persistent, which events are permitted to update it (simulation, measurement, actuation), and how strongly execution is temporally and causally coupled to neurobiological dynamics. Building on modeling and simulation theory, I propose a taxonomy of execution regimes ranging from isolated offline models to coordinated co-simulation, to continuously executing digital twins sustained by online data assimilation, and ultimately to neuro-neuromorphic physical systems in which biological and computational dynamics are co-executed under shared physical constraints. The executability concept clarifies why accuracy alone is insufficient, and motivates an agenda centered on semantic interoperability, hybrid-time correctness, evaluation protocols, scalable reproducible workflows, and safe closed-loop validation. This survey adopts a systems and runtime-oriented perspective, enabling comparison of heterogeneous approaches based on their execution semantics rather than on model form or application domain alone.
Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long rollouts. Generative models avoid compounding error by sampling states independently, but diffusion and flow-matching methods, while accurate, are limited by the cost of many evaluations over the entire mesh. We introduce scale-autoregressive modeling (SAR) for sampling flows on unstructured meshes hierarchically from coarse to fine: it first generates a low-resolution field, then refines it by progressively sampling higher resolutions conditioned on coarser predictions. This coarse-to-fine factorization improves efficiency by concentrating computation at coarser scales, where uncertainty is greatest, while requiring fewer steps at finer scales. Across unsteady-flow benchmarks of varying complexity, SAR attains substantially lower distributional error and higher per-sample accuracy than state-of-the-art diffusion models based on multi-scale GNNs, while matching or surpassing a flow-matching Transolver (a linear-time transformer) yet running 2-7x faster than this depending on the task. Overall, SAR provides a practical tool for fast and accurate estimation of statistical flow quantities (e.g., turbulent kinetic energy and two-point correlations) in real-world settings.
We present a solver-agnostic framework in which coordinated large language model (LLM) agents autonomously execute the complete computational mechanics workflow, from perceptual data of an engineering component through geometry extraction, material inference, discretisation, solver execution, uncertainty quantification, and code-compliant assessment, to an engineering report with actionable recommendations. Agents are formalised as conditioned operators on a shared context space with quality gates that introduce conditional iteration between pipeline layers. We introduce a mathematical framework for extracting engineering information from perceptual data under uncertainty using interval bounds, probability densities, and fuzzy membership functions, and introduce task-dependent conservatism to resolve the ambiguity of what `conservative' means when different limit states are governed by opposing parameter trends. The framework is demonstrated through a finite element analysis pipeline applied to a photograph of a steel L-bracket, producing a 171,504-node tetrahedral mesh, seven analyses across three boundary condition hypotheses, and a code-compliant assessment revealing structural failure with a quantified redesign. All results are presented as generated in the first autonomous iteration without manual correction, reinforcing that a professional engineer must review and sign off on any such analysis.
The field of cybersecurity is confronted with two interrelated challenges: a worldwide deficit of qualified practitioners and ongoing human-factor weaknesses that account for the bulk of security incidents. To tackle these issues, we present SentinelSphere, a platform driven by artificial intelligence that unifies machine learning-based threat identification with security training powered by a Large Language Model (LLM). The detection module uses an Enhanced Deep Neural Network (DNN) trained on the CIC-IDS2017 and CIC-DDoS2019 benchmark datasets, enriched with novel HTTP-layer feature engineering that captures application level attack signatures. For the educational component, we deploy a quantised variant of Phi-4 model (Q4_K_M), fine-tuned for the cybersecurity domain, enabling deployment on commodity hardware requiring only 16 GB of RAM without dedicated GPU resources. Experimental results show that the Enhanced DNN attains high detection accuracy while substantially lowering false positives relative to baseline models, and maintains strong recall across critical attack categories such as DDoS, brute force, and web-based exploits. Validation workshops involving industry professionals and university students confirmed that the Traffic Light visualisation system and conversational AI assistant are both intuitive and effective for users without technical backgrounds. SentinelSphere illustrates that coupling intelligent threat detection with adaptive, LLM-driven security education can meaningfully address both technical and human-factor cybersecurity vulnerabilities within a single, cohesive framework.
Conventional career guidance platforms rely on static, text-driven interfaces that struggle to engage users or deliver personalised, evidence-based insights. Although Computer-Assisted Career Guidance Systems have evolved since the 1960s, they remain limited in interactivity and pay little attention to the narrative dimensions of career development. We introduce XR-CareerAssist, a platform that unifies Extended Reality (XR) with several Artificial Intelligence (AI) modules to deliver immersive, multilingual career guidance. The system integrates Automatic Speech Recognition for voice-driven interaction, Neural Machine Translation across English, Greek, French, and Italian, a Langchain-based conversational Training Assistant for personalised dialogue, a BLIP-based Vision-Language model for career visualisations, and AWS Polly Text-to-Speech delivered through an interactive 3D avatar. Career trajectories are rendered as dynamic Sankey diagrams derived from a repository of more than 100,000 anonymised professional profiles. The application was built in Unity for Meta Quest 3, with backend services hosted on AWS. A pilot evaluation at the University of Exeter with 23 participants returned 95.6% speech recognition accuracy, 78.3% overall user satisfaction, and 91.3% favourable ratings for system responsiveness, with feedback informing subsequent improvements to motion comfort, audio clarity, and text legibility. XR-CareerAssist demonstrates how the fusion of XR and AI can produce more engaging, accessible, and effective career development tools, with the integration of five AI modules within a single immersive environment yielding a multimodal interaction experience that distinguishes it from existing career guidance platforms.
Granular flows govern many natural and industrial processes, yet their interior kinematics and mechanics remain largely unobservable, as experiments access only boundaries or free surfaces. Conventional numerical simulations are computationally expensive for fast inverse reconstruction, and deterministic models tend to collapse to over-smoothed mean predictions in ill-posed settings. This study, to the best of the authors' knowledge, presents the first conditional flow matching (CFM) framework for granular-flow reconstruction from sparse boundary observations. Trained on high-fidelity particle-resolved discrete element simulations, the generative model is guided at inference by a differentiable forward operator with a sparsity-aware gradient guidance mechanism, which enforces measurement consistency without hyperparameter tuning and prevents unphysical velocity predictions in non-material regions. A physics decoder maps the reconstructed velocity fields to stress states and energy fluctuation quantities, including mean stress, deviatoric stress, and granular temperature. The framework accurately recovers interior flow fields from full observation to only 16% of the informative window, and it remains effective under strongly diluted spatial resolution with only 11% of data. It also outperforms a deterministic CNN baseline in the most ill-posed reconstruction regime and provides spatially resolved uncertainty estimates through ensemble generation. These results demonstrate that conditional generative modeling offers a practical route for non-invasive inference of hidden bulk mechanics in granular media, with broader applicability for inverse problems in particulate and multiphase systems.
This work introduces a modular platform that brings together six AI services, automatic speech recognition via OpenAI Whisper, multilingual translation through Meta NLLB, speech synthesis using AWS Polly, emotion classification with RoBERTa, dialogue summarisation via flan t5 base samsum, and International Sign (IS) rendering through Google MediaPipe. A corpus of IS gesture recordings was processed to derive hand landmark coordinates, which were subsequently mapped onto three dimensional avatar animations inside a virtual reality (VR) environment. Validation comprised technical benchmarking of each AI component, including comparative assessments of speech synthesis providers and multilingual translation models (NLLB 200 and EuroLLM 1.7B variants). Technical evaluations confirmed the suitability of the platform for real time XR deployment. Speech synthesis benchmarking established that AWS Polly delivers the lowest latency at a competitive price point. The EuroLLM 1.7B Instruct variant attained a higher BLEU score, surpassing NLLB. These findings establish the viability of orchestrating cross modal AI services within XR settings for accessible, multilingual language instruction. The modular design permits independent scaling and adaptation to varied educational contexts, providing a foundation for equitable learning solutions aligned with European Union digital accessibility goals.
Video conferencing has become central to professional collaboration, yet most platforms offer limited support for deaf, hard-of-hearing, and multilingual users. The World Health Organisation estimates that over 430 million people worldwide require rehabilitation for disabling hearing loss, a figure projected to exceed 700 million by 2050. Conventional accessibility measures remain constrained by high costs, limited availability, and logistical barriers, while Extended Reality (XR) technologies open new possibilities for immersive and inclusive communication. This paper presents INTERACT (Inclusive Networking for Translation and Embodied Real-Time Augmented Communication Tool), an AI-driven XR platform that integrates real-time speech-to-text conversion, International Sign Language (ISL) rendering through 3D avatars, multilingual translation, and emotion recognition within an immersive virtual environment. Built on the CORTEX2 framework and deployed on Meta Quest 3 headsets, INTERACT combines Whisper for speech recognition, NLLB for multilingual translation, RoBERTa for emotion classification, and Google MediaPipe for gesture extraction. Pilot evaluations were conducted in two phases, first with technical experts from academia and industry, and subsequently with members of the deaf community. The trials reported 92% user satisfaction, transcription accuracy above 85%, and 90% emotion-detection precision, with a mean overall experience rating of 4.6 out of 5.0 and 90% of participants willing to take part in further testing. The results highlight strong potential for advancing accessibility across educational, cultural, and professional settings. An extended version of this work, including full pilot data and implementation details, has been published as an Open Research Europe article [Tantaroudas et al., 2026a].
Macroscopic unmanned aerial vehicle (UAV) traffic organization in three-dimensional airspace faces significant challenges from static wind fields and complex obstacles. A critical difficulty lies in simultaneously capturing the strong anisotropy induced by wind while strictly preserving transport consistency and boundary semantics, which are often compromised in standard physics-informed learning approaches. To resolve this, we propose a constraint-preserving hybrid solver that integrates a physics-informed neural network for the anisotropic Eikonal value problem with a conservative finite-volume method for steady density transport. These components are coupled through an outer Picard iteration with under-relaxation, where the target condition is hard-encoded and strictly conservative no-flux boundaries are enforced during the transport step. We evaluate the framework on reproducible homing and point-to-point scenarios, effectively capturing value slices, induced-motion patterns, and steady density structures such as bands and bottlenecks. Ultimately, our perspective emphasizes the value of a reproducible computational framework supported by transparent empirical diagnostics to enable the traceable assessment of macroscopic traffic phenomena.
We investigate the data-driven discovery of constitutive closures in nonlinear reaction-diffusion systems with known governing PDE structures. Our objective is to robustly recover diffusion and reaction laws from spatiotemporal observations while avoiding the common pitfall where low residuals or short-horizon predictions are conflated with physical recovery. We propose a three-stage neural-symbolic framework: (1) learning numerical surrogates under physical constraints using a noise-robust weak-form-driven objective; (2) compressing these surrogates into restricted interpretable symbolic families (e.g., polynomial, rational, and saturation forms); and (3) validating the symbolic closures through explicit forward re-simulation on unseen initial conditions. Extensive numerical experiments reveal two distinct regimes. Under matched-library settings, weak polynomial baselines behave as correctly specified reference estimators, showing that neural surrogates do not uniformly outperform classical bases. Conversely, under function-class mismatch, neural surrogates provide necessary flexibility and can be compressed into compact symbolic laws with minimal rollout degradation. However, we identify a critical "bias inheritance" mechanism where symbolic compression does not automatically repair constitutive bias. Across various observation regimes, the true error of the symbolic closure closely tracks that of the neural surrogate, yielding a bias inheritance ratio near one. These findings demonstrate that the primary bottleneck in neural-symbolic modeling lies in the initial numerical inverse problem rather than the subsequent symbolic compression. We underscore that constitutive claims must be rigorously supported by forward validation rather than residual minimization alone.
Biomedical knowledge resources often either preserve evidence as unstructured text or compress it into flat triples that omit study design, provenance, and quantitative support. Here we present EvidenceNet, a framework and dataset for building disease-specific knowledge graphs from full-text biomedical literature. EvidenceNet uses a large language model (LLM)-assisted pipeline to extract experimentally grounded findings as structured evidence nodes, normalize biomedical entities, score evidence quality, and connect evidence records through typed semantic relations. We release two resources: EvidenceNet-HCC with 7,872 evidence records, 10,328 graph nodes, and 49,756 edges, and EvidenceNet-CRC with 6,622 records, 8,795 nodes, and 39,361 edges. Technical validation shows high component fidelity, including 98.3% field-level extraction accuracy, 100.0% high-confidence entity-link accuracy, 87.5% fusion integrity, and 90.0% semantic relation-type accuracy. In downstream evaluation, EvidenceNet improves internal and external retrieval-augmented question answering and retains structural signal for future link prediction and target prioritization. These results establish EvidenceNet as a disease-specific resource for evidence-aware biomedical reasoning and hypothesis generation.
We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. Objectivity, material symmetry, and normalization are embedded directly into the architecture through invariant-based representations and zero-anchored formulations. We demonstrate the performance of the proposed framework on synthetic and experimental datasets, including purely thermal problems and fully coupled thermomechanical responses of soft tissues and filled rubbers. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via https://doi.org/10.5281/zenodo.19248596.
Biomedical knowledge resources often either preserve evidence as unstructured text or compress it into flat triples that omit study design, provenance, and quantitative support. Here we present EvidenceNet, a framework and dataset for building disease-specific knowledge graphs from full-text biomedical literature. EvidenceNet uses a large language model (LLM)-assisted pipeline to extract experimentally grounded findings as structured evidence nodes, normalize biomedical entities, score evidence quality, and connect evidence records through typed semantic relations. We release two resources: EvidenceNet-HCC with 7,872 evidence records, 10,328 graph nodes, and 49,756 edges, and EvidenceNet-CRC with 6,622 records, 8,795 nodes, and 39,361 edges. Technical validation shows high component fidelity, including 98.3% field-level extraction accuracy, 100.0% high-confidence entity-link accuracy, 87.5% fusion integrity, and 90.0% semantic relation-type accuracy. In downstream evaluation, EvidenceNet improves internal and external retrieval-augmented question answering and retains structural signal for future link prediction and target prioritization. These results establish EvidenceNet as a disease-specific resource for evidence-aware biomedical reasoning and hypothesis generation.
We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. Objectivity, material symmetry, and normalization are embedded directly into the architecture through invariant-based representations and zero-anchored formulations. We demonstrate the performance of the proposed framework on synthetic and experimental datasets, including purely thermal problems and fully coupled thermomechanical responses of soft tissues and filled rubbers. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via https://doi.org/10.5281/zenodo.19248596.
In a previous work (Elaarabi et al., 2025b), the Sequence Encoder for online dynamical system identification (Elaarabi et al., 2025a) and its combination with PINN (PINN-SE) were introduced and tested on both synthetic and real data case scenarios. The sequence encoder is able to effectively encode time series into feature vectors, which the PINN then uses to map to dynamical behavior, predicting system response under changes in parameters, ICs and BCs. Previously (Elaarabi et al., 2025b), the tests on real data were limited to simple 1D problems and only 1D time series inputs of the Sequence Encoder. In this work, the possibility of applying PINN-SE to a more realistic case is investigated: heating and early cooling of the thermo-stamping process, which is a critical stage in the forming process of continuous fiber reinforced composite materials with thermoplastic polymer. The possibility of extending the PINN-SE inputs to multimodal data, such as sequences of temporal 2D images and to scenarios involving variable geometries, is also explored. The results show that combining multiple encoders with the previously proposed method (Elaarabi et al., 2025b) is feasible, we also show that training the model on synthetic data generated based on experimental data can help the model to generalize well for real experimental data, unseen during the training phase.
We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time, state-conditioned parameter decisions. At every $k$-th iteration, the LLM receives a structured observation$-$current compliance, grayness index, stagnation counter, checkerboard measure, volume fraction, and budget consumption$-$and outputs numerical values for the penalization exponent $p$, projection sharpness $β$, filter radius $r_{\min}$, and move limit $δ$ via a Direct Numeric Control interface. A hard grayness gate prevents premature binarization, and a meta-optimization loop uses a second LLM pass to tune the agent's call frequency and gate threshold across runs. We benchmark the agent against four baselines$-$fixed (no-continuation), standard three-field continuation, an expert heuristic, and a schedule-only ablation$-$on three 2-D problems (cantilever, MBB beam, L-bracket) at $120\!\times\!60$ resolution and two 3-D problems (cantilever, MBB beam) at $40\!\times\!20\!\times\!10$ resolution, all run for 300 iterations. A standardized 40-iteration sharpening tail is applied from the best valid snapshot so that compliance differences reflect only the exploration phase. The LLM agent achieves the lowest final compliance on every benchmark: $-5.7\%$ to $-18.1\%$ relative to the fixed baseline, with all solutions fully binary. The schedule-only ablation underperforms the fixed baseline on two of three problems, confirming that the LLM's real-time intervention$-$not the schedule geometry$-$drives the gain. Code and reproduction scripts will be released upon publication.
Geotechnical site characterisation relies on sparse, heterogeneous borehole data where uncertainty quantification and model interpretability are as critical as predictive accuracy for reliable engineering decisions. This paper presents an exploratory investigation into the use of TabPFN, a transformer-based tabular foundation model using in-context learning, and its extension library tabpfn-extensions for two geotechnical inference tasks: (1) soil-type classification using N-value and shear-wave velocity data from a synthetic geotechnical dataset, and (2) iterative imputation of five missing mechanical parameters ($s_\mathrm{u}$, $E_{\mathrm{u}}$, ${σ'}_\mathrm{p}$, $C_\mathrm{c}$, $C_\mathrm{v}$) in benchmark problem BM/AirportSoilProperties/2/2025. We apply cosine-similarity analysis to TabPFN-derived embeddings, visualise full posterior distributions from an iterative inference procedure, and compute SHAP-based feature importance, all without model retraining. Learned embeddings clearly separate Clay and Sand samples without explicit soil-type supervision; iterative imputation improves predictions for four of five target parameters, with posterior widths that reflect physically reasonable parameter-specific uncertainty; and SHAP analysis reveals the inter-parameter dependency structure, recovering established geotechnical relationships including the Skempton compression index correlation and the inverse dependence of preconsolidation pressure on water content. These results suggest the potential of foundation-model-based tools to support interpretable, uncertainty-aware parameter inference in data-scarce geotechnical practice.
Engineering system design -- whether mechatronic, control, or embedded -- often proceeds in an ad hoc manner, with requirements left implicit and traceability from intent to parameters largely absent. Existing specification-driven and systematic design methods mostly target software, and AI-assisted tools tend to enter the workflow at solution generation rather than at problem framing. Human--AI collaboration in the design of physical systems remains underexplored. This paper presents Design-OS, a lightweight, specification-driven workflow for engineering system design organized in five stages: concept definition, literature survey, conceptual design, requirements definition, and design definition. Specifications serve as the shared contract between human designers and AI agents; each stage produces structured artifacts that maintain traceability and support agent-augmented execution. We position Design-OS relative to requirements-driven design, systematic design frameworks, and AI-assisted design pipelines, and demonstrate it on a control systems design case using two rotary inverted pendulum platforms -- an open-source SimpleFOC reaction wheel and a commercial Quanser Furuta pendulum -- showing how the same specification-driven workflow accommodates fundamentally different implementations. A blank template and the full design-case artifacts are shared in a public repository to support reproducibility and reuse. The workflow makes the design process visible and auditable, and extends specification-driven orchestration of AI from software to physical engineering system design.
Real-world financial decision-making is a challenging problem that requires reasoning over heterogeneous signals, including company fundamentals derived from regulatory filings and trading signals computed from price dynamics. Recently, with the advancement of Large Language Models (LLMs), financial analysts have begun to use them for financial decision-making tasks. However, existing financial question answering benchmarks for testing these models primarily focus on company balance sheet data and rarely evaluate reasoning over how company stocks trade in the market or their interactions with fundamentals. To take advantage of the strengths of both approaches, we introduce FinTradeBench, a benchmark for evaluating financial reasoning that integrates company fundamentals and trading signals. FinTradeBench contains 1,400 questions grounded in NASDAQ-100 companies over a ten-year historical window. The benchmark is organized into three reasoning categories: fundamentals-focused, trading-signal-focused, and hybrid questions requiring cross-signal reasoning. To ensure reliability at scale, we adopt a calibration-then-scaling framework that combines expert seed questions, multi-model response generation, intra-model self-filtering, numerical auditing, and human-LLM judge alignment. We evaluate 14 LLMs under zero-shot prompting and retrieval-augmented settings and witness a clear performance gap. Retrieval substantially improves reasoning over textual fundamentals, but provides limited benefit for trading-signal reasoning. These findings highlight fundamental challenges in the numerical and time-series reasoning for current LLMs and motivate future research in financial intelligence.
Efficient and accurate prediction of Multiphysics evolution across diverse cell geometries is fundamental to the design, management and safety of lithium-ion batteries. However, existing computational frameworks struggle to capture the coupled electrochemical, thermal, and mechanical dynamics across diverse cell geometries and varying operating conditions. Here, we present a Neural Bundle Map (NBM), a mathematically rigorous framework that reformulates multiphysics evolution as a bundle map over a geometric base manifold. This approach enables the complete decoupling of geometric complexity from underlying physical laws, ensuring strong operator continuity across varying domains. Our framework achieves high-fidelity spatiotemporal predictions with a normalized mean absolute error of less than 1% across varying configurations, while maintaining stability during long-horizon forecasting far beyond the training window and reducing computational costs by two orders of magnitude compared with conventional solvers. Leveraging this capability, we rapidly explored a vast configurational space to identify an optimal battery design that yields a 38% increase in energy density while adhering to thermal safety constraints. Furthermore, the NBM demonstrates remarkable scalability to multi-cell systems through few-shot transfer learning, providing a foundational paradigm for the intelligent design and real-time monitoring of complex energy storage infrastructures.
Although multigrid is asymptotically optimal for solving many important partial differential equations, its efficiency relies heavily on the careful selection of the individual algorithmic components. In contrast to recent approaches that can optimize certain multigrid components using deep learning techniques, we adopt a complementary strategy, employing evolutionary algorithms to construct efficient multigrid cycles from proven algorithmic building blocks. Here, we will present its application to generate efficient algebraic multigrid methods with so-called \emph{flexible cycling}, that is, level-specific smoothing sequences and non-recursive cycling patterns. The search space with such non-standard cycles is intractable to navigate manually, and is generated using genetic programming (GP) guided by context-free grammars. Numerical experiments with the linear algebra library, \emph{hypre}, demonstrate the potential of these non-standard GP cycles to improve multigrid performance both as a solver and a preconditioner.
We review thirteen generative systems and five supporting datasets for quantum circuit and quantum code generation, identified through a structured scoping review of Hugging Face, arXiv, and provenance tracing (January-February 2026). We organize the field along two axes: artifact type (Qiskit code, OpenQASM programs, circuit graphs); crossed with training regime (supervised fine-tuning, verifier-in-the-loop RL, diffusion/graph generation, agentic optimization); and systematically apply a three-layer evaluation framework covering syntactic validity, semantic correctness, and hardware executability. The central finding is that while all reviewed systems address syntax and most address semantics to some degree, none reports end-to-end evaluation on quantum hardware (Layer 3b), leaving a significant gap between generated circuits and practical deployment. Scope note: quantum code refers throughout to quantum program artifacts (QASM, Qiskit); we do not cover generation of quantum error-correcting codes (QEC).
Mechanistic modeling provides a biophysically grounded framework for studying the spread of pathological tau protein in tauopathies like Alzheimer's disease. Existing approaches typically model tau propagation as a diffusive process on the brain's structural connectome, reproducing macroscopic patterns but neglecting microscale cellular transport and reaction mechanisms. The Network Transport Model (NTM) was introduced to fill this gap, explaining how region-level progression of tau emerges from microscale biophysical processes. However, the NTM faces a common challenge for complex models defined by large systems of partial differential equations: the inability to perform parameter inference and mechanistic discovery due to high computational burden and slow model simulations. To overcome this barrier, we propose Tau-BNO, a Brain Neural Operator surrogate framework for rapidly approximating NTM dynamics that captures both intra-regional reaction kinetics and inter-regional network transport. Tau-BNO combines a function operator that encodes kinetic parameters with a query operator that preserves initial state information, while approximating anisotropic transport through a spectral kernel that retains directionality. Empirical evaluations demonstrate high predictive accuracy ($R^2\approx$ 0.98) across diverse biophysical regimes and an 89\% performance improvement over state-of-the-art sequence models like Transformers and Mamba, which lack inherent structural priors. By reducing simulation time from hours to seconds, we show that the surrogate model is capable of producing new insights and generating new hypotheses. This framework is readily extensible to a broader class of connectome-based biophysical models, showcasing the transformative value of deep learning surrogates to accelerate analysis of large-scale, computationally intensive dynamical systems.
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times, Physics-Informed Extreme Learning Machines (PIELMs) offer a rapid, closed-form linear solution but are fundamentally limited by physics-agnostic, random initialization. We introduce the Gaussian Mixture Model Adaptive PIELM (GMM-PIELM), a probabilistic framework that learns a probability density function representing the ``location of physics'' for adaptively sampling kernels of PIELMs. By employing a weighted Expectation-Maximization (EM) algorithm, GMM-PIELM autonomously concentrates radial basis function centers in regions of high numerical error, such as shock fronts and boundary layers. This approach dynamically improves the conditioning of the hidden layer without the expensive gradient-based optimization(of PINNs) or Bayesian search. We evaluate our methodology on 1D singularly perturbed convection-diffusion equations with diffusion coefficients $ν=10^{-4}$. Our method achieves $L_2$ errors up to $7$ orders of magnitude lower than baseline RBF-PIELMs, successfully resolving exponentially thin boundary layers while retaining the orders-of-magnitude speed advantage of the ELM architecture.