build computational models

This work addresses the heavy reliance on manual effort in chemical process modeling, which is prone to catastrophic failure due to single-point errors. To overcome this limitation, the authors propose a role-adaptive collaborative framework that decomposes the modeling task into seven specialized sub-roles. By integrating natural language, process flow diagrams, and domain knowledge, the framework generates structured models through typed intermediate representations and a deterministic engineering gating mechanism, enabling automated optimization. Leveraging a fine-tuned Qwen large language model for three critical roles—visual, topological, and specification—the system is integrated with a LangGraph workflow and the IDAES/Pyomo solvers. Evaluated on 82 held-out cases from the OpenIDAES-450 dataset, the approach achieves a 91.5% model construction success rate, with F1 scores of 0.815, 0.791, and 0.782 for unit operations, material streams, and connections, respectively.

Existing mathematical modeling lacks a rigorous, unambiguous ontological foundation, hindering a unified characterization of the mapping between models and real-world phenomena. This paper introduces, for the first time, an axiomatic definition of mathematical models grounded in Hilbert-space operator theory: a model is formalized as a computable operator acting on random variables, systematically unifying theoretical derivation, experimental implementation, and statistical identification. We further establish a geometric correspondence between the model manifold and the prediction surface, exposing intrinsic structural properties and the fundamental nature of model computability. This framework fills a critical gap in the formal ontology of modeling, providing a unified mathematical foundation for interdisciplinary model construction. It significantly enhances the logical rigor of theoretical inference and the reliability of empirical validation.

In model-based systems engineering, low experimental data reuse efficiency and excessive redundant experiments hinder digital engineering agility. To address this, this paper proposes a case-based reasoning (CBR)-driven experimental management framework that explicitly integrates domain knowledge. The framework features structured experimental metadata modeling, digital twin–enabled scenario semantic alignment, and an interpretable similarity assessment mechanism to intelligently determine whether historical experiments can be transferred to address new verification queries. Its key innovation lies in embedding domain knowledge explicitly into both the CBR retrieval and adaptation stages, thereby enabling trustworthy cross-operating-condition and cross-configuration experimental data reuse. Evaluated on an industrial-scale vehicle energy system design case, the framework reduces redundant experiments by 37% and shortens early verification cycles by 42% on average, significantly enhancing iterative efficiency in digital engineering and advancing intelligent experimental management.

This work proposes an end-to-end scientific workflow framework for partial differential equations (PDEs) based on large language models (LLMs), aiming to bridge the gap between simulation and real-world systems. The framework systematically integrates LLMs across the entire PDE pipeline—spanning discovery of governing equations, automated generation and iterative refinement of numerical solvers, and simulation-informed decision-making—thereby establishing an intelligent interface that connects natural language, symbolic mathematics, executable code, and physical constraints. Experimental results demonstrate the framework’s significant potential in automating PDE-centric scientific workflows, while also highlighting critical challenges such as the scarcity of high-quality data and difficulties in transferring learned capabilities to real-world scenarios.

This study investigates whether control systems—including non-digital and purely mechanical ones—inherently possess computational properties. By systematically introducing the Abstract/Representational Theory (ART) into control theory for the first time, the authors model the controlled plant as a representational entity and analyze canonical cases such as digital thermostats, electromechanical thermostats, centrifugal governors, and open-loop artificial systems. The analysis reveals that all examined control systems perform computation to varying degrees, thereby challenging the long-standing view in cognitive science that treats the centrifugal governor as a paradigmatic non-computational counterexample. These findings offer novel theoretical support for computationalism in cognitive science, suggesting that computation may be a more pervasive feature of control mechanisms than previously assumed.

This study addresses the susceptibility of Transformer-based models to overfitting, limited extrapolation capabilities, and insufficient noise robustness in symbolic regression. To overcome these challenges, we propose an optimization strategy based on training set reshaping and noise-aware fine-tuning. Specifically, the method reconstructs the distribution of training formulas to enhance extrapolative generalization, while incorporating fine-tuning on noisy data to improve robustness against perturbations, thereby enabling rapid synthesis of physical equations. Experimental results demonstrate that the proposed approach generates candidate formulas within approximately ten seconds on standard benchmarks. Furthermore, it achieves significantly superior extrapolation accuracy compared to conventional search-based algorithms while maintaining higher computational efficiency. This work provides an efficient and reliable solution for deep learning-based symbolic regression.

This study addresses the challenges of control design in complex industrial processes characterized by multivariable coupled dynamics by proposing an automated control strategy generation framework that integrates large language models (LLMs) with Bayesian optimization. The approach decomposes control design into structured code generation steps, ensuring physical consistency through execution-based validation and feedback-driven repair. It pioneers the automatic synthesis of decentralized PI controller architectures and their tuning environments directly from dynamic process models. Evaluated on a nonlinear gas preheater benchmark, the generated control schemes—subsequently refined via Bayesian optimization—achieve a 26.5% improvement in closed-loop performance and significantly enhance the transient response of pressure loops, thereby demonstrating the method’s effectiveness and novelty.

This study addresses the limitation of existing numerical solvers that rely on execution-feedback-driven trial-and-error optimization, which hinders root-cause identification of performance bottlenecks. We propose ADSD, a framework adhering to a "diagnosis-first" paradigm that pioneers the integration of automated diagnosis with skill discovery. By employing AI agents to analyze failure mechanisms and encapsulate reusable numerical skills, ADSD transforms blind code editing into a structured knowledge accumulation process encompassing diagnosis, discovery, and implementation. Experimental results demonstrate that this approach significantly enhances solution accuracy and robustness across four major domains, including power flow equations. Notably, it achieves a 71-fold error reduction on the GOC-500 benchmark while exhibiting strong cross-scenario generalization capabilities.

This work investigates whether pretrained image editing models can serve as a universal interface for solving diverse physical equations. The approach encodes both inputs and solutions of physical problems as images, incorporates lightweight adapters to embed scalar parameters, and trains the model under a unified architecture using numerical or analytical solutions across multiple equation types—including elliptic, heat, and Navier-Stokes equations. For the first time, it systematically demonstrates that general-purpose generative models can effectively represent both static and dynamic physical mappings, even capturing shocks and unstable phenomena, thereby expanding their applicability in scientific computing. Experiments across more than ten problem classes yield promising results, yet also reveal limitations of image-based representations in handling wide numerical ranges, enforcing constraints, and simulating long-term chaotic dynamics, such as those in the Kuramoto–Sivashinsky equation.

Researchers often encounter fragmented information when selecting mathematical models, as formulas, variables, assumptions, and their variants are scattered across disparate literature and domain-specific conventions. To address this challenge, this work proposes and constructs MathModDB—the first open knowledge graph dedicated to mathematical models—built upon the Wikibase framework and grounded in a prior ontological design. MathModDB systematically integrates model metadata, core equations, modeling assumptions, and associated variants. The knowledge graph has been incorporated into the MaRDI portal, forming a synergistic ecosystem with the numerical algorithms knowledge graph MathAlgoDB and the documentation tool MaRDMO. Its practical utility and value are demonstrated through a case study on arc discharge modeling in plasma physics.