Dynamic process modeling is essential for simulating time-evolving biochemical systems, particularly those with multistate interactions and combinatorial complexity. Traditional Ordinary Differential Equation (ODE) models offer mechanistic clarity but struggle with scalability and context-sensitive encoding. Rule-Based Modeling (RBM) frameworks address these limitations through modular rule abstraction, yet require manual specification and lack adaptive learning. This study introduces algorithmic innovations within the Neural Ordinary Differential Equation (Neural ODE) paradigm to bridge the gap between mechanistic interpretability and scalable expressivity. Neural ODEs can be considered as a revolutionary approach in the field of modeling dynamic biochemical interactions. They have made it possible to create models of such interactions that are flexible enough to adapt to different scenarios and do so without requiring any manual intervention in terms of rule encoding or predefined reaction schemes. This is achieved by employing differential solvers within the framework of neural networks, thus enabling a learning process that is in accordance with the behavior of the system. Using the DARPP-32 signaling network—a benchmark system characterized by multivalent phosphorylation and dynamic perturbations—the proposed Neural ODE framework demonstrates the ability to replicate key dynamic behaviors observed in ODE and RBM models. Comparative simulations under baseline and perturbed conditions reveal that Neural ODEs maintain trajectory fidelity while offering enhanced modularity and computational efficiency. Feature importance analysis and latent space visualizations further validate the model's interpretability and robustness. Unlike ODEs and RBMs, Neural ODEs adapt to structural mutations and binding schemes through latent trajectory learning, enabling flexible simulation of biochemical variability without manual rule encoding. This work establishes Neural ODEs as a viable and scalable alternative for modeling complex biochemical systems, combining the strengths of data-driven learning with the interpretability of differential equations.
动态过程建模对于模拟随时间变化的生化系统,特别是那些具有多状态相互作用和组合复杂性的系统是必不可少的。传统的常微分方程(ODE)模型提供了机制上的清晰度,但在可伸缩性和上下文敏感编码方面存在困难。基于规则的建模(rule - based Modeling, RBM)框架通过模块化规则抽象解决了这些限制,但是需要手工规范并且缺乏自适应学习。本研究在神经常微分方程(Neural ODE)范式中引入了算法创新,以弥合机制可解释性和可扩展表达性之间的差距。神经ode可以被认为是动态生化相互作用建模领域的一种革命性方法。它们使得创建这种交互的模型成为可能,这些模型足够灵活,可以适应不同的场景,并且不需要在规则编码或预定义的反应方案方面进行任何人工干预。这是通过在神经网络框架内使用微分解算器来实现的,从而使学习过程与系统的行为相一致。利用DARPP-32信号网络-一个以多价磷酸化和动态扰动为特征的基准系统-提出的神经ODE框架证明了复制ODE和RBM模型中观察到的关键动态行为的能力。在基线和扰动条件下的对比仿真表明,神经ode在保持轨迹保真度的同时,提供了增强的模块化和计算效率。特征重要性分析和潜在空间可视化进一步验证了模型的可解释性和鲁棒性。与ode和rbm不同,神经ode通过潜在轨迹学习适应结构突变和结合方案,无需手动规则编码即可灵活模拟生化变异。本研究将数据驱动学习的优势与微分方程的可解释性相结合,建立了神经ode作为复杂生化系统建模的可行且可扩展的替代方案。
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In this work, the influence of strut thickness on the deformation and failure mechanisms of new vascular bundle–inspired structures, which exhibit comparable or better mechanical properties than honeycomb and star-shaped lattices, is presented. The novelty of the work lies on the design of the structure; this is a new structure, and its behavior has not been reported elsewhere. Structures consisting of 0.2, 0.5, 1.0-, and 1.15-mm strut thicknesses were designed, modeled, fabricated, and tested. A finite element model of a quasi-static compression test is developed in ANSYS Explicit Dynamics to evaluate the deformation and failure mechanisms of the various structures. It is demonstrated that 0.2- and 0.5-mm structures exhibit stretch-dominated stress–strain behavior, whereas 1.0- and 1.15-mm structures show bend-dominated stress–strain characteristics. As the strut thickness increases, there is an increase in peak stresses (with reported peak stresses of 1.3, 1.4, 5, and 5.1 MPa for 0.2, 0.5, 1.0, and 1.15 mm, respectively) and energy absorption (reported values of 33.84, 31.48, 159.28, and 179.07 J for thicknesses of 0.2, 0.5, 1.0, and 1.15 mm, respectively) characteristics. Poisson's ratio values of the samples ranged between 0.6 and 1.2. Additionally, the deformation mechanisms transform from perpendicular collapse of the structure to 45° bending (shearing) of the structure from low to higher strut thickness. As the strut thickness increases, the failure mechanisms transform from ductile fracture to near-brittle failure of the structures. The findings in this paper provide key insights into the design and fabrication of next-generation vascular bundle–inspired multifunctional materials for lightweight structural applications. As a contribution, the energy absorption and peak stress values for the vascular bundle structures presented in this paper are comparable to published data on similar PLA lattice structures.
{"title":"Effect of the Strut Thickness on the Mechanical Properties, Deformation, and Failure Mechanisms of Vascular Bundle–Inspired Structures","authors":"Fredrick Mwema, Ndivhuwo Ndou","doi":"10.1002/eng2.70622","DOIUrl":"https://doi.org/10.1002/eng2.70622","url":null,"abstract":"<p>In this work, the influence of strut thickness on the deformation and failure mechanisms of new vascular bundle–inspired structures, which exhibit comparable or better mechanical properties than honeycomb and star-shaped lattices, is presented. The novelty of the work lies on the design of the structure; this is a new structure, and its behavior has not been reported elsewhere. Structures consisting of 0.2, 0.5, 1.0-, and 1.15-mm strut thicknesses were designed, modeled, fabricated, and tested. A finite element model of a quasi-static compression test is developed in ANSYS Explicit Dynamics to evaluate the deformation and failure mechanisms of the various structures. It is demonstrated that 0.2- and 0.5-mm structures exhibit stretch-dominated stress–strain behavior, whereas 1.0- and 1.15-mm structures show bend-dominated stress–strain characteristics. As the strut thickness increases, there is an increase in peak stresses (with reported peak stresses of 1.3, 1.4, 5, and 5.1 MPa for 0.2, 0.5, 1.0, and 1.15 mm, respectively) and energy absorption (reported values of 33.84, 31.48, 159.28, and 179.07 J for thicknesses of 0.2, 0.5, 1.0, and 1.15 mm, respectively) characteristics. Poisson's ratio values of the samples ranged between 0.6 and 1.2. Additionally, the deformation mechanisms transform from perpendicular collapse of the structure to 45° bending (shearing) of the structure from low to higher strut thickness. As the strut thickness increases, the failure mechanisms transform from ductile fracture to near-brittle failure of the structures. The findings in this paper provide key insights into the design and fabrication of next-generation vascular bundle–inspired multifunctional materials for lightweight structural applications. As a contribution, the energy absorption and peak stress values for the vascular bundle structures presented in this paper are comparable to published data on similar PLA lattice structures.</p>","PeriodicalId":72922,"journal":{"name":"Engineering reports : open access","volume":"8 2","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/eng2.70622","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146136220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study develops the Fractional Novel Analytical Method (FNAM), a Taylor-series–oriented approach for constructing approximate analytical solutions of NFDΔEs prevalent in control, integrability studies, and arithmetic modeling. Grounded in the Caputo fractional derivative, the method attains rapid convergence of truncated series and eliminates dependence on Adomian polynomial decompositions, multiplier methods, auxiliary parameters, perturbative schemes, and transform operators. Testing on three well-known NFDΔEs with fractional order