The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in ordinary differential equations is considered, with the typical application of finding weights of a neural ordinary differential equation (NODE) for a residual network with time continuous layers. The differential equation is treated as an abstract and isolated entity, termed a standalone NODE (sNODE), to facilitate for a wide range of applications. The proposed parameter reconstruction is performed by minimizing a cost functional covering a variety of loss functions and penalty terms. Regularization via penalty terms is incorporated to enhance ethical and trustworthy AI formulations. A nonlinear conjugate gradient mini-batch optimization scheme (NCG) is derived for the training having the benefit of including a sensitivity problem. The model (differential equation)-based approach is thus combined with a data-driven learning procedure. Mathematical properties are stated for the differential equation and the cost functional. The adjoint problem needed is derived together with the sensitivity problem. The sensitivity problem itself can estimate changes in the output under perturbation of the trained parameters. To preserve smoothness during the iterations, the Sobolev gradient is calculated and incorporated. Numerical results are included to validate the procedure for a NODE and synthetic datasets and compared with standard gradient approaches. For stability, using the sensitivity problem, a strategy for adversarial attacks is constructed, and it is shown that the given method with Sobolev gradients is more robust than standard approaches for parameter identification.

In this paper, we study economic dynamics in a standard overlapping generations model without production. In particular, using numerical methods, we obtain a necessary and sufficient condition for the existence of a topological chaos. This is a new application of a recent result characterising the existence of a topological chaos for a unimodal interval map by Deng, Khan, Mitra (2022).

This paper introduces the Open Knowledge Resilience Framework (OKRF), a set of seven cooperative data standards, and demonstrates its alignment with the Supply Chain Interoperability Specification (SCIS) Platform. Building upon the Internet of Production Alliance (IoPA) work, this article explores how integrating OKRF and SCIS can enhance production flexibility and efficiency through substitutability and resource repurposing strategies. The OKRF-SCIS integration exhibits the potential to enhance Supply Chain Resilience (SCR) by empowering organizations to adapt to fluctuating demand and availability through adaptability strategies such as supplier/product substitution and resource repurposing. While this study primarily focuses on the conceptual design of OKRF and SCIS, further empirical research is needed to validate its effectiveness. Additionally, investigating the framework’s applicability across various industries and contexts would provide valuable insights. The integration of OKRF and SCIS can enable organizations to optimize supply chain operations, enhancing resilience and facilitating adaptation to changing demands through seamless substitutability and resource repurposing. This integration can also reduce transportation costs and increase responsiveness to local demand. Furthermore, it can enhance SCR and promote sustainable, resilient supply chain ecosystems by improving data transparency and resource utilization efficiency. This paper illustrates the potential of OKRF and SCIS in healthcare supply chains.