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Abstract Industrial ecosystems are coupled with natural systems, which causes the material flow dynamics in the network to be affected by the mechanistic dynamics of each node. However, current material flow dynamics studies do not capture these mechanistic and nonlinear dynamics to evaluate material flows in networks, thus missing its role in designing resilient industrial ecosystems. In this work, we present a methodology to overcome this limitation and model material flow dynamics in a coupled natural‐industrial network by accounting for underlying nonlinear dynamics at each node. We propose a three‐step methodology: first, creating accurate surrogate models using liquid time‐constant (LTC) neural networks to capture node‐specific behavior; second, coupling these individual node models to simulate material flow dynamics in the network; and third, evaluating resilience by measuring the system's ability to maintain production levels under climate stress. Applied to a soybean‐based biodiesel production network in Champaign County, Illinois (2006–2096), our analysis reveals significant vulnerability differences between climate scenarios, with the RCP 8.5 scenario triggering production failures approximately 10 years earlier than RCP 4.5 (2016 vs. 2026), exhibiting higher failure frequency and requiring longer recovery periods. Smaller farms (450 ha) demonstrated substantially higher import dependency, while medium farms (500 ha) reached a critical bifurcation point around 2050 under RCP 8.5, indicating a systemic tipping point. These findings provide insights for policymakers and industrial managers to implement targeted interventions, supply chain diversification, and adaptive management strategies, thereby enhancing system resilience while offering industrial ecology practitioners a methodology for modeling material flow dynamics in a coupled natural‐industrial network. 

Machine learning presents opportunities to improve the scale-specific accuracy of mechanistic models in a data-driven manner. Here we demonstrate the use of a machine learning technique called Sparse Identification of Nonlinear Dynamics (SINDy) to improve a simple mechanistic model of algal growth. Time-series measurements of the microalga Chlorella Vulgaris were generated under controlled photobioreactor conditions at the University of Technology Sydney. A simple mechanistic growth model based on intensity of light and temperature was integrated over time and compared to the time-series data. While the mechanistic model broadly captured the overall growth trend, discrepancies remained between the model and data due to the model's simplicity and non-ideal behavior of real-world measurement. SINDy was applied to model the residual error by identifying an error derivative correction term. Addition of this SINDy-informed error dynamics term shows improvement to model accuracy while maintaining interpretability of the underlying mechanistic framework. This work demonstrates the potential for machine learning techniques like SINDy to aid simple mechanistic models in scale-specific predictive accuracy. 

Designing a digital twin will be crucial in developing automation-based future manufacturing systems. The design of digital twins involves data-driven modelling of individual manufacturing units and interactions between the various entities. The goals of future manufacturing units such as zero waste at the plant scale can be formulated as a model-based optimal control problem by identifying the necessary state, control inputs, and manipulated variables. The fundamental assumption of any model-based control scheme is the availability of a reasonable model, and hence, assessing the goodness of the model in terms of stability and sensitivity around the optimal parameter value becomes imperative. This work analyses the data-driven model of an acetaminophen production plant obtained from SINDy, a nonlinear system identification algorithm using sparse identification techniques. Initially, we linearize the system around optimal parameter values and use local stability analysis to assess the stability of the identified model. Further, we use what is known as a conditional sloppiness analysis to identify the sensitivity of the parameters around the optimal parameter values to non-infinitesimal perturbations. The conditional sloppiness analysis will reveal the geometry of the parameter space around the optimal parameter values. This analysis eventually gives valuable information on the robustness of the predictions to the changes in the parameter values. We also identify sensitive and insensitive parameter direction. Finally, we show using numerical simulations that the linearized SINDy model is not good enough for control system design. The pole-placement controller is not robust, and with high probability, the control system becomes unstable to very minimum parameter uncertainty in the gain matrix. 

Industrial networks consist of multiple industrial nodes interacting with each other through material exchanges that support the overall production goal of the network. 

Dynamical equations form the basis of design for manufacturing processes and control systems; however, identifying governing equations using a mechanistic approach is tedious. Recently, Machine learning (ML) has shown promise to identify the governing dynamical equations for physical systems faster. This possibility of rapid identification of governing equations provides an exciting opportunity for advancing dynamical systems modeling. However, applicability of the ML approach in identifying governing mechanisms for the dynamics of complex systems relevant to manufacturing has not been tested. We test and compare the efficacy of two white-box ML approaches (SINDy and SymReg) for predicting dynamics and structure of dynamical equations for overall dynamics in a distillation column. Results demonstrate that a combination of ML approaches should be used to identify a full range of equations. In terms of physical law, few terms were interpretable as related to Fick’s law of diffusion and Henry’s law in SINDy, whereas SymReg identified energy balance as driving dynamics. 

Sustainable transition to low carbon and zero waste economy requires a macroscopic evaluation of opportunities and impact of adopting emerging technologies in a region. However, a full assessment of current physical flows and wastes is a tedious task, thus leading to lack of comprehensive assessment before scale up and adoption of emerging technologies. Utilizing the mechanistic models developed for engineering and biological systems with macroeconomic framework of Input-Output models, we propose a novel integrated approach to fully map the physical economy, that automates the process of mapping industrial flows and wastes in a region. The approach is demonstrated by mapping the agro-based physical economy of the state of Illinois, USA by using mechanistic models for 10 sectors, which have high impact on waste generation. Each model mechanistically simulates the material transformation processes in the economic sector and provides the material flow information for mapping. The model for physical economy developed in the form of a Physical Input-Output Table (PIOT) captures the interindustry physical interactions in the region and waste flows, thus providing insights into the opportunities to implement circular economy strategies i.e., adoption of recycling technologies at large scale. In Illinois, adoption of technologies for industrial waste-water & hog manure recycling will have the highest impact by reducing > 62 % of hog industry waste, > 99 % of soybean hull waste, and > 96 % of dry corn milling (corn ethanol production) waste reduction. Small % reduction in fertilizer manufacturing waste was also observed. The physical economy model revealed that Urea sector had the highest material use of 5.52E+08 tons and green bean farming with lowest material use of 1.30E+05 tons for the year modeled (2018). The mechanistic modeling also allowed to capture elemental flows across the physical economy with Urea sector using 8.25E+07 tons of carbon per operation-year (highest) and bean farming using 3.90E+04 tons of elemental carbon per operation-year (least). The approach proposed here establishes a connection between engineering and physical economy modeling community for standardizing the mapping of physical economy that can provide insights for successfully transitioning to a low carbon and zero waste circular economy.