At Bowling Green State University, the Nigerian doctoral researcher is combining physical models with machine learning to estimate melting rates and explore more responsive furnace control.

Inside an industrial glass furnace, a critical production variable can be difficult to observe directly: how quickly incoming raw material becomes molten glass. Operators need that process to keep pace with the glass leaving the furnace, but the measurements available do not necessarily reveal everything happening inside.

For Toheeb Babatunde Ibrahim, a doctoral researcher in Applied Mathematics at Bowling Green State University in Ohio, that gap is a mathematical problem with a practical purpose. His research combines physics and artificial intelligence to estimate internal furnace conditions from existing measurements, then uses those estimates to investigate how the supply of raw material could respond to changing production demands.

Since August 2025, Ibrahim has worked as a research assistant in BGSU’s College of Engineering on the project in partnership with industry. The aim is to give a control system a more useful picture of a process whose internal dynamics cannot all be measured directly.

The work offers a focused example of industrial AI: a relatively small neural network used alongside established physical knowledge to address a specific problem in manufacturing.

Learning what the physical model misses

The team begins with a physical model of how material moves through the furnace and melts. That model provides the foundation, while a neural network learns a correction for the differences between its predictions and the furnace data.

The distinction matters. The network does not have to discover the entire process from data alone. It concentrates on the behaviour that the physical model does not fully capture.

“It’s small because it isn’t learning a furnace from nothing,” Ibrahim says. “It’s learning a correction to something that’s already mostly right.”

The network has roughly 5,300 trainable parameters. Its role is deliberately limited, allowing the researchers to combine a mathematical description of the process with patterns learned from operating data.

The team then uses an observer, a mathematical method for estimating internal conditions that are not directly measured. It compares predicted measurements with available readings and uses the differences to update estimates of seven internal furnace states.

“Think about a car with a broken speedometer,” Ibrahim says. “You can still see the odometer. If you know how a car works, watching distance accumulate tells you the speed. You’re not measuring it. You’re inferring it from something related, using a model.”

In the furnace application, those estimates feed a controller designed to adjust the rate at which raw material enters. The objective is to help melting keep pace with the glass drawn off for production. Ibrahim has also compared alternative control methods and automated their tuning to reduce manual adjustment of controller settings.

Testing beyond the next prediction

A model that predicts the next moment successfully may still drift when asked to follow an industrial process over a longer period. To examine that challenge, the researchers withheld complete operating runs from training and tested predictions over 72 hours.

Starting from an initial condition, the model predicted the process over three days without further measurement corrections. That is a different test from repeatedly updating a prediction with fresh readings.

Across 20 unseen runs, the team reported best-fit scores of 99.21 per cent for glass level, 90.95 per cent for the rate of change in level and 81.94 per cent for melting rate. These are model-fit scores for the reported evaluation, rather than evidence of equivalent gains in factory output or efficiency.

The lower score for melting rate highlights the difficulty at the centre of the work. Melting develops through stages and transport delays, making it harder to infer than a quantity such as glass level. The results show that the model tracked some variables more closely than others, an important distinction when considering its use in control decisions.

For operators, the potential benefit is better visibility into internal conditions without adding sensors for every variable. A sufficiently reliable model could also help assess production schedules before they are attempted on the furnace. Those possibilities remain distinct from demonstrated improvements in commercial operation.

The research is described in Neural ODE-Based Dynamic Modeling and Observer-Based Control of Industrial Glass Melting Processes, co-authored with Owais Khan, Xuan Dung James Nguyen, Mohammed Abouheaf and Josh Peeno. The manuscript is under review at Chemical Engineering Research and Design. Ibrahim also presented a poster on the project at the 87th Glass Problems Conference and Symposium in Toledo in September 2026.

From Ilorin to industrial mathematics

Ibrahim’s route into furnace modelling began at the University of Ilorin in Nigeria, where he graduated in mathematics with First Class Honours in 2017. He had won a gold medal at the National Mathematics Competition the previous year.

A fully funded master’s programme at the African Institute for Mathematical Sciences in Cameroon followed in 2019. Between 2019 and 2021, DAAD scholarship support took him to the University of Tübingen and Hochschule Mittweida University of Applied Sciences in Germany for research in mathematical epidemiology.

He co-authored two papers published in PLOS One in 2021 on COVID-19 herd immunity and vaccination, and presented work on mosquito breeding sites for malaria control. These projects addressed different subject matter from glass manufacturing, but similarly used mathematics to investigate processes that change over time.

His later studies moved towards engineering and materials. He completed a master’s in Mathematical Engineering at the University of L’Aquila in Italy in 2023 and a master’s in Nanotechnology at Gdańsk University of Technology in Poland in 2025. His Gdańsk thesis examined the mathematics of an interatomic potential used in molecular dynamics simulations.

He began his BGSU doctorate in 2024, while completing the Polish degree, and expects to finish in 2028. Alongside research, he has taught college algebra and calculus at BGSU, building on earlier teaching roles at AIMS Cameroon and Adekunle Ajasin University in Nigeria.

Bringing control decisions closer to the hardware

The next stage of the furnace project concerns a limitation that a successful prediction alone cannot resolve. A real batch charger has a maximum operating speed and limits on how quickly that speed can change. A controller must account for both.

The current controller does not explicitly enforce those restrictions, meaning it can request a response that the equipment cannot deliver. Ibrahim plans to incorporate them into a predictive controller that considers future furnace behaviour when choosing its actions.

That step is central to the project’s practical direction. Estimating what is happening inside the furnace is one challenge; turning those estimates into feasible equipment commands is another. The research must connect the two before its potential value can be judged in operation.

“Furnaces are just an unusually strict place to find out whether your idea works,” Ibrahim says.