Tiger and Fox Algorithms Team Up to Sharpen Battery Forecasts for Flying Taxis

Electric air taxis promise to reshape city travel, but their future hinges on a deceptively simple question: how much charge is actually left in the battery? Unlike a car on a highway, an electric vertical take-off and landing aircraft, or eVTOL, spends enormous energy climbing, hovering, and descending, and its lithium-ion cells behave unpredictably under those swinging loads. A team of researchers in India now reports a hybrid deep learning framework that reads a battery’s state of charge, or SoC, with striking precision, and their results could help make urban air mobility safer and longer-ranged.

The study, published in the International Journal of Aeronautical and Space Sciences by T. Santiago Arockiam and S. Kalimuthu Kumar of Kalasalingam Academy of Research and Education and Alagar Karthick of Saveetha Institute of Medical and Technical Sciences, centers on a Long Short-Term Memory network, a form of recurrent neural network built to learn patterns in sequential data. Battery behavior is exactly that: a time series of currents, voltages, and temperatures whose history shapes what comes next. LSTMs are well suited to such problems because their internal memory gates allow them to retain information over long stretches of a signal, capturing the slow, nonlinear drift of a battery as it discharges.

Yet an LSTM is only as good as its configuration. The network’s hyperparameters, the settings chosen before training begins, such as the number of hidden units, learning rates, and window lengths, can make the difference between a model that tracks the battery faithfully and one that wanders off course. Tuning these knobs by hand is tedious and unreliable, so the researchers turned to nature-inspired optimization, a family of algorithms that search vast parameter spaces by mimicking the hunting and survival strategies of animals.

The twist in this work is the pairing of two such algorithms with very different personalities. The Siberia Tiger Optimisation, or ST, algorithm performs aggressive global exploration, sweeping broadly across the search space to avoid getting trapped in mediocre solutions. The Polar Fox Optimization, or PF, algorithm does the opposite: it exploits promising regions, refining candidate solutions with fine-grained local searches. By combining the tiger’s wide-ranging hunt with the fox’s careful pursuit, the hybrid optimizer can both discover good regions of hyperparameter space and lock onto the best settings within them, a division of labor that the authors say yields faster convergence and lower prediction error than either algorithm alone.

When tested against real-time battery datasets, the hybrid LSTM_PF_ST model delivered a mean squared error of 0.00034, a root mean square error of 0.01844, and a coefficient of determination, R², of 0.9978. In practical terms, an R² this close to one means the model’s predicted state of charge curve overlays the measured curve almost perfectly across multiple charge–discharge cycles, with only slight variation. Models tuned with the individual algorithms performed respectably but were consistently outperformed by the combined framework, underscoring the value of blending exploration with exploitation.

The stakes for this kind of accuracy are unusually high in aviation. State of charge is the fuel gauge of an electric aircraft, and the battery management system that monitors it must make split-second decisions about how much power can be safely drawn during take-off or reserved for an emergency landing. Overestimate the remaining charge and a pilot could be stranded mid-air; underestimate it and the aircraft forfeits range and payload it could otherwise use. Conventional estimation methods, from coulomb counting to Kalman filtering and equivalent circuit models, struggle with the drift, hysteresis, and temperature sensitivity that plague lithium-ion cells under the aggressive load profiles of vertical flight.

Deep learning approaches have gained ground because they learn these nonlinear behaviors directly from data rather than relying on simplified physical models. Earlier work, including deep neural network estimators of lithium-ion state of charge and integrated frameworks that jointly estimate state of charge and state of health, demonstrated the promise of data-driven methods. The new study pushes further by showing that the optimization layer wrapped around the network matters as much as the network architecture itself. The authors report that their hybrid model also shows improved performance under dynamic load scenarios, the rapidly changing demands that characterize real eVTOL missions, along with quicker convergence during training.

Generalization is the property that separates a laboratory curiosity from a flight-worthy tool, and the researchers highlight it explicitly. A predicted SoC curve that fits the real data across varied cycles, they note, indicates an adaptive level of learning, meaning the network has not merely memorized one discharge pattern but has internalized the battery’s underlying dynamics. That adaptivity matters because real cells age, temperatures fluctuate with altitude and season, and mission profiles differ from one flight to the next. An estimator that can track those shifts in real time becomes a foundation for intelligent energy management, potentially extending flight duration and reinforcing operational safety in electric propulsion systems.

The research arrives at a moment when urban air mobility is moving from concept to certification. Market studies and design analyses of on-demand aviation have identified battery energy density and reliability as the critical bottlenecks for eVTOL aircraft, and reviews of electric propulsion concepts repeatedly flag battery state estimation as a key technical challenge. Wind effects on eVTOL operations, autonomous flight research, and vertiport traffic planning all assume that the aircraft’s energy accounting is trustworthy. A battery management system powered by a highly accurate, real-time SoC estimator feeds directly into that trust, informing route planning, reserve margins, and charging schedules between flights.

There are, of course, familiar caveats. The study was validated on real-time battery datasets rather than in flight, and deploying a hybrid optimizer alongside a recurrent network aboard an aircraft raises questions about computational cost, certification, and robustness to sensor faults that the published abstract does not address. The authors received no external funding for the work and declare no competing interests. Still, the numbers are hard to ignore: an R² of 0.9978 and an RMSE below 0.02 represent the kind of precision that battery engineers typically chase for years. If the framework survives the transition from test bench to flight deck, the tiger and the fox may end up doing more than tuning a neural network; they may help decide when the age of electric flight truly takes off.

Subject of Research: Hybrid optimization of LSTM deep learning models for lithium-ion battery state of charge estimation in eVTOL aircraft

Article Title: Hybrid Deep Learning Framework for Accurate SoC Estimation in eVTOL Systems

Article References: Santiago Arockiam, T., Kalimuthu Kumar, S., & Karthick, A. (2026). Hybrid Deep Learning Framework for Accurate SoC Estimation in eVTOL Systems. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01271-y

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01271-y

Keywords: eVTOL, state of charge, lithium-ion battery, LSTM, deep learning, Siberia Tiger Optimisation, Polar Fox Optimization, hybrid optimization, battery management system, urban air mobility, electric propulsion, machine learning