Physics-based simulation codes for fuel cells and batteries are highly complex, involving coupled nonlinear PDEs, numerous constitutive laws, complex geometries, multiphase transport and multiple layers with disparate spatial scales. Even for relatively simplified geometries and single scales, they can be highly expensive to run. In many important applications, however, accurate but rapid simulations are essential, rendering these full, 'high-fidelity' models impractical. To lower the computational burden, surrogate models can be employed as approximations.

Given the complexity of fuel cell and battery models, the vast number of parameters they involve and the unavoidable uncertainties in parameter values and model assumptions, there is enormous scope for developing surrogates for application that include, but are not limited to, Design optimization (DO), Sensitivity analysis (SA), Uncertainty quantification (UQ), real-time control and inverse parameter estimation. These areas represent the next-generation challenges for those working in fuel cell and battery modelling and the activities within this proposal are aimed at establishing a systematic programme of research activity at the forefront of these areas through fundamental developments combined with large-scale applications, with a focus on high-dimensional (spatio-temporal) data sets.

The focus in this project is on establishing an ambitious long term activity for predictive modelling for DO, SA and UQ by developing and implementing new surrogate assisted approaches, specifically for patio-temporal models (very high dimensional input and output spaces). General frameworks for DO, SA and UQ (using the surrogate models) will be explored and tested on high-fidelity models of H2 fuel cells and vanadium flow batteries. The methods developed will be of direct relevance to other areas such as real-time control and inverse parameter estimation, and will be directly applicable to other fuel cell/battery systems.

We wish to explore a number of ambitious surrogate-assisted approaches building upon our very recent work. The overseas visits will allow us to identify promising methods, which will form the basis of collaborative work over the next few years on all aspects listed above. The lists will establishing/reinforcing international collaborations and will form the foundations for establishing internationally-leading activity in battery and fuel cell modelling with respect to the current and future challenges faced in modelling, developing and commercialising these technologies.

Potential Impact:
The academic impact relates to a number of areas, namely computational statistics, design optimisation, machine learning, manifold learning, uncertainty quantification, multi scale modelling, and fuel cell and battery science, covering electrochemical engineering, computer science and mechanical engineering/design.

The intended outcome will promote and strengthen the position of the University of Warwick in fuel cell and battery modelling by establishing world-leading activity in these emerging areas. By dissemination of results between the research partners and through leading academic journals and conferences, the research will contribute to the continued development of energy storage research, UQ, and development in the UK.

This proposed project aims to establish Warwick as the leader in Predictive modelling of fuel cells and batteries. Predictive modelling, especially uncertainty quantification and (UQ) is seen as a critical future need in both academia (fundamental research) as well as industry. The techniques are already well-established in certain fields, notably Finance, medical research/life sciences and Aerospace (see for example Innovate UK: The Uncertainty Quantification and Management in High Value Manufacturing Special interest Group). There is currently a rapidly growing interest in these methods in other fields involving complex systems and high uncertainty. Batteries and fuel cells fall into this category and while activity in this area is emerging, it remains largely unexplored, primarily due to the enormous complexity of the systems and the concomitant need for detailed (spatio-temporally resolved) data and the steep learning curve for predictive modelling experts in terms of understanding the electrochemistry, transport processes, phase changes and other multi-physics phenomena. Potential future applications for the proposed work include real-time monitoring, control and diagnostics of fuel cell/battery stacks and cells in portable, vehicular or stationary applications, design and optimization of new systems, quantifying uncertainty for specific applications, e.g., when connecting energy storage to wind generation.

Key findings will be presented at leading international conferences in electrochemical engineering, simulation and modelling and computational statistics, reaching a very wide audience. We will contribute to the UK Energy Storage conference, allowing us to engage with the national energy storage research community and thus to inspire future collaboration within the UK.
Publication: Publish in leading high impact factor journals: Dissemination through articles published in international journals, e.g., Journal Power Sources, Journal of Computational Physics, SIAM Journal of Uncertainty Quantification and other leading journals in electrochemical engineering, computational statistics and uncertainty quantification. Visits to universities in China, Canada and the US during the main visits will permit further dissemination and foster further collaboration. Potential collaborators include Notre Dame (US), University of Victoria (Canada) and Beihang University, Chongqing University and Tianjin University (China).