IAP-24-057

Physics-informed neural networks for urban flood modelling

Flooding poses a significant hydrological threat, affecting over 1.81 billion people, 23% of the global population [1]. This threat is real, as demonstrated by the human disaster in Nepal (2024) after the heaviest monsoon rains in two decades, and the floods of Rio Grande do Sul in Brazil (2024), considered the country’s worst flooding in over 80 years. Lives lost, population displacement, power blackouts, and lack of clean water are some of the consequences of these extreme events. In the UK, the floods of September 2024 caused travel disruptions, closed schools, and made properties uninhabitable after a month’s worth of rain fell in a single day across England.

Despite the efforts of governments and society in disaster preparedness and mitigation, there still is a need to enhance our work toward greater resilience to major flood events. Research has been made in various fields to address it, including advancements in hydrodynamic modelling [2], the development of more accurate flood prediction systems [3], and the implementation of resilient infrastructure designs [4].

Physics-based models are suitable for predictive analysis and testing of flood mitigation strategies under future climate scenarios. However, these models require significant computational resources due to their complexity and high spatial resolution and this makes them unsuitable for real-time applications. On the other hand, machine learning models such as neural networks are highly efficient once trained with observed data or data derived from physics-based models, making them suitable for real-time applications. Despite their efficiency, these models lack the capability to simulate future scenarios or assess the effectiveness of flood mitigation strategies. Physics-informed neural networks (PINNs) could be an option to address the disadvantages of neural networks for these applications [5]. PINNS integrate known physical laws into the learning process and require less data. There is the potential to be used to simulate future scenarios in real time as they incorporate physical laws. The incorporation of physical laws into neural networks can complicate the design and training of the model and they haven’t been applied in this field yet. However, it is an emerging field and PINNs could soon become a powerful tool in managing water systems.

In the last decades, advancements in machine learning have led to significant progress in flood modelling, establishing a new paradigm of data-driven model development in hydrology. However, one of the major challenges in applying machine learning to physical and engineering problems is that data-driven models frequently disregard the established scientific and physical principles that have been developed over centuries. PINNs address this issue by including physics-based constraints into the loss function (objective function) used to train and optimise deep learning models. While standard deep learning loss functions typically only focus on minimising the difference between observed and estimated values, PINNs augment this by using constraints that enforce compliance to the underlying physical laws governing the system under study. The process embeds, then, the physical laws into the neural network architecture, enabling it to function as a solver of partial differential equations (PDEs) or to make use of simulated values from a physics-based model as a surrogate component within the deep learning process. In flood modelling, PDEs are related to hydrodynamic equations such as the Shallow Water Equations and Navier-Stokes [6,7], which aid to model flood evolution in urban environments.

The use of PINNs offers benefits such as: (1) enhanced efficiency of flood models for decision-making; (2) improved adaptability to future weather patterns and urban environments; and, (3) the capability to assess flood mitigation strategies, such as blue-green infrastructure.

Overall, PINNs bring a fresh perspective to flood modelling, blending machine learning’s analytics with the rigour of the principles of physical laws. This integration not only improves the accuracy and reliability of flood modelling but also opens a research avenue towards more resilient and adaptive urban infrastructure, capable of preparing for and mitigating the impacts of future flood events.
Research objectives

This PhD research focuses on developing and implementing PINNs for urban flood modelling. The aim is to develop a decision-making support system for flood management informed by machine learning models enhanced through the integration of physical laws such as conservation of mass, momentum and energy. Ultimately, the outcome will be a decision-support system that uses PINNs to aid stakeholders in making informed decisions. The research is structured around the following detailed objectives and corresponding activities:

• Develop a neural network architecture capable of integrating hydrodynamic data and flooding scenarios. The tasks to complete are: (1) formally define the flood modelling problem; (2) curate data from diverse sources like flood records, rainfall measurements, and real-time sensors, across various scenarios; (3) design a neural network architecture capable of capturing complex urban flood dynamics; (4) define a custom loss function to tune the network’s parameters; (5) employ a suitable optimisation algorithm to minimise the loss function and optimise the model parameters using the curated data.

• Embedding physics from multiple perspectives. Tasks: (1) include physical loss constraints derived from the Shallow Water s Equations to enforce mass and momentum conservation; (2) incorporate simulations to enable learning from both observed data and outcomes simulated from physics; (3) develop an optimisation process that balances data-driven and physics-based loss components; (4) apply regularisation techniques to prevent overfitting and improve generalisation.

• Real-time data integration and model performance. Tasks: (1) work with real-time data assimilation from sources like IoT sensors and weather stations; (2) implement adaptive learning techniques to update the model in real-time; (3) apply uncertainty quantification methods for robust predictions; (4) conduct comparative analyses against traditional and data-driven models in diverse urban environments; and (5) conduct performance metrics and sensitivity analyses to evaluate model effectiveness and identify key influencing factors.

• Decision-support system. Tasks: (1) design algorithms to interpret PINN predictions and generate targeted recommendations; (2) implement scenario analysis tools to assess the impact of different factors on flood risk; (3) develop risk assessment tools to identify vulnerable areas and critical infrastructure; (4) collaborate with stakeholders to ensure the recommender system provides practical and relevant insights for decision-making.

Year 1

a. Literature review and problem definition: Establish a comprehensive understanding of flood modelling, hydrodynamic equations, and machine learning applications in hydrodynamics.

b. Data collection and neural network design

Year 2

a. Neural network development and tailored loss function

b. Embedding physics-based constraints

c. Preliminary results and preparation of first journal article

Year 3

a. Real-Time Data Assimilation Integration into the Model(s)

b. Performance evaluation and comparison to data-driven models, physics-based models, observations and lab measurements

c. Publication of journal articles and participation in international conferences

d. Preparation of the first chapters of the thesis

Year 3.5

Thesis write-up

– Advanced programming
– Implementation of physics-informed neural networks
– Cloud computing
– Hydrodynamics and flood modelling