Physics-informed nEuRal networks for SEVERe wEather event prediction

Project Information

PERSEVERE

Grant agreement ID: 101059984

DOI

10.3030/101059984

Project terminated on 31 August 2025

EC signature date 1 July 2022

Start date 1 June 2023

End date 31 May 2027

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 165 312,96

Coordinated by

UNIVERSIDAD CARLOS III DE MADRID
Spain

Periodic Reporting for period 1 - PERSEVERE (Physics-informed nEuRal networks for SEVERe wEather event prediction)

Reporting period: 2023-06-01 to 2027-05-31

Summary of the context and overall objectives of the project

Currently, there is constant word about how artificial intelligence is affecting our daily lives and how its progress may have a significant impact in the way we approach our daily tasks and challenges. Neural networks, a particular kind of artificial intelligence resembling the human brain, are entering our work environments with strength and many useful perspectives for the future.

The novel development of physics-informed neural networks (PINNs), which incorporate the constraints given by physics laws into the training process, has open the gates to numerous applications, e.g. the reconstruction of fluid flows. PINNs may regularize fluid information by means of applying the Navier-Stokes equations as a relevant contribution to the loss function during the training of such networks, recovering / regularizing / reconstructing the fluid domain in areas where experiments are limited by technology.

On the other hand, the development of variational autoencoders (VAEs), which aim to learn compact probabilistic representations of complex data, offers an efficient and low-cost alternative for generative modeling in high-dimensional systems. VAEs are particularly suited for capturing the intrinsic variability of fluid flow fields and reconstructing incomplete or noisy measurements in spatiotemporal systems such as atmospheric dynamics. In weather forecasting applications, where high-resolution measurements of wind, humidity, or temperature may be unavailable or partially corrupted, VAEs can learn a latent representation of historical meteorological patterns and reconstruct plausible realizations of missing data.

When combined with PINNs, which enforce physical consistency in the latent space by embedding governing equations like Navier-Stokes, the resulting hybrid models can both respect the physical laws and generalize from learned data distributions. This synergy proves especially powerful in scenarios involving the prediction of severe weather conditions, where rapid and accurate reconstructions of atmospheric flow fields are needed, for example, around airports, where storms have a severe impact on aircraft performance and safety. Following that trend, the estimation and forecast of storms is essential to the air transport industry, since the losses incurred due to delays and deviations of air traffic caused by the presence of storms have been reported to be over $38.5 billion in USA. The forecast of severe weather events is therefore of crucial importance.

We aim to develop an artificial intelligence based on neural networks which combines the strengths of PINNs and VAEs, so that one may rapidly estimate the fluidic behaviour of a moving storm and be able to take preventive measurements.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

During the course of the action, the project was structured into three main technical work packages, each targeting a specific scientific objective aimed at developing a storm prediction framework grounded in physical laws and temporal consistency.

Work Package 1 – Development and assessment of physics-informed neural networks (PINNs):
This phase focused on the adaptation and testing of PINNs when applied to experimentally acquired data, as opposed to idealized synthetic datasets such as those from Direct Numerical Simulations (DNSs). DNSs inherently satisfy the physical laws embedded in the calculation process, while real-world weather station data present inconsistencies, noise, and sparse spatial resolution. PINNs were trained using wind velocity and pressure measurements obtained from ground-based stations to reconstruct the evolution of weather fields at enhanced resolution. Results demonstrated that PINNs outperform classical interpolation methods when extrapolating beyond the convex hull defined by available sensors. While standard methods degrade rapidly outside this region, PINNs maintained reliable inference accuracy, revealing their robustness and suitability for sparse-data scenarios. These results were validated and published in a peer-reviewed journal, establishing the viability of physics-informed learning for real atmospheric applications.

Work Package 2 – Latent-space modeling through variational autoencoders (VAEs):
The second work package concentrated on learning compact, interpretable representations of high-dimensional meteorological data using various VAE architectures. Starting with the standard autoencoder framework, the analysis progressed toward beta-VAEs to enhance disentanglement in the latent space. Additionally, nested or hierarchical-prior VAE (HP-VAE) architectures were introduced to promote modularity and variable independence in the latent representation. The objective was to strike a balance between high disentanglement (which facilitates interpretability and downstream modeling) and reconstruction fidelity (which ensures consistency with observed fields). In scenarios involving DNS-type data,HP-VAEs provided a superior trade-off compared to simpler models. When applied to real weather evolution datasets, challenges related to chaotic behavior and data variability were mitigated through dimensionality reduction strategies. Notably, significant improvements were achieved by constraining the latent space to a reduced number of well-separated components, thus demonstrating both efficient compressibility and functional interpretability of the encoded variables. These developments laid the foundation for generative forecasting models capable of capturing temporal evolution while remaining tractable.

Work Package 3 – Integration of PINNs and VAEs within a physics-informed image inpaintor (P3I):
The final phase of the project integrated the two previous approaches into a unified architecture for the inference of missing or partially observed data. A standard autoencoder was augmented with physics-based constraints during reconstruction, forming the core of a physics-informed image inpaintor (P3I). In this formulation, spatiotemporal fluid data were treated as image-like fields, where missing regions corresponded to unmeasured or corrupted values. The P3I was trained to perform image inpainting, constrained by the Navier-Stokes equations and other relevant physical laws to ensure that reconstructed regions were not only statistically plausible but also physically consistent. This hybrid architecture demonstrated the capacity to recover unobserved data segments with high fidelity, preserving coherent flow structures and adhering to dynamic constraints. The resulting system represents a robust mechanism for dealing with incomplete meteorological datasets, and has potential applications in both retrospective analysis and real-time forecasting under uncertainty. The full implementation of P3I has been successfully completed and validated through numerical experiments, confirming its feasibility for storm reconstruction and prediction in data-sparse conditions.

In summary, the scientific and technical work conducted throughout the project has resulted in a functional and novel architecture combining physics-informed learning and latent-variable modeling for weather prediction. The main outcomes include:

- A validated PINN methodology for spatial extrapolation from sparse sensor data.
- A modular and interpretable VAE architecture optimized for compressing meteorological dynamics.
- A physics-informed image inpainting system capable of reconstructing missing flow information in realistic atmospheric scenarios.

These achievements contribute to the development of next-generation weather forecasting tools that are physically grounded, data-efficient, and robust under uncertainty.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The project has successfully demonstrated the feasibility and potential of combining physics-informed neural networks (PINNs) and variational autoencoders (VAEs) to reconstruct, extrapolate, and predict complex fluid phenomena such as atmospheric storms. The main result is the development of a hybrid architecture capable of both learning from real-world sparse measurements and generating physically consistent outputs under uncertainty. This approach bridges the gap between data-driven methods and first-principles modeling, offering an innovative path forward for weather forecasting, especially in critical applications such as aviation safety and emergency response.

In addition to methodological innovation, the project has yielded a functioning physics-informed image inpaintor (P3I), capable of reconstructing missing fluid data in a reliable and consistent manner. The ability to generate high-resolution predictions from low-resolution or partially missing measurements has clear advantages for decision-making in meteorology and beyond.

The broader potential impacts of this work include:

- Enhanced operational forecasting tools that reduce reliance on costly and time-consuming simulations.
- Improved preparedness and risk mitigation for severe weather events, with positive implications for sectors such as air transport, logistics, agriculture, and civil protection.
- Scalability to other fields, such as oceanography, pollutant dispersion, and biomedical flows, where physics-informed reconstruction of sparse data is also critical.

To ensure further uptake and success of the proposed technologies, the following key needs have been identified:

- Further research and development: while the current prototypes have shown robust performance, additional research is required to adapt the hybrid models to a broader range of environmental conditions, temporal scales, and sensor types.
- Demonstration in operational environments:pPilot deployments in collaboration with meteorological agencies or airport authorities would be crucial to validate the models under real-time constraints and feedback loops.
- Access to high-quality datasets: continued progress depends on the availability of diverse and representative datasets, particularly multi-modal measurements (e.g. satellite, radar, and ground stations) with high spatial-temporal resolution.
- Integration into decision-support systems: for full exploitation, the hybrid models must be embedded into user-facing software tools capable of interacting with existing data infrastructures and forecasting pipelines.
- IPR support and technology transfer: protection of novel architectures and training methodologies through intellectual property frameworks is recommended to facilitate licensing and collaboration with commercial stakeholders.
- Access to finance and commercialization channels: the transition from proof-of-concept to market-ready solutions will require funding mechanisms to support upscaling, cloud deployment, and user interface development.
- Regulatory and standardization alignment: ensuring that AI-driven forecasting models comply with safety, traceability, and transparency requirements in regulated sectors (e.g. aviation) will be key to building user trust and acceptance.
- International collaboration and dissemination: engagement with international research and operational forecasting communities (e.g. ECMWF, NOAA) will accelerate adoption and standardisation, as well as stimulate feedback and improvement cycles.

By addressing these needs, the outcomes of the project can evolve into robust, scalable tools that support sustainable and efficient decision-making under complex atmospheric conditions.

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