The Data Driven Modelling strategic axis gathers the related themes of Data Assimilation (DA), Uncertainty Quantification (UQ) and Physics-based Artificial Intelligence (AI). CERFACS is a leader in DA, with well-established research activities in the development of DA algorithms and in applications of DA in diverse fields. The UQ activity has intensified with a focus on the development of non-intrusive ensemble methods. Physics-based AI is a field of research that has rapidly matured at CERFACS during the previous strategic period. By including these themes under the same Data Driven Modelling strategic axis, we aim to exploit their synergy and to encourage the development of methods that combine aspects of each.
AS3.1. UNCERTAINTY QUANTIFICATION
Uncertainty quantification (UQ) research at CERFACS is driven by the need to support ensemble data assimilation (DA), where uncertainties in model simulations must be effectively sampled and model error statistics estimated robustly and cost-efficiently. A key challenge is generating ensembles that represent the true probability distribution while integrating this information into DA algorithms. UQ also serves broader goals, including better understanding of physical processes, sensitivity analysis, and stochastic estimation for optimization and extreme event prediction.
CERFACS faces three main challenges in UQ for its legacy codes and complex, multi-physics problems: high dimensionality requiring input/output reduction, limited training data due to high simulation costs, and diverse sources of uncertainty (both aleatory and epistemic). To address these, CERFACS has developed and tested various approaches—metamodeling, multi-fidelity strategies, and sensitivity analysis—often in collaboration with academic and industrial partners such as LISN, IRT, EDF, and ONERA.
CERFACS also contributes to UQ software development, particularly OpenTURNS, supported by shareholders Airbus, EDF, and ONERA. Application areas span environmental science, aeronautics, and climate change. Recent progress has expanded UQ expertise and collaborations. CERFACS now aims to join the GIS LARTISSTE consortium, further solidifying its role in state-of-the-art UQ research and applications.
AS3.2 DATA ASSIMILATION
Data Assimilation (DA) is a method for estimating model states or parameters by combining observations with prior information, grounded in Bayesian estimation theory. In practice, implementing DA involves a range of algorithms, each with trade-offs depending on the application, and often relies on advanced optimization and numerical techniques. Originally developed for forecasting systems like Numerical Weather Prediction, DA operates cyclically—updating model states over time—and differs from static inverse problems or traditional machine learning approaches. Unlike standard ML/DL methods, DA integrates heterogeneous observations and explicitly accounts for uncertainty.
CERFACS has a strong background in both variational and ensemble-based DA. Its current strategy focuses on hybrid ensemble-variational methods that combine the strengths of both approaches. Ensemble DA is closely linked with uncertainty quantification (UQ), as it involves sensitivity analysis and aims to generate forecast ensembles that realistically represent uncertainties. It also connects to physics-informed AI, where statistical surrogates replace costly physical models to estimate flow-dependent errors.
Given the scale of modern applications, DA at CERFACS deals with “Big Data” problems, requiring algorithms optimized for massively parallel computing. Future research will explore integrating ML/DL techniques into DA workflows and incorporating new types of data to enhance algorithm robustness and support digital twin applications and observational network optimization.
AS3.3 PHYSICS-BASED AI
Since 2018, CERFACS has developed a dedicated team—structured around the Helios academic workgroup—to explore how Artificial Intelligence (AI) can enhance physical modeling. This interdisciplinary initiative has addressed diverse applications, including subsurface parameterization, atmospheric data assimilation, hydrology, wildfire modeling, aerodynamics, and propulsion. Through these projects, the team has gained insight into both the specific challenges and the broader potential of AI in scientific computing.
Over the next five years, CERFACS will continue expanding this research, focusing on real-world applications relevant to its shareholders. While AI has been surrounded by significant hype, the focus is now shifting toward concrete demonstrators that showcase practical benefits and tradeoffs. Three strategic priorities will guide this effort. First, the team will pursue innovative AI applications in physical modeling—particularly those that could revolutionize the resolution of partial differential equations (PDEs) through learned approximations. Second, it aims to bring hybrid CFD-AI applications to maturity, demonstrating their feasibility on complex industrial cases. Third, it will strengthen the integration of computational models with experimental or observational data by leveraging AI and CERFACS’ expertise in data assimilation. These actions aim to position AI as a reliable tool for improving accuracy, efficiency, and insight in physical modeling and prediction workflows.
