Invited speakers

George Haller (ETH Zürich)

Data-driven modeling and control via spectral submanifolds

The recent concept of spectral submanifolds (SSMs) uncovers very low dimensional attractors in virtually all dynamics problems of physical importance. A data-driven identification of the reduced dynamics on these SSMs gives a mathematically justified way to construct accurate and predictive reduced-order models for solids, fluids, and controls without the use of governing equations. I review these concepts and recent progress in applying them to the reduced modeling of fluid flows from numerical and experimental data. I also show very recent comparisons of SSM-based model-predictive control with reinforcement learning (RL)-based control in soft robotics. Additionally, I show results comparing the use SSM-reduced models with the use of recurrent neural networks and transformers in training RL policies.

Olga Fink (EPFL Lausanne)

Momentum-conserving physics-informed graph neural networks for dynamical systems

Accurate and interpretable modeling of multi-body dynamical systems is a fundamental challenge in domains ranging from robotics and aerospace to biophysics and materials science. Traditional physics-based approaches are often computationally expensive and difficult to scale, while purely data-driven methods like graph neural networks (GNNs) may lack physical consistency and generalization. This talk presents Dynami-CAL GraphNet, a new physics-informed GNN framework that explicitly integrates conservation laws, specifically, the pairwise conservation of linear and angular momentum, into its architecture. By leveraging edge-local reference frames that are equivariant to rotations and translations, our model produces physically consistent predictions and offers interpretable insights into the forces and moments governing each interaction. We demonstrate the effectiveness of Dynami-CAL GraphNet across a wide spectrum of tasks. Beyond standard 3D granular systems with inelastic collisions, we systematically evaluated the model on complex, real-world datasets, including human body motion prediction and protein molecular dynamics simulations. In all cases, Dynami-CAL GraphNet was benchmarked against several established baseline methods. Our results show not only stable error accumulation over extended prediction horizons and superior maintenance of physical constraints, but also a strong ability to extrapolate to previously unseen system configurations and interaction regimes, a key capability for robust deployment in real-world scenarios. This talk will highlight how embedding physical principles within machine learning architectures enables not only accuracy and interpretability, but also robust extrapolation to previously unseen scenarios, opening new avenues for real-time, scalable, and generalizable modeling of complex systems in science and engineering.

Denis Sipp (Onera)

Memory closure for bilinear representation of non-autonomous systems with application to adaptive model predictive control

Co-authors: Priyam Gupta, Taraneh Sayadi, Peter J. Schmid, and Georgios Rigas

Data-driven system identification of nonlinear non-autonomous dynamical systems is a powerful paradigm for the design of efficient and robust controllers. Specifically, recent data-driven efforts to identify simplified linear/bilinear representations of these complex systems in suitable latent spaces have shown to be effective for state estimation and control. These representations rely on finite-dimensional approximations of the Koopman operator, which is inherently infinite-dimensional. This necessitates truncation, which introduces approximation errors and can undermine control performance. The Mori–Zwanzig (MZ) formalism has been shown to provide a closure for such finite-dimensional approximations of autonomous systems by incorporating memory kernels that account for the influence of unresolved observables. In this work, we present an extension of the MZ formalism to non-autonomous systems and develop a closure strategy suited for control-affine nonlinear systems. By retaining the non-Markovian contributions, the resulting reduced-order model captures dynamical features that would otherwise be lost in a purely Markovian finite-dimensional approximation. We demonstrate how the resulting memory-corrected model can be integrated into an adaptive Model Predictive Control (MPC) scheme. The memory terms are estimated online from data, allowing the controller to adapt to changing operating conditions and unmodeled dynamics. This yields a data-driven control architecture that is both accurate and robust for nonlinear systems. Numerical experiments on chaotic nonlinear systems illustrate the improved performance of the proposed approach compared with Markovian Koopman-MPC methods.

Elie Hachem (CEMEF - Mines Paris - PSL)

Coupling Reinforcement Learning and CFD to support decision making

This talk presents recent work combining computational fluid dynamics (CFD), advanced numerical methods, and reinforcement learning for flow and energyrelated problems. The focus is on data-driven optimization strategies based on high-fidelity simulations, stabilized finite element methods, and adaptive anisotropic meshing. Several applications will be discussed, including reinforcement-learning approaches for flow and thermal systems. In particular, recent work will be presented on the optimisation of industrial furnaces using reinforcement learning coupled with CFD-based simulations, as well as a framework for the optimization of photovoltaic panel configurations under strong wind conditions. In the latter case, the control problem is formulated as a reinforcement learning task in which the agent interacts with a CFD environment to identify panel arrangements that reduce aerodynamic loads and flow-induced fluctuations. The presentation will discuss the numerical framework, optimization methodology, and perspectives for data-driven control of complex fluid and thermal systems.