Solving Turbulent Rayleigh-Bénard Convection using Fourier Neural Operators

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO surrogates to two popular surrogates used in fluid dynamics: the Dynamic Mode Decomposition and the Linearly-Recurrent Autoencoder Network. We regard Direct Numerical Simulations (DNS) of the RBC equations as the ground truth on which the models are trained and evaluated in different settings. The FNO performs favorably when compared to the DMD and LRAN and its predictions are fast and highly accurate for this task. Additionally, we show its zero-shot super-resolution ability for the convection dynamics. The FNO model has a high potential to be used in downstream tasks such as flow control in RBC.

Adaptive Kinematic Modeling for Improved Hand Posture Estimates Using a Haptic Glove

Most commercially available haptic gloves compromise the accuracy of hand-posture measurements in favor of a simpler design with fewer sensors. While inaccurate posture data is often sufficient for the task at hand in biomedical settings such as VR-therapy-aided rehabilitation, measurements should be as precise as possible to digitally recreate hand postures as accurately as possible. With these applications in mind, we have added extra sensors to the commercially available Dexmo haptic glove by Dexta Robotics and applied kinematic models of the haptic glove and the user's hand to improve the accuracy of hand-posture measurements. In this work, we describe the augmentations and the kinematic modeling approach. Additionally, we present and discuss an evaluation of hand posture measurements as a proof of concept.

Koopman-Based Surrogate Modelling of Turbulent Rayleigh-Bénard Convection

Several related works have introduced Koopman-based Machine Learning architectures as a surrogate model for dynamical systems. These architectures aim to learn non-linear measurements (also known as observables) of the system's state that evolve by a linear operator and are, therefore, amenable to model-based linear control techniques. So far, mainly simple systems have been targeted, and Koopman architectures as reduced-order models for more complex dynamics have not been fully explored. Hence, we use a Koopman-inspired architecture called the Linear Recurrent Autoencoder Network (LRAN) for learning reduced-order dynamics in convection flows of a Rayleigh B\'enard Convection (RBC) system at different amounts of turbulence. The data is obtained from direct numerical simulations of the RBC system. A traditional fluid dynamics method, the Kernel Dynamic Mode Decomposition (KDMD), is used to compare the LRAN. For both methods, we performed hyperparameter sweeps to identify optimal settings. We used a Normalized Sum of Square Error measure for the quantitative evaluation of the models, and we also studied the model predictions qualitatively. We obtained more accurate predictions with the LRAN than with KDMD in the most turbulent setting. We conjecture that this is due to the LRAN's flexibility in learning complicated observables from data, thereby serving as a viable surrogate model for the main structure of fluid dynamics in turbulent convection settings. In contrast, KDMD was more effective in lower turbulence settings due to the repetitiveness of the convection flow. The feasibility of Koopman-based surrogate models for turbulent fluid flows opens possibilities for efficient model-based control techniques useful in a variety of industrial settings.