Tarcísio Déda

Graph neural networks (GNNs) show promise as surrogate models for fluid flows, being typically deployed on the same meshes used by numerical solvers. In many engineering applications, however, accurately predicting only a subset of the system's degrees of freedom is sufficient. Motivated by this, we explore GNNs deployed on coarse meshes as reduced-order models (ROMs) for parameterized fluid flows, using a confined cylinder and an unevenly heated cavity across a range of Reynolds and Rayleigh numbers as test beds. Model performance is assessed through prediction accuracy at sparse probe locations, as well as identification and state-estimation tasks. Our results show that models trained on coarse meshes achieve comparable or superior accuracy to those trained on finer meshes, while offering faster training and lower memory requirements. Additionally, we propose an adaptive sampling strategy for constructing training datasets, which reduces maximum errors by up to 2.5× relative to implementations utilizing a uniform sampling strategy. Leveraging the reduced cost of coarse-mesh training, we employ unrolling during training, yielding more accurate models within the same computational cost. Combined, these techniques reduce errors by 57% compared to baselines trained on fine meshes with uniform sampling, demonstrating that coarse-mesh GNNs are a viable and efficient alternative for ROMs of parameterized systems.

Neural network observers (NNOs) are proposed for online estimation of fluid flows, addressing a key challenge in flow control: obtaining flow states online from a limited set of sparse and noisy sensor data. For this task, we propose a generalisation of the classical Luenberger observer. In the present framework, the estimation loop is composed of subsystems modelled as neural networks (NNs). By combining flow information from selected probes and a neural network surrogate model (NNSM) of the flow system, we train NNOs capable of fusing information to provide the best estimation of the states, that can in turn be fed back to a neural network controller (NNC). The NNO capabilities are demonstrated for three nonlinear dynamical systems. First, a variation of the Kuramoto–Sivashinsky (KS) equation with control inputs is studied, where variables are sparsely probed. We show that the NNO is able to track states even when probes are contaminated with random noise or with sensors at insufficient sample rates to match the control time step. Then, a confined cylinder flow is investigated, where velocity signals along the cylinder wake are estimated by using a small set of wall pressure sensors. In both the KS and cylinder problems, we show that the estimated states can be used to enable closed-loop control, taking advantage of stabilising NNCs. Finally, we present a legacy dataset of a turbulent boundary layer experiment, where convolutional NNs are employed to implement the models required for the estimation loop. We show that, by combining low-resolution noise-corrupted sensor data with an imperfect NNSM, it is possible to produce more accurate and robust estimates. Our approach presents better robustness to noise when compared with direct reconstructions via super-resolution NNs and predictions from graph NNs and Fourier neural operators.

This work presents a methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated in four different study cases: the Lorenz system, a modified version of the Kuramoto-Sivashinsky equation, a streamwise-periodic two-dimensional channel flow, and a confined cylinder flow. Neural networks are trained as models to capture the complex system dynamics and estimate equilibrium points through a Newton method, enabled by back-propagation. These neural network surrogate models (NNSMs) are leveraged to train a second neural network, which is designed to act as a stabilizing closed-loop controller. The training process employs a recurrent approach, whereby the NNSM and the neural network controller are chained in closed loop along a finite time horizon. By cycling through phases of combined random open-loop actuation and closed-loop control, an iterative training process is introduced to overcome the lack of data near equilibrium points. This approach improves the accuracy of the models in the most critical region for achieving stabilization. Through the use of L1 regularization within loss functions, the NNSMs can also guide optimal sensor placement, reducing the number of sensors from an initial candidate set. The data sets produced during the iterative training process are also leveraged for conducting a linear stability analysis through a modified dynamic mode decomposition approach. The results demonstrate the effectiveness of computationally inexpensive neural networks in modeling, controlling, and enabling stability analysis of nonlinear systems, providing insights into the system behavior and offering potential for stabilization of complex fluid systems.

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the Kuramoto-Sivashinsky equation, a streamwise-periodic 2D channel flow, and a confined cylinder flow. Neural networks are trained as models to capture the complex system dynamics and estimate equilibrium points through a Newton method, enabled by backpropagation. These neural network surrogate models (NNSMs) are leveraged to train a second neural network, which is designed to act as a stabilizing closed-loop controller. The training process employs a recurrent approach, whereby the NNSM and the neural network controller (NNC) are chained in closed loop along a finite time horizon. By cycling through phases of combined random open-loop actuation and closed-loop control, an iterative training process is introduced to overcome the lack of data near equilibrium points. This approach improves the accuracy of the models in the most critical region for achieving stabilization. Through the use of L1 regularization within loss functions, the NNSMs can also guide optimal sensor placement, reducing the number of sensors from an initial candidate set. The datasets produced during the iterative training process are also leveraged for conducting a linear stability analysis through a modified dynamic mode decomposition approach. The results demonstrate the effectiveness of computationally inexpensive neural networks in modeling, controlling, and enabling stability analysis of nonlinear systems, providing insights into the system behaviour and offering potential for stabilization of complex fluid systems.

Extremum seeking control (ESC) and its slope seeking generalization are applied in a high-fidelity flow simulation framework for reduction of acoustic noise generated by a NACA0012 airfoil. Two Rey...

This article reports a mechatronic project of a two- wheeled inverted pendulum system in a modular approach. A mathematical model for the three-dimensional plant was obtained by using Lagrange mechanics, and a turning control module was incorporated so the system could perform free movement along the plane. This controller allowed the system to achieve rapid turning speed responses, with rising times less than 1s, overshoots of around 4% and null steady-state error. The overall system was then simulated so the reference signals were generated by different methods using five approaches: (i) direct leaning reference input with turning speed input; (ii) direct longitudinal speed reference input with turning speed input; (iii) limited speed by bounding the leaning reference input at high speeds; (iv) independent speed control for each wheel; and (v) automatic trajectory following. A stabilization time of 5.5s for the maximum longitudinal speed of 5.5m/s was obtained by using the bounded torque approach. The results showed that every performance requirement in terms of each control module were fulfilled when working with non-extreme situations.