arXiv subjects

Defne E. Ozan

Publications and source records attributed to Defne E. Ozan.

6 recordsLinked to original sources

arXiv2026

Adjoint-based optimization with quantized local reduced-order models for spatiotemporally chaotic systems

We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based optimization. We employ the methodology in a variational data assimilation problem for the chaotic Kuramoto-Sivashinsky equation and show that it successfully reconstructs the full trajectory for up to 0.25 Lyapunov times given full state measurements at the final time. The proposed algorithm provides 3.5 times speed-up when compared to the full-order model. The proposed method opens up new possibilities for the reduced order modelling of spatiotemporally chaotic systems.

nlin.CD↗

arXiv2025

Data-assimilated model-informed reinforcement learning

The control of spatio-temporally chaos is challenging because of high dimensionality and unpredictability. Model-free reinforcement learning (RL) discovers optimal control policies by interacting with the system, typically requiring observations of the full physical state. In practice, sensors often provide only partial and noisy measurements (observations) of the system. The objective of this paper is to develop a framework that enables the control of chaotic systems with partial and noisy observability. The proposed method, data-assimilated model-informed reinforcement learning (DA-MIRL), integrates (i) low-order models to approximate high-dimensional dynamics; (ii) sequential data assimilation to correct the model prediction when observations become available; and (iii) an off-policy actor-critic RL algorithm to adaptively learn an optimal control strategy based on the corrected state estimates. We test DA-MIRL on the spatiotemporally chaotic solutions of the Kuramoto-Sivashinsky equation. We estimate the full state of the environment with (i) a physics-based model, here, a coarse-grained model; and (ii) a data-driven model, here, the control-aware echo state network, which is proposed in this paper. We show that DA-MIRL successfully estimates and suppresses the chaotic dynamics of the environment in real time from partial observations and approximate models. This work opens opportunities for the control of partially observable chaotic systems.

eess.SY↗

arXiv2025

Data-Assimilated Model-Based Reinforcement Learning for Partially Observed Chaotic Flows

The goal of many applications in energy and transport sectors is to control turbulent flows. However, because of chaotic dynamics and high dimensionality, the control of turbulent flows is exceedingly difficult. Model-free reinforcement learning (RL) methods can discover optimal control policies by interacting with the environment, but they require full state information, which is often unavailable in experimental settings. We propose a data-assimilated model-based RL (DA-MBRL) framework for systems with partial observability and noisy measurements. Our framework employs a control-aware Echo State Network for data-driven prediction of the dynamics, and integrates data assimilation with an Ensemble Kalman Filter for real-time state estimation. An off-policy actor-critic algorithm is employed to learn optimal control strategies from state estimates. The framework is tested on the Kuramoto-Sivashinsky equation, demonstrating its effectiveness in stabilizing a spatiotemporally chaotic flow from noisy and partial measurements.

eess.SY↗

arXiv2024

Data-driven computation of adjoint sensitivities without adjoint solvers: An application to thermoacoustics

Adjoint methods have been the pillar of gradient-based optimization for decades. They enable the accurate computation of a gradient (sensitivity) of a quantity of interest with respect to all system's parameters in one calculation. When the gradient is embedded in an optimization routine, the quantity of interest can be optimized for the system to have the desired behaviour. Adjoint methods require the system's governing equations and their Jacobian. We propose a computational strategy to infer the adjoint sensitivities from data when the governing equations might be unknown (or partly unknown), and noise might be present. The key component of this strategy is an echo state network, which learns the dynamics of nonlinear regimes with varying parameters, and evolves dynamically via a hidden state. Although the framework is general, we focus on thermoacoustics governed by nonlinear and time-delayed systems. First, we show that a parameter-aware Echo State Network (ESN) infers the parameterized dynamics. Second, we derive the adjoint of the ESN to compute the sensitivity to parameters and initial conditions. Third, we propose the Thermoacoustic Echo State Network (T-ESN), which embeds the physical knowledge in the network architecture. Fourth, we apply the framework to a variety of nonlinear thermoacoustic regimes of a prototypical system. We show that the T-ESN accurately infers the correct adjoint sensitivities of the time-averaged acoustic energy with respect to the flame parameters. The results are robust to noisy data, from periodic, through quasiperiodic, to chaotic regimes. A single network predicts the nonlinear bifurcations on unseen scenarios, and so the inferred adjoint sensitivities are employed to suppress an instability via steepest descent. This work opens new possibilities for gradient-based data-driven design optimization.

physics.flu-dyn↗

arXiv2024

Adjoint Sensitivities of Chaotic Flows without Adjoint Solvers: A Data-Driven Approach

In one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system's parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which can be a cumbersome task and is code-specific. To propose an adjoint solver that is not code-specific, we develop a data-driven strategy. We demonstrate its application on the computation of gradients of long-time averages of chaotic flows. First, we deploy a parameter-aware echo state network (ESN) to accurately forecast and simulate the dynamics of a dynamical system for a range of system's parameters. Second, we derive the adjoint of the parameter-aware ESN. Finally, we combine the parameter-aware ESN with its adjoint version to compute the sensitivities to the system parameters. We showcase the method on a prototypical chaotic system. Because adjoint sensitivities in chaotic regimes diverge for long integration times, we analyse the application of ensemble adjoint method to the ESN. We find that the adjoint sensitivities obtained from the ESN match closely with the original system. This work opens possibilities for sensitivity analysis without code-specific adjoint solvers.

cs.LG↗

arXiv2022

Kernel-Based Identification of Local Limit Cycle Dynamics with Linear Periodically Parameter-Varying Models

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be modelled as systems experiencing limit cycle behavior. The goal of this work is to identify from data, the local dynamics around the limit cycle using linear periodically parameter-varying models. Using a coordinate transformation onto transversal surfaces, the dynamics are decomposed into two parts: one along the limit cycle, and one on the transversal surfaces. Then, the model is identified from trajectory data using kernel-based methods with a periodic kernel design. The kernel-based model is extended to also account for variations in system parameters associated with different operating conditions. The performance of the proposed identification method is demonstrated on a benchmark nonlinear system and on a simplified airborne wind energy model. The method provides accurate model parameter estimation, compared to the analytical linearization, and good prediction capability.

eess.SY↗