Scientific machine learning for modelling and optimisation of nonlinear partial differential equations in fluids
File(s)
Author(s)
Ozan, Defne Ege
Type
Thesis
Abstract
The prediction and control of flow and acoustic systems present a fundamental challenge due to the high-dimensional, nonlinear and chaotic dynamics with multi-physics interactions. This thesis proposes scientific machine learning methods for modelling these systems, reconstruction of their full state from partial observations, and their optimisation. First, we model thermoacoustic dynamics from synthetic sensor data. We develop Galerkin neural networks, which learn from data, whilst being constrained with prior knowledge of the acoustics by (i) employing periodic activations; (ii) a physics-informed loss in the training; and (iii) a hard-constrained architecture in a physically-motivated solution space. We test the network on a prototypical nonlinear time-delayed model, i.e., the Rijke tube, and a higher-fidelity model. We accurately reconstruct the velocity from only pressure measurements. Second, we infer gradients (sensitivities) from data with the adjoint method. The parameter-aware echo state network learns the dynamics of nonlinear regimes with varying parameters. We derive its adjoint, and infer the climate sensitivity of the chaotic Lorenz system to the system's parameters. The time-delayed thermoacoustic echo state network improves generalisability on the Rijke tube, and accurately infers the adjoint sensitivities of the acoustic energy with respect to the flame parameters and initial conditions, whilst identifying local bifurcations. We suppress a nonlinear oscillation via gradient-based optimisation. Third, we enable the active control of chaotic systems with partial observability. Data-assimilated model-informed reinforcement learning 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 reinforcement learning algorithm to discover an optimal control strategy. We test the framework on the chaotic solutions of the Kuramoto-Sivashinsky equation. We estimate its full state with (i) a physics-based coarse-grained model; and (ii) the control-aware echo state network to stabilise its chaotic dynamics.
Version
Open Access
Date Issued
2025-08-09
Date Awarded
2026-02-01
License URL
Advisor
Magri, Luca
Sponsor
European Research Council
UK Research and Innovation
Grant Number
PhyCo (949388)
AI for Net Zero (EP/Y005619/1)
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)