arXiv subjects

Taraneh Sayadi

Publications and source records attributed to Taraneh Sayadi.

At least 19 recordsLinked to original sources

arXiv2026

Data-driven modeling of hypersonic flows in chemical non-equilibrium with catalytic surfaces

Hypersonic flows involve extreme thermochemical non-equilibrium, where strong energy dissipation leads to tightly coupled chemical reactions, radiation, and energy exchange. In this regime, surface chemistry, particularly catalytic wall reactions, can significantly affect boundary-layer composition and surface heat transfer. Accurate simulations of such flows may require repeated evaluations of detailed thermochemical libraries, which represent a major computational bottleneck in high-fidelity reactive-flow simulations. To mitigate this cost, we employ the data-driven reduced-order framework introduced by Scherding et al. (2023), which combines nonlinear dimensionality reduction, community clustering, and local surrogate models to efficiently approximate high-dimensional thermochemical mappings. In this work, this framework is extended for the first time to hypersonic reactive flows with localized catalytic surface discontinuities, introducing sharp variations in wall chemistry and heat transfer. To address the increased complexity of the thermochemical state space, the dimensionality reduction method is enhanced with a Sammon-type stress penalty that mitigates topological folding of the latent manifold and improves the robustness of the clustering and surrogate stages. The resulting model accurately captures the effects of discontinuous catalytic properties, including sharp gradients in wall species mass fractions, diffusion fluxes, and surface heat transfer, while reducing the overall simulation cost by 50% without compromising accuracy.

physics.flu-dyn↗

arXiv2026

Modelisation of chaotic systems with a latent Stochastic Differential Equation

Stochastic Differential Equations (SDEs) have become a cornerstone of scientific machine learning, though they are predominantly utilized as algorithmic tools for uncertainty quantification or distribution matching. In contrast, leveraging SDEs fundamentally to model macroscopic, nonlinear physics as stochastic processes remains largely unexplored. This work introduces a probabilistic, non-intrusive reduced-order model (ROM) for chaotic dynamical systems. We argue that projecting high-dimensional nonlinear dynamics onto a low-dimensional manifold introduces irreducible uncertainty, compounded by the chaotic attractors and multi-admissible futures inherent to turbulent flows. Consequently, a chaotic system governed by a partial differential equation can be effectively modeled by an SDE in a suitable latent space. To this end, a nonlinear autoencoder is employed to map the flow field into a low-dimensional representation, within which the temporal evolution is explicitly governed by an SDE. The predictable component of the dynamics is captured by a learned drift term, while state-dependent stochasticity is absorbed by a diffusion term. We demonstrate that this probabilistic framework successfully propagates highly nonlinear states, offering a robust alternative to traditional deterministic methodologies for chaotic regimes. Ultimately, our model generates new chaotic flow trajectories that remain locally and globally consistent with the true transition kernel learned from Direct Numerical Simulation (DNS) data. Even though these generated trajectories are unique and distinct from the training set, they preserve the underlying statistics and manifolds, validating the strong generative performance and robustness of our methodology.

physics.flu-dyn↗

arXiv2026

An ensemble-variational approach for open-loop flow control

The design of effective control strategies for unsteady flows governed by complex, nonlinear dynamics remains a central challenge in fluid mechanics. Adjoint-based optimisation methods, while efficient for high-dimensional problems, require the derivation and implementation of adjoint equations and can exhibit numerical sensitivities in systems that are not smoothly differentiable. This work proposes an ensemble-variational (EnVar) framework as a non-intrusive alternative, in which cost-function gradients are approximated through a finite ensemble of perturbed control vectors, requiring no modification of the forward solver. The present approach is tailored to address high-dimensional control problems, here considering the case where the actuator is represented as a spatially distributed forcing field. The methodology is assessed on two-dimensional open-cavity flows across Reynolds regimes spanning from quasi-periodic to chaotic dynamics. In the quasi-periodic regime, the EnVar framework recovers control strategies consistent with adjoint-based optimisation, achieving significant reductions in kinetic energy fluctuations and driving the flow toward a periodic limit cycle. In the chaotic regime, the framework remains effective in estimating gradient information and mitigating flow fluctuations. Taken together, these results demonstrate that the EnVar method constitutes a computationally efficient, parallelisable, and non-intrusive alternative to adjoint-based approaches for high-dimensional flow optimisation across a broad range of unsteady and chaotic regimes.

physics.flu-dyn↗

arXiv2026

Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilation

We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse observations of the full system. The architecture employs an encode-process-decode structure: a Variational Autoencoder (VAE) to perform dimensionality reduction, and a transformer network to evolve the latent states and model the dynamics. The ROM is parameterized by an external control variable, the Reynolds number in the Navier-Stokes setting, with the transformer exploiting attention mechanisms to capture both temporal dependencies and parameter effects. The probabilistic VAE enables stochastic sampling of trajectory ensembles, providing predictive means and uncertainty quantification through the first two moments. After initial training on a limited set of dynamical regimes, the model is adapted to out-of-sample parameter regions using only sparse data. Its probabilistic formulation naturally supports ensemble generation, which we employ within an ensemble Kalman filtering framework to assimilate data and reconstruct full-state trajectories from minimal observations. We further show that, for the dynamical system considered, the dominant source of error in out-of-sample forecasts stems from distortions of the latent manifold rather than changes in the latent dynamics. Consequently, retraining can be limited to the autoencoder, allowing for a lightweight, computationally efficient adaptation procedure with very sparse fine-tuning data.

cs.LG↗

arXiv2025

HFNO: an interpretable data-driven decomposition strategy for turbulent flows

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often constitute an obstacle to physical interpretability. This work introduces Hierarchical Fourier Neural Operators (HFNOs), a novel FNO-based architecture tailored for reduced-order modeling of turbulent fluid flows, designed to enhance interpretability by explicitly separating fluid behavior across scales. The proposed architecture processes wavenumber bins in parallel, enabling the approximation of dispersion relations and non-linear interactions. Inputs are lifted to a higher-dimensional space, Fourier-transformed, and partitioned into wavenumber bins. Each bin is processed by a Fully Connected Neural Network (FCNN), with outputs subsequently padded, summed, and inverse-transformed back into physical space. A final transformation refines the output in physical space as a correction model, by means of one of the following architectures: Convolutional Neural Network (CNN) and Echo State Network (ESN). We evaluate the proposed model on a series of increasingly complex dynamical systems: first on the one-dimensional Kuramoto-Sivashinsky equation, then on the two-dimensional Kolmogorov flow, and finally on the prediction of wall shear stress in turbulent channel flow, given the near-wall velocity field. In all test cases, the model demonstrates its ability to decompose turbulent flows across various scales, opening up the possibility of increased interpretability and multiscale modeling of such flows.

physics.flu-dyn↗

arXiv2025

Leveraging Scale Separation and Stochastic Closure for Data-Driven Prediction of Chaotic Dynamics

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct numerical simulation (DNS) applied to real-world turbulent applications. Consequently, extensive research has focused on analysing turbulent flows from a data-driven perspective. However, due to the complex and chaotic nature of these systems, traditional models often become unstable as they accumulate errors through autoregression, severely degrading even short-term predictions. To overcome these limitations, we propose a purely stochastic approach that separately addresses the evolution of large-scale coherent structures and the closure of high-fidelity statistical data. To this end, the dynamics of the filtered data (i.e. coherent motion) are learnt using an autoregressive model. This combines a VAE and Transformer architecture. The VAE projection is probabilistic, ensuring consistency between the model's stochasticity and the flow's statistical properties. To recover high-fidelity velocity fields from the filtered latent space, Gaussian Process (GP) regression is employed. This strategy has been tested in the context of a Kolmogorov flow exhibiting chaotic behaviour analogous to real-world turbulence. We compare the performance of our model with state-of-the-art probabilistic baselines, including a VAE and a diffusion model. We demonstrate that our Gaussian process-based closure outperforms these baselines in capturing first and second moment statistics in this particular test bed, providing robust and adaptive confidence intervals.

physics.flu-dyn↗

arXiv2025

Mori-Zwanzig latent space Koopman closure for nonlinear autoencoder

The Koopman operator presents an attractive approach to achieve global linearization of nonlinear systems, making it a valuable method for simplifying the understanding of complex dynamics. While data-driven methodologies have exhibited promise in approximating finite Koopman operators, they grapple with various challenges, such as the judicious selection of observables, dimensionality reduction, and the ability to predict complex system behaviours accurately. This study presents a novel approach termed Mori-Zwanzig autoencoder (MZ-AE) to robustly approximate the Koopman operator in low-dimensional spaces. The proposed method leverages a nonlinear autoencoder to extract key observables for approximating a finite invariant Koopman subspace and integrates a non-Markovian correction mechanism using the Mori-Zwanzig formalism. Consequently, this approach yields an approximate closure of the dynamics within the latent manifold of the nonlinear autoencoder, thereby enhancing the accuracy and stability of the Koopman operator approximation. Demonstrations showcase the technique's improved predictive capability for flow around a cylinder. It also provides a low dimensional approximation for Kuramoto-Sivashinsky (KS) with promising short-term predictability and robust long-term statistical performance. By bridging the gap between data-driven techniques and the mathematical foundations of Koopman theory, MZ-AE offers a promising avenue for improved understanding and prediction of complex nonlinear dynamics.

cs.LG↗

arXiv2025

UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise well across different regimes, but also provide a measure of confidence in their predictions. While recent data-driven approaches have begun to address nonlinear reduction techniques to improve predictions in transient environments, challenges remain in terms of robustness and parametrisation. In this work, we present a nonlinear reduction strategy specifically designed for transient flows that incorporates parametrisation and uncertainty quantification. Our reduction strategy features a variational auto-encoder (VAE) that uses variational inference for confidence measurement. We use a latent space transformer that incorporates recent advances in attention mechanisms to predict dynamical systems. Attention's versatility in learning sequences and capturing their dependence on external parameters enhances generalisation across a wide range of dynamics. Prediction, coupled with confidence, enables more informed decision making and addresses the need for more robust models. In addition, this confidence is used to cost-effectively sample the parameter space, improving model performance a priori across the entire parameter space without requiring evaluation data for the entire domain.

cs.LG↗

arXiv2025

Adjoint-based optimization of the Rayleigh-B\'enard instability with melting boundary

In this work, we propose an adjoint-based optimization procedure to control the onset of the Rayleigh-B\'enard instability with a melting front. A novel cut cell method is used to solve the Navier-Stokes equations in the Boussinesq approximation and the convection-diffusion equation in the fluid layer, as well as the heat equation in the solid phase. To track the interface we use the level set method where its evolution is simply governed by an advection equation. An incomplete continuous adjoint problem is then derived by treating the velocity field obtained from the forward problem as a known variable in the adjoint convection-diffusion equation, thereby avoiding the need to solve a Navier-Stokes adjoint in the fluid phase. To the best of our knowledge, this provides the first adjoint-based optimization framework for Rayleigh-B\'enard instability with a melting boundary. Two optimization problems, together with a comparison against a derivative-free particle-swarm method, demonstrate that the proposed incomplete adjoint yields gradients accurate enough to control the front shape while reducing the number of expensive function evaluations by about an order of magnitude.

math-ph↗

arXiv2024

Equation-informed data-driven identification of flow budgets and dynamics

Computational Fluid Dynamics (CFD) is an indispensable method of fluid modelling in engineering applications, reducing the need for physical prototypes and testing for tasks such as design optimisation and performance analysis. Depending on the complexity of the system under consideration, models ranging from low to high fidelity can be used for prediction, allowing significant speed-up. However, the choice of model requires information about the actual dynamics of the flow regime. Correctly identifying the regions/clusters of flow that share the same dynamics has been a challenging research topic to date. In this study, we propose a novel hybrid approach to flow clustering. It consists of characterising each sample point of the system with equation-based features, i.e. features are budgets that represent the contribution of each term from the original governing equation to the local dynamics at each sample point. This was achieved by applying the Sparse Identification of Nonlinear Dynamical systems (SINDy) method pointwise to time evolution data. The method proceeds with equation-based clustering using the Girvan-Newman algorithm. This allows the detection of communities that share the same physical dynamics. The algorithm is implemented in both Eulerian and Lagrangian frameworks. In the Lagrangian, i.e. dynamic approach, the clustering is performed on the trajectory of each point, allowing the change of clusters to be represented also in time. The performance of the algorithm is first tested on a flow around a cylinder. The construction of the dynamic clusters in this test case clearly shows the evolution of the wake from the steady state solution through the transient to the oscillatory solution. Dynamic clustering was then successfully tested on turbulent flow data. Two distinct and well-defined clusters were identified and their temporal evolution was reconstructed.

physics.flu-dyn↗

arXiv2023

RONAALP: Reduced-Order Nonlinear Approximation with Active Learning Procedure

Many engineering applications rely on the evaluation of expensive, non-linear high-dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order Nonlinear Approximation with Active Learning Procedure) to incrementally learn a fast and accurate reduced-order surrogate model of a target function on-the-fly as the application progresses. First, the combination of nonlinear auto-encoder, community clustering and radial basis function networks allows to learn an efficient and compact surrogate model with limited training data. Secondly, the active learning procedure overcome any extrapolation issue when evaluating the surrogate model outside of its initial training range during the online stage. This results in generalizable, fast and accurate reduced-order models of high-dimensional functions. The method is demonstrated on three direct numerical simulations of hypersonic flows in chemical nonequilibrium. Accurate simulations of these flows rely on detailed thermochemical gas models that dramatically increase the cost of such calculations. Using RONAALP to learn a reduced-order thermodynamic model surrogate on-the-fly, the cost of such simulation was reduced by up to 75% while maintaining an error of less than 10% on relevant quantities of interest.

physics.flu-dyn↗

arXiv2023

Data-driven framework for input/output lookup tables reduction: Application to hypersonic flows in chemical non-equilibrium

In this paper, we present a novel model-agnostic machine learning technique to extract a reduced thermochemical model for reacting hypersonic flows simulation. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on a simulation of a hypersonic flat-plate boundary layer with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by 50% while maintaining overall accuracy.

physics.flu-dyn↗

arXiv2022

A Conservative Cartesian Cut Cell Method for the Solution of the Incompressible Navier-Stokes Equations on Staggered Meshes

The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods however introduce new challenges, as the formulation of accurate and well-posed discrete operators becomes nontrivial. Here, a conservative cartesian cut cell method is proposed for the solution of the incompressible Navier--Stokes equation on staggered Cartesian grids. Emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, a divergence is proposed and shown to also be skew-symmetric as long as the divergence-free condition is satisfied, ensuring mass, momentum and kinetic energy conservation (the latter in the inviscid limit). For viscous transport, conservative and symmetric operators are proposed for Dirichlet boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The cut-cell discretization possesses the much desired summation-by-parts (SBP) properties. In addition, it is fully conservative, mathematically provably stable and supports arbitrary geometries. The accuracy and robustness of the method are then demonstrated with flows past a circular cylinder and an airfoil.

physics.comp-ph↗

arXiv2022

Symmetry-Aware Autoencoders: s-PCA and s-nlPCA

Nonlinear principal component analysis (NLPCA) via autoencoders has attracted attention in the dynamical systems community due to its larger compression rate when compared to linear principal component analysis (PCA). These model reduction methods experience an increase in the dimensionality of the latent space when applied to datasets that exhibit invariant samples due to the presence of symmetries. In this study, we introduce a novel machine learning embedding for autoencoders, which uses Siamese networks and spatial transformer networks to account for discrete and continuous symmetries, respectively. The Siamese branches autonomously find a fundamental domain to which all samples are transformed, without introducing human bias. The spatial transformer network discovers the optimal slicing template for continuous translations so that invariant samples are aligned in the homogeneous direction. Thus, the proposed symmetry-aware autoencoder is invariant to predetermined input transformations. This embedding can be employed with both linear and nonlinear reduction methods, which we term symmetry-aware PCA (s-PCA) and symmetry-aware NLPCA (s-NLPCA). We apply the proposed framework to the Kolmogorov flow to showcase the capabilities for a system exhibiting both a continuous symmetry as well as discrete symmetries.

physics.flu-dyn↗

arXiv2022

Development of a high-fidelity computational tool for chemically reacting hypersonic flow simulations

In this paper, we present a methodology to achieve high-fidelity simulations of chemically reacting hypersonic flows and demonstrate our numerical solver's capabilities on a selection of configurations. The numerical tools are developed based on previous in-house codes for high-speed simulations with improvements in both numerical and physical modeling. Additionally, a modular, open-source library is coupled with the flow solver for modeling real-gas effects in variable atmospheric mixtures. Verification against literature is done for canonical flat-plate boundary layers with various choices for gas modeling, with excellent agreement observed in all cases. The implementation of an artificial-diffusivity shock-capturing numerical scheme is then verified for supersonic shockwave--boundary-layer interaction (SBLI) cases and the improved code's capabilities are demonstrated for the cases of hypersonic SBLI and a sonic jet injection in a hypersonic crossflow, at higher enthalpy levels than those previously investigated. The results show excellent agreement with previous observations in the literature. The work presented in this paper demonstrates the range of applications that can be investigated with this tool, highlights the need for accurate physicochemical modeling, and paves the way for addressing increasingly more complex configurations and flows.

physics.flu-dyn↗

arXiv2022

A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation

In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers' equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.

physics.comp-ph↗

arXiv2022

Adjoint-based optimization of two-dimensional Stefan problems

A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary (cut cell) method coupled with an implicit time-advancement scheme is employed to solve the heat equation. A conservative implicit-explicit scheme is then used for solving the level set transport equation. The resulting numerical framework is validated with respect to existing analytical solutions of the forward Stefan problem. An adjoint-based algorithm is then employed to efficiently compute the gradient used in the optimisation algorithm (L-BFGS). The algorithm follows a continuous adjoint framework, where adjoint equations are formally derived using shape calculus and transport theorems. A wide range of control objectives are presented, and the results show that using parameterised boundary actuation leads to effective control strategies in order to suppress interfacial instabilities or to maintain a desired crystal shape.

math-ph↗

arXiv2020

Adjoint-Based Sensitivity Analysis of Steady Char Burnout

Simulations of pulverised coal combustion rely on various models, required in order to correctly approximate the flow, chemical reactions, and behavior of solid particles. These models, in turn, rely on multiple model parameters, which are determined through experiments or small-scale simulations and contain a certain level of uncertainty. The competing effects of transport, particle physics, and chemistry give rise to various scales and disparate dynamics, making it a very challenging problem to analyse. Therefore, the steady combustion process of a single solid particle is considered as a starting point for this study. As an added complication, the large number of parameters present in such simulations makes a purely forward approach to sensitivity analysis very expensive and almost infeasible. Therefore, the use of adjoint-based algorithms, to identify and quantify the underlying sensitivities and uncertainties, is proposed. This adjoint framework bears a great advantage in this case, where a large input space is analysed, since a single forward and backward sweep provides sensitivity information with respect to all parameters of interest. In order to investigate the applicability of such methods, both discrete and continuous adjoints are considered, and compared to the conventional approaches, such as finite differences, and forward sensitivity analysis. Various quantities of interest are considered, and sensitivities with respect to the relevant combustion parameters are reported for two different freestream compositions, describing air and oxy-atmospheres. This study serves as a benchmark for future research, where unsteady and finally turbulent cases will be considered.

physics.chem-ph↗