Sepehr Maleki

Giuseppe Bruni, Sepehr Maleki, Senthil K. Krishnababu

Deep Learning methods have seen a wide range of successful applications across different industries. Up until now, applications to physical simulations such as CFD (Computational Fluid Dynamics), have been limited to simple test-cases of minor industrial relevance. This paper demonstrates the development of a novel deep learning framework for real-time predictions of the impact of manufacturing and build variations on the overall performance of axial compressors in gas turbines, with a focus on tip clearance variations. The associated scatter in efficiency can significantly increase the CO2 emissions, thus being of great industrial and environmental relevance. The proposed C(NN)FD architecture achieves in real-time accuracy comparable to the CFD benchmark. Predicting the flow field and using it to calculate the corresponding overall performance renders the methodology generalisable, while filtering only relevant parts of the CFD solution makes the methodology scalable to industrial applications.

Giuseppe Bruni, Sepehr Maleki, Senthil K. Krishnababu

Applications of deep learning to physical simulations such as Computational Fluid Dynamics have recently experienced a surge in interest, and their viability has been demonstrated in different domains. However, due to the highly complex, turbulent, and three-dimensional flows, they have not yet been proven usable for turbomachinery applications. Multistage axial compressors for gas turbine applications represent a remarkably challenging case, due to the high-dimensionality of the regression of the flow field from geometrical and operational variables. This paper demonstrates the development and application of a deep learning framework for predictions of the flow field and aerodynamic performance of multistage axial compressors. A physics-based dimensionality reduction approach unlocks the potential for flow-field predictions, as it re-formulates the regression problem from an unstructured to a structured one, as well as reducing the number of degrees of freedom. Compared to traditional "black-box" surrogate models, it provides explainability to the predictions of the overall performance by identifying the corresponding aerodynamic drivers. The model is applied to manufacturing and build variations, as the associated performance scatter is known to have a significant impact on $CO_2$ emissions, which poses a challenge of great industrial and environmental relevance. The proposed architecture is proven to achieve an accuracy comparable to that of the CFD benchmark, in real-time, for an industrially relevant application. The deployed model is readily integrated within the manufacturing and build process of gas turbines, thus providing the opportunity to analytically assess the impact on performance with actionable and explainable data.

Sepehr Maleki, Negar Pourmoazemi

Anomalies in multivariate time series often arise from temporal context and cross-channel coordination rather than isolated outliers. We present Pi-Transformer, a physics-informed transformer with two attention pathways: a data-driven series attention and a smoothly evolving prior attention that encodes temporal invariants such as scale-related self-similarity and phase synchrony. The prior acts as a stable reference that calibrates reconstruction error. During training, we pair a reconstruction objective with a divergence term that encourages agreement between the two attentions while keeping them meaningfully distinct; the prior is regularised to evolve smoothly and is lightly distilled towards dataset-level statistics. At inference, the model combines an alignment-weighted reconstruction signal (Energy) with a mismatch signal that highlights timing and phase disruptions, and fuses them into a single score for detection. Across five benchmarks (SMD, MSL, SMAP, SWaT, and PSM), Pi-Transformer achieves state-of-the-art or highly competitive F1, with particular strength on timing and phase-breaking anomalies. Case analyses show complementary behaviour of the two streams and interpretable detections around regime changes. Embedding physics-informed priors into attention yields a calibrated and robust approach to anomaly detection in complex multivariate systems. Code is publicly available at this GitHub repository\footnote{https://github.com/sepehr-m/Pi-Transformer}.

Sepehr Maleki, Negar Pourmoazemi

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we construct denoising diffusion probabilistic models from first principles. This includes the forward noising process, its closed-form marginals, the exact discrete reverse posterior, and the related variational bound. This bound simplifies to the standard noise-prediction goal used in practice. We then discuss likelihood estimation and accelerated sampling, covering DDIM, adversarially learned reverse dynamics (DDGAN), and multi-scale variants such as nested and latent diffusion, with Stable Diffusion as a canonical example. A continuous-time formulation follows, in which we derive the probability-flow ODE from the diffusion SDE via the continuity and Fokker-Planck equations, introduce flow matching, and show how rectified flows recover DDIM up to a time re-parameterisation. Finally, we treat guided diffusion, interpreting classifier guidance as a posterior score correction and classifier-free guidance as a principled interpolation between conditional and unconditional scores. Throughout, the focus is on transparent algebra, explicit intermediate steps, and consistent notation, so that readers can both follow the theory and implement the corresponding algorithms in practice.

Shafagh Abband Pashaki, Sepehr Maleki, Amir Badiee

This paper presents a capacity-constrained incentive-based demand response approach for residential smart grids. It aims to maintain electricity grid capacity limits and prevent congestion by financially incentivising end users to reduce or shift their energy consumption. The proposed framework adopts a hierarchical architecture in which a service provider adjusts hourly incentive rates based on wholesale electricity prices and aggregated residential load. The financial interests of both the service provider and end users are explicitly considered. A deep reinforcement learning approach is employed to learn optimal real-time incentive rates under explicit capacity constraints. Heterogeneous user preferences are modelled through appliance-level home energy management systems and dissatisfaction costs. Using real-world residential electricity consumption and price data from three households, simulation results show that the proposed approach effectively reduces peak demand and smooths the aggregated load profile. This leads to an approximately 22.82% reduction in the peak-to-average ratio compared to the no-demand-response case.

Afila Ajithkumar Sophiya, Akarsh K Nair, Sepehr Maleki et al.

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.

Kenechukwu Ogbuagu, Sepehr Maleki, Giuseppe Bruni et al.

The accurate prediction of flow fields around airfoils is crucial for aerodynamic design and optimisation. Computational Fluid Dynamics (CFD) models are effective but computationally expensive, thus inspiring the development of surrogate models to enable quicker predictions. These surrogate models can be based on deep learning architectures, such as Convolutional Neural Networks (CNNs), Graph Neural Networks (GNNs), and Diffusion Models (DMs). Diffusion models have shown significant promise in predicting complex flow fields. In this work, we propose FoilDiff, a diffusion-based surrogate model with a hybrid-backbone denoising network. This hybrid design combines the power of convolutional feature extraction and transformer-based global attention to generate more adaptable and accurate representations of flow structures. FoilDiff takes advantage of Denoising Diffusion Implicit Model (DDIM) sampling to optimise the efficiency of the sampling process at no additional cost to model generalisation. We used encoded representations of Reynolds number, angle of attack, and airfoil geometry to define the input space for generalisation across a wide range of aerodynamic conditions. When evaluated against state-of-the-art models, FoilDiff shows significant performance improvements, with mean prediction errors reducing by up to 85\% on the same datasets. The results have demonstrated that FoilDiff can provide both more accurate predictions and better-calibrated predictive uncertainty than existing diffusion-based models.

Giuseppe Bruni, Sepehr Maleki, Senthil K Krishnababu

The field of scientific machine learning and its applications to numerical analyses such as CFD has recently experienced a surge in interest. While its viability has been demonstrated in different domains, it has not yet reached a level of robustness and scalability to make it practical for industrial applications in the turbomachinery field. The highly complex, turbulent, and three-dimensional flows of multi-stage axial compressors for gas turbine applications represent a remarkably challenging case. This is due to the high-dimensionality of the regression of the flow-field from geometrical and operational variables, and the high computational cost associated with the large scale of the CFD domains. This paper demonstrates the development and application of a generalized deep learning framework for predictions of the flow field and aerodynamic performance of multi-stage axial compressors, also potentially applicable to any type of turbomachinery. A physics-based dimensionality reduction unlocks the potential for flow-field predictions for large-scale domains, re-formulating the regression problem from an unstructured to a structured one. The relevant physical equations are used to define a multi-dimensional physical loss function. Compared to "black-box" approaches, the proposed framework has the advantage of physically explainable predictions of overall performance, as the corresponding aerodynamic drivers can be identified on a 0D/1D/2D/3D level. An iterative architecture is employed, improving the accuracy of the predictions, as well as estimating the associated uncertainty. The model is trained on a series of dataset including manufacturing and build variations, different geometries, compressor designs and operating conditions. This demonstrates the capability to predict the flow-field and the overall performance in a generalizable manner, with accuracy comparable to the benchmark.