Adil Rasheed

Oluwaleke Yusuf, Adil Rasheed, Frank Lindseth

Passenger count data from public transit systems reveals urban mobility patterns and is essential for planning, operation, and optimisation. However, non-linear spatiotemporal interdependencies across stops and lines make modelling and prediction challenging. Existing approaches often rely on fixed temporal, spatial, or stop-level formulations, limiting their ability to capture within-trip evolution and network context. This study proposes SMT-GraphFormer, a spatiotemporal multi-task graph transformer that frames trip-level transit prediction as sequence-to-sequence modelling. Given a line's stop sequence and trip-level context, the model predicts successive boarding and alighting counts, with delay and dwell time treated as encoder-side surrogate tasks. Key components include graph embeddings for multi-relational stop similarity, a context encoder for weather and temporal information, and a multi-gate mixture-of-experts module that produces task-specific decoder representations for boarding and alighting predictions. Evaluation on public bus transit data from Trondheim, Norway, shows that SMT-GraphFormer outperforms stop-level tabular benchmarks, with ablation studies examining each component's contribution. The sequential formulation yields substantial gains on alighting prediction ($+$0.24 in $R^2$) and consistent improvements on boarding, delay, and dwell, confirming the value of explicit trip-level sequential bias and inter-target dependencies. These findings demonstrate the potential of transformer-based sequence modelling for capturing complex spatiotemporal dynamics in public transit and underscore the value of architectures tailored to transit data rather than off-the-shelf tabular models. The proposed framework provides a horizon-agnostic basis for scenario analysis in digital twin environments, supporting informed decision-making by planners and transit operators.

Haakon Robinson, Suraj Pawar, Adil Rasheed et al.

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data efficiency and sensitivity to hyperparameters and initialisation. This work demonstrates that injection of partially known information at an intermediate layer in a DNN can improve model accuracy, reduce model uncertainty, and yield improved convergence during the training. The value of these physics-guided neural networks has been demonstrated by learning the dynamics of a wide variety of nonlinear dynamical systems represented by five well-known equations in nonlinear systems theory: the Lotka-Volterra, Duffing, Van der Pol, Lorenz, and Henon-Heiles systems.

Florian Stadtman, Adil Rasheed, Trond Kvamsdal et al.

This article presents a comprehensive overview of the digital twin technology and its capability levels, with a specific focus on its applications in the wind energy industry. It consolidates the definitions of digital twin and its capability levels on a scale from 0-5; 0-standalone, 1-descriptive, 2-diagnostic, 3-predictive, 4-prescriptive, 5-autonomous. It then, from an industrial perspective, identifies the current state of the art and research needs in the wind energy sector. The article proposes approaches to the identified challenges from the perspective of research institutes and offers a set of recommendations for diverse stakeholders to facilitate the acceptance of the technology. The contribution of this article lies in its synthesis of the current state of knowledge and its identification of future research needs and challenges from an industry perspective, ultimately providing a roadmap for future research and development in the field of digital twin and its applications in the wind energy industry.

Sindre Stenen Blakseth, Adil Rasheed, Trond Kvamsdal et al.

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately, the two most commonly used modeling approaches, physics-based modeling (PBM) and data-driven modeling (DDM) fail to satisfy all these requirements. In the current work, we demonstrate how a hybrid approach combining the best of PBM and DDM can result in models which can outperform them both. We do so by combining partial differential equations based on first principles describing partially known physics with a black box DDM, in this case, a deep neural network model compensating for the unknown physics. First, we present a mathematical argument for why this approach should work and then apply the hybrid approach to model two dimensional heat diffusion problem with an unknown source term. The result demonstrates the method's superior performance in terms of accuracy, and generalizability. Additionally, it is shown how the DDM part can be interpreted within the hybrid framework to make the overall approach reliable.

Elias Mohammed Elfarri, Adil Rasheed, Omer San

A digital twin is a powerful tool that can help monitor and optimize physical assets in real-time. Simply put, it is a virtual representation of a physical asset, enabled through data and simulators, that can be used for a variety of purposes such as prediction, monitoring, and decision-making. However, the concept of digital twin can be vague and difficult to understand, which is why a new concept called "capability level" has been introduced. This concept categorizes digital twins based on their capability and defines a scale from zero to five, with each level indicating an increasing level of functionality. These levels are standalone, descriptive, diagnostic, predictive, prescriptive, and autonomous. By understanding the capability level of a digital twin, we can better understand its potential and limitations. To demonstrate the concepts, we use a modern house as an example. The house is equipped with a range of sensors that collect data about its internal state, which can then be used to create digital twins of different capability levels. These digital twins can be visualized in virtual reality, allowing users to interact with and manipulate the virtual environment. The current work not only presents a blueprint for developing digital twins but also suggests future research directions to enhance this technology. Digital twins have the potential to transform the way we monitor and optimize physical assets, and by understanding their capabilities, we can unlock their full potential.

Erlend Torje Berg Lundby, Adil Rasheed, Ivar Johan Halvorsen et al.

Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always overparameterized and challenging to interpret due to their internal complexity. Furthermore, the optimization process to find the learned model parameters can be unstable due to the process getting stuck in local minima. In this work, we demonstrate the value of sparse regularization techniques to significantly reduce the model complexity. We demonstrate this for the case of an aluminium extraction process, which is highly nonlinear system with many interrelated subprocesses. We trained a densely connected deep neural network to model the process and then compared the effects of sparsity promoting l1 regularization on generalizability, interpretability, and training stability. We found that the regularization significantly reduces model complexity compared to a corresponding dense neural network. We argue that this makes the model more interpretable, and show that training an ensemble of sparse neural networks with different parameter initializations often converges to similar model structures with similar learned input features. Furthermore, the empirical study shows that the resulting sparse models generalize better from small training sets than their dense counterparts.

Omer San, Suraj Pawar, Adil Rasheed

In this paper, we introduce a decentralized digital twin (DDT) framework for dynamical systems and discuss the prospects of the DDT modeling paradigm in computational science and engineering applications. The DDT approach is built on a federated learning concept, a branch of machine learning that encourages knowledge sharing without sharing the actual data. This approach enables clients to collaboratively learn an aggregated model while keeping all the training data on each client. We demonstrate the feasibility of the DDT framework with various dynamical systems, which are often considered prototypes for modeling complex transport phenomena in spatiotemporally extended systems. Our results indicate that federated machine learning might be a key enabler for designing highly accurate decentralized digital twins in complex nonlinear spatiotemporal systems.

Shady E. Ahmed, Omer San, Adil Rasheed et al.

We propose a new physics guided machine learning (PGML) paradigm that leverages the variational multiscale (VMS) framework and available data to dramatically increase the accuracy of reduced order models (ROMs) at a modest computational cost. The hierarchical structure of the ROM basis and the VMS framework enable a natural separation of the resolved and unresolved ROM spatial scales. Modern PGML algorithms are used to construct novel models for the interaction among the resolved and unresolved ROM scales. Specifically, the new framework builds ROM operators that are closest to the true interaction terms in the VMS framework. Finally, machine learning is used to reduce the projection error and further increase the ROM accuracy. Our numerical experiments for a two-dimensional vorticity transport problem show that the novel PGML-VMS-ROM paradigm maintains the low computational cost of current ROMs, while significantly increasing the ROM accuracy.

Eivind Fonn, Harald van Brummelen, Trond Kvamsdal et al.

Reduced-basis methods (RB methods or RBMs) form one of the most promising techniques to deliver numerical solutions of parametrized PDEs in real-time performance with reasonable accuracy. For incompressible flow problems, RBMs based on LBB stable velocity-pressure spaces do not generally inherit the stability of the underlying high-fidelity model and, instead, additional stabilization techniques must be introduced. One way of bypassing the loss of LBB stability in the RBM is to inflate the velocity space with supremizer modes. This however deteriorates the performance of the RBM in the performance-critical online stage, as additional DOFs must be introduced to retain stability, while these DOFs do not effectively contribute to accuracy of the RB approximation. In this work we consider a velocity-only RB approximation, exploiting a solenoidal velocity basis. The solenoidal reduced basis emerges directly from the high-fidelity velocity solutions in the offline stage. By means of Piola transforms, the solenoidality of the velocity space is retained under geometric transformations, making the proposed RB method suitable also for the investigation of geometric parameters. To ensure exact solenoidality of the high-fidelity velocity solutions that constitute the RB, we consider approximations based on divergence-conforming compatible B-splines. We show that the velocity-only RB method leads to a significant improvement in computational efficiency in the online stage, and that the pressure solution can be recovered a posteriori at negligible extra cost. We illustrate the solenoidal RB approach by modeling steady two-dimensional Navier-Stokes flow around a NACA0015 airfoil at various angles of attack.

Omer San, Suraj Pawar, Adil Rasheed

A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL (MMRL) to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

Haakon Robinson, Erlend Lundby, Adil Rasheed et al.

With the ever-increasing availability of data, there has been an explosion of interest in applying modern machine learning methods to fields such as modeling and control. However, despite the flexibility and surprising accuracy of such black-box models, it remains difficult to trust them. Recent efforts to combine the two approaches aim to develop flexible models that nonetheless generalize well; a paradigm we call Hybrid Analysis and modeling (HAM). In this work we investigate the Corrective Source Term Approach (CoSTA), which uses a data-driven model to correct a misspecified physics-based model. This enables us to develop models that make accurate predictions even when the underlying physics of the problem is not well understood. We apply CoSTA to model the Hall-Héroult process in an aluminum electrolysis cell. We demonstrate that the method improves both accuracy and predictive stability, yielding an overall more trustworthy model.

Abdallah Alshantti, Damiano Varagnolo, Adil Rasheed et al.

Generative adversarial networks (GANs) have drawn considerable attention in recent years for their proven capability in generating synthetic data which can be utilised for multiple purposes. While GANs have demonstrated tremendous successes in producing synthetic data samples that replicate the dynamics of the original datasets, the validity of the synthetic data and the underlying privacy concerns represent major challenges which are not sufficiently addressed. In this work, we design a cascaded tabular GAN framework (CasTGAN) for generating realistic tabular data with a specific focus on the validity of the output. In this context, validity refers to the the dependency between features that can be found in the real data, but is typically misrepresented by traditional generative models. Our key idea entails that employing a cascaded architecture in which a dedicated generator samples each feature, the synthetic output becomes more representative of the real data. Our experimental results demonstrate that our model is capable of generating synthetic tabular data that can be used for fitting machine learning models. In addition, our model captures well the constraints and the correlations between the features of the real data, especially the high dimensional datasets. Furthermore, we evaluate the risk of white-box privacy attacks on our model and subsequently show that applying some perturbations to the auxiliary learners in CasTGAN increases the overall robustness of our model against targeted attacks.

Erlend Torje Berg Lundby, Adil Rasheed, Ivar Johan Halvorsen et al.

The exploding research interest for neural networks in modeling nonlinear dynamical systems is largely explained by the networks' capacity to model complex input-output relations directly from data. However, they typically need vast training data before they can be put to any good use. The data generation process for dynamical systems can be an expensive endeavor both in terms of time and resources. Active learning addresses this shortcoming by acquiring the most informative data, thereby reducing the need to collect enormous datasets. What makes the current work unique is integrating the deep active learning framework into nonlinear system identification. We formulate a general static deep active learning acquisition problem for nonlinear system identification. This is enabled by exploring system dynamics locally in different regions of the input space to obtain a simulated dataset covering the broader input space. This simulated dataset can be used in a static deep active learning acquisition scheme referred to as global explorations. The global exploration acquires a batch of initial states corresponding to the most informative state-action trajectories according to a batch acquisition function. The local exploration solves an optimal control problem, finding the control trajectory that maximizes some measure of information. After a batch of informative initial states is acquired, a new round of local explorations from the initial states in the batch is conducted to obtain a set of corresponding control trajectories that are to be applied on the system dynamics to get data from the system. Information measures used in the acquisition scheme are derived from the predictive variance of an ensemble of neural networks. The novel method outperforms standard data acquisition methods used for system identification of nonlinear dynamical systems in the case study performed on simulated data.

Jacob Wulff Wold, Florian Stadtmann, Adil Rasheed et al.

Atmospheric flows are governed by a broad variety of spatio-temporal scales, thus making real-time numerical modeling of such turbulent flows in complex terrain at high resolution computationally intractable. In this study, we demonstrate a neural network approach motivated by Enhanced Super-Resolution Generative Adversarial Networks to upscale low-resolution wind fields to generate high-resolution wind fields in an actual wind farm in Bessaker, Norway. The neural network-based model is shown to successfully reconstruct fully resolved 3D velocity fields from a coarser scale while respecting the local terrain and that it easily outperforms trilinear interpolation. We also demonstrate that by using appropriate cost function based on domain knowledge, we can alleviate the use of adversarial training.

Omer San, Suraj Pawar, Adil Rasheed

Physics-based models have been mainstream in fluid dynamics for developing predictive models. In recent years, machine learning has offered a renaissance to the fluid community due to the rapid developments in data science, processing units, neural network based technologies, and sensor adaptations. So far in many applications in fluid dynamics, machine learning approaches have been mostly focused on a standard process that requires centralizing the training data on a designated machine or in a data center. In this letter, we present a federated machine learning approach that enables localized clients to collaboratively learn an aggregated and shared predictive model while keeping all the training data on each edge device. We demonstrate the feasibility and prospects of such decentralized learning approach with an effort to forge a deep learning surrogate model for reconstructing spatiotemporal fields. Our results indicate that federated machine learning might be a viable tool for designing highly accurate predictive decentralized digital twins relevant to fluid dynamics.

Erlend Torje Berg Lundby, Haakon Robinsson, Adil Rasheed et al.

Neural networks are rapidly gaining interest in nonlinear system identification due to the model's ability to capture complex input-output relations directly from data. However, despite the flexibility of the approach, there are still concerns about the safety of these models in this context, as well as the need for large amounts of potentially expensive data. Aluminum electrolysis is a highly nonlinear production process, and most of the data must be sampled manually, making the sampling process expensive and infrequent. In the case of infrequent measurements of state variables, the accuracy and open-loop stability of the long-term predictions become highly important. Standard neural networks struggle to provide stable long-term predictions with limited training data. In this work, we investigate the effect of combining concatenated skip-connections and the sparsity-promoting $\ell_1$ regularization on the open-loop stability and accuracy of forecasts with short, medium, and long prediction horizons. The case study is conducted on a high-dimensional and nonlinear simulator representing an aluminum electrolysis cell's mass and energy balance. The proposed model structure contains concatenated skip connections from the input layer and all intermittent layers to the output layer, referred to as InputSkip. $\ell_1$ regularized InputSkip is called sparse InputSkip. The results show that sparse InputSkip outperforms dense and sparse standard feedforward neural networks and dense InputSkip regarding open-loop stability and long-term predictive accuracy. The results are significant when models are trained on datasets of all sizes (small, medium, and large training sets) and for all prediction horizons (short, medium, and long prediction horizons.)

Omer San, Adil Rasheed, Eda Bozdemir et al.

Digital twins are evolving into self-learning, autonomous systems that link models, data, and human interaction. Realizing their full potential depends on interoperability, standardization, and the integration of artificial intelligence and advanced computational reasoning across sectors.

Oluwaleke Yusuf, Adil Rasheed, Frank Lindseth

The growth of urban areas intensifies the need for sustainable, efficient transportation infrastructure and mobility systems, driving initiatives to enhance infrastructure and public transit while reducing traffic congestion and emissions. By utilizing real-world data, a data-driven approach can provide crucial insights for urban mobility planning and decision-making. This study explores the efficacy of leveraging telecoms data from cellular network signals for studying crowd movement patterns, focusing on Trondheim, Norway. It examines routing reports to understand the spatiotemporal dynamics of various transportation routes and modes. A data preprocessing and feature engineering framework was developed to process raw routing reports for historical analysis. This enabled the examination of geospatial trends and temporal patterns, including a comparative analysis of various transportation modes, along with public transit usage. Specific routes and areas were analyzed in-depth to compare their mobility patterns with the broader city context. The study highlights the potential of cellular network data as a resource for shaping urban transportation and mobility systems. By identifying deficiencies and potential improvements, city planners and stakeholders can foster more sustainable and effective transportation and mobility solutions.

Mohammed Ayalew Belay, Adil Rasheed, Pierluigi Salvo Rossi

Anomaly detection is increasingly becoming crucial for maintaining the safety, reliability, and efficiency of industrial systems. Recently, with the advent of digital twins and data-driven decision-making, several statistical and machine-learning methods have been proposed. However, these methods face several challenges, such as dependence on only real sensor datasets, limited labeled data, high false alarm rates, and privacy concerns. To address these problems, we propose a suite of digital twin-integrated federated learning (DTFL) methods that enhance global model performance while preserving data privacy and communication efficiency. Specifically, we present five novel approaches: Digital Twin-Based Meta-Learning (DTML), Federated Parameter Fusion (FPF), Layer-wise Parameter Exchange (LPE), Cyclic Weight Adaptation (CWA), and Digital Twin Knowledge Distillation (DTKD). Each method introduces a unique mechanism to combine synthetic and real-world knowledge, balancing generalization with communication overhead. We conduct an extensive experiment using a publicly available cyber-physical anomaly detection dataset. For a target accuracy of 80%, CWA reaches the target in 33 rounds, FPF in 41 rounds, LPE in 48 rounds, and DTML in 87 rounds, whereas the standard FedAvg baseline and DTKD do not reach the target within 100 rounds. These results highlight substantial communication-efficiency gains (up to 62% fewer rounds than DTML and 31% fewer than LPE) and demonstrate that integrating DT knowledge into FL accelerates convergence to operationally meaningful accuracy thresholds for IIoT anomaly detection.

Oluwaleke Yusuf, M. Tsaqif Wismadi, Adil Rasheed

Urban bike-sharing systems require strategic station expansion to meet growing demand. Traditional allocation approaches rely on explicit demand modelling that may not capture the urban characteristics distinguishing successful stations. This study addresses the need to exploit patterns from existing stations to inform expansion decisions, particularly in data-constrained environments. We present a data-driven framework leveraging existing stations deemed desirable by operational metrics. A hybrid denoising autoencoder (HDAE) learns compressed latent representations from multi-source grid-level features (socio-demographic, built environment, and transport network), with a supervised classification head regularising the embedding space structure. Expansion candidates are selected via greedy allocation with spatial constraints based on latent-space similarity to existing stations. Evaluation on Trondheim's bike-sharing network demonstrates that HDAE embeddings yield more spatially coherent clusters and allocation patterns than raw features. Sensitivity analyses across similarity methods and distance metrics confirm robustness. A consensus-based procedure across multiple parametrisations distils 32 high-confidence extension zones where all parametrisations agree. The results demonstrate how representation learning captures complex patterns that raw features miss, enabling evidence-based expansion planning without explicit demand modelling. The consensus procedure strengthens recommendations by requiring agreement across parametrisations, while framework configurability allows planners to incorporate operational knowledge. The methodology generalises to any location-allocation problem where existing desirable instances inform the selection of new candidates.

Andrine Elsetrønning, Adil Rasheed, Jon Bekker et al.

Lung sounds refer to the sound generated by air moving through the respiratory system. These sounds, as most biomedical signals, are non-linear and non-stationary. A vital part of using the lung sound for disease detection is discrimination between normal lung sound and abnormal lung sound. In this paper, several approaches for classifying between no-crackle and crackle lung sounds are explored. Decomposition methods such as Empirical Mode Decomposition, Ensemble Empirical Mode Decomposition, and Discrete Wavelet Transform are used along with several feature extraction techniques like Principal Component Analysis and Autoencoder, to explore how various classifiers perform for the given task. An open-source dataset downloaded from Kaggle, containing chest auscultation of varying quality is used to determine the results of using the different decomposition and feature extraction combinations. It is found that when higher-order statistical and spectral features along with the Mel-frequency cepstral coefficients are fed to the classier we get the best performance with the kNN classifier giving the best accuracy. Furthermore, it is also demonstrated that using a combination of feature selection methods one can significantly reduce the number of input features without adversely affecting the accuracy of the classifiers.

Adil Rasheed, Mikael Aleksander Jansen Shahly, Muhammad Faisal Aftab

Compressed sensing enables sparse sampling but relies on generic bases and random measurements, limiting efficiency and reconstruction quality. Optimal sensor placement uses historcal data to design tailored sampling patterns, yet its fixed, linear bases cannot adapt to nonlinear or sample-specific variations. Generative model-based compressed sensing improves reconstruction using deep generative priors but still employs suboptimal random sampling. We propose an adaptive sparse sensing framework that couples a variational autoencoder prior with reinforcement learning to select measurements sequentially. Experiments show that this approach outperforms CS, OSP, and Generative model-based reconstruction from sparse measurements.

Abdallah Alshantti, Adil Rasheed, Frank Westad

Generative models are subject to overfitting and thus may potentially leak sensitive information from the training data. In this work. we investigate the privacy risks that can potentially arise from the use of generative adversarial networks (GANs) for creating tabular synthetic datasets. For the purpose, we analyse the effects of re-identification attacks on synthetic data, i.e., attacks which aim at selecting samples that are predicted to correspond to memorised training samples based on their proximity to the nearest synthetic records. We thus consider multiple settings where different attackers might have different access levels or knowledge of the generative model and predictive, and assess which information is potentially most useful for launching more successful re-identification attacks. In doing so we also consider the situation for which re-identification attacks are formulated as reconstruction attacks, i.e., the situation where an attacker uses evolutionary multi-objective optimisation for perturbing synthetic samples closer to the training space. The results indicate that attackers can indeed pose major privacy risks by selecting synthetic samples that are likely representative of memorised training samples. In addition, we notice that privacy threats considerably increase when the attacker either has knowledge or has black-box access to the generative models. We also find that reconstruction attacks through multi-objective optimisation even increase the risk of identifying confidential samples.

Daniel Menges, Florian Stadtmann, Henrik Jordheim et al.

This paper explores the development and practical application of a predictive digital twin specifically designed for condition monitoring, using advanced mathematical models and thermal imaging techniques. Our work presents a comprehensive approach to integrating Proper Orthogonal Decomposition (POD), Robust Principal Component Analysis (RPCA), and Dynamic Mode Decomposition (DMD) to establish a robust predictive digital twin framework. We employ these methods in a real-time experimental setup involving a heated plate monitored through thermal imaging. This system effectively demonstrates the digital twin's capabilities in real-time predictions, condition monitoring, and anomaly detection. Additionally, we introduce the use of a human-machine interface that includes virtual reality, enhancing user interaction and system understanding. The primary contributions of our research lie in the demonstration of these advanced techniques in a tangible setup, showcasing the potential of digital twins to transform industry practices by enabling more proactive and strategic asset management.

Daniel Menges, Adil Rasheed

In the current data-intensive era, big data has become a significant asset for Artificial Intelligence (AI), serving as a foundation for developing data-driven models and providing insight into various unknown fields. This study navigates through the challenges of data uncertainties, storage limitations, and predictive data-driven modeling using big data. We utilize Robust Principal Component Analysis (RPCA) for effective noise reduction and outlier elimination, and Optimal Sensor Placement (OSP) for efficient data compression and storage. The proposed OSP technique enables data compression without substantial information loss while simultaneously reducing storage needs. While RPCA offers an enhanced alternative to traditional Principal Component Analysis (PCA) for high-dimensional data management, the scope of this work extends its utilization, focusing on robust, data-driven modeling applicable to huge data sets in real-time. For that purpose, Long Short-Term Memory (LSTM) networks, a type of recurrent neural network, are applied to model and predict data based on a low-dimensional subset obtained from OSP, leading to a crucial acceleration of the training phase. LSTMs are feasible for capturing long-term dependencies in time series data, making them particularly suited for predicting the future states of physical systems on historical data. All the presented algorithms are not only theorized but also simulated and validated using real thermal imaging data mapping a ship's engine.

Thomas Nakken Larsen, Eirik Runde Barlaug, Adil Rasheed

Modern control systems are increasingly turning to machine learning algorithms to augment their performance and adaptability. Within this context, Deep Reinforcement Learning (DRL) has emerged as a promising control framework, particularly in the domain of marine transportation. Its potential for autonomous marine applications lies in its ability to seamlessly combine path-following and collision avoidance with an arbitrary number of obstacles. However, current DRL algorithms require disproportionally large computational resources to find near-optimal policies compared to the posed control problem when the searchable parameter space becomes large. To combat this, our work delves into the application of Variational AutoEncoders (VAEs) to acquire a generalized, low-dimensional latent encoding of a high-fidelity range-finding sensor, which serves as the exteroceptive input to a DRL agent. The agent's performance, encompassing path-following and collision avoidance, is systematically tested and evaluated within a stochastic simulation environment, presenting a comprehensive exploration of our proposed approach in maritime control systems.

Aksel Vaaler, Svein Jostein Husa, Daniel Menges et al.

Many autonomous systems face safety challenges, requiring robust closed-loop control to handle physical limitations and safety constraints. Real-world systems, like autonomous ships, encounter nonlinear dynamics and environmental disturbances. Reinforcement learning is increasingly used to adapt to complex scenarios, but standard frameworks ensuring safety and stability are lacking. Predictive Safety Filters (PSF) offer a promising solution, ensuring constraint satisfaction in learning-based control without explicit constraint handling. This modular approach allows using arbitrary control policies, with the safety filter optimizing proposed actions to meet physical and safety constraints. We apply this approach to marine navigation, combining RL with PSF on a simulated Cybership II model. The RL agent is trained on path following and collision avpodance, while the PSF monitors and modifies control actions for safety. Results demonstrate the PSF's effectiveness in maintaining safety without hindering the RL agent's learning rate and performance, evaluated against a standard RL agent without PSF.

Adil Rasheed, Oscar Ravik, Omer San

This work investigates the use of digital twins for dynamical system modeling and control, integrating physics-based, data-driven, and hybrid approaches with both traditional and AI-driven controllers. Using a miniature greenhouse as a test platform, four predictive models Linear, Physics-Based Modeling (PBM), Long Short Term Memory (LSTM), and Hybrid Analysis and Modeling (HAM) are developed and compared under interpolation and extrapolation scenarios. Three control strategies Model Predictive Control (MPC), Reinforcement Learning (RL), and Large Language Model (LLM) based control are also implemented to assess trade-offs in precision, adaptability, and implementation effort. Results show that in modeling HAM provides the most balanced performance across accuracy, generalization, and computational efficiency, while LSTM achieves high precision at greater resource cost. Among controllers, MPC delivers robust and predictable performance, RL demonstrates strong adaptability, and LLM-based controllers offer flexible human-AI interaction when coupled with predictive tools.

Mrigank Dhingra, Romit Maulik, Adil Rasheed et al.

Neural operator learning has emerged as a powerful approach for solving partial differential equations (PDEs) in a data-driven manner. However, applying principal component analysis (PCA) to high-dimensional solution fields incurs significant computational overhead. To address this, we propose a patch-based PCA-Net framework that decomposes the solution fields into smaller patches, applies PCA within each patch, and trains a neural operator in the reduced PCA space. We investigate two different patch-based approaches that balance computational efficiency and reconstruction accuracy: (1) local-to-global patch PCA, and (2) local-to-local patch PCA. The trade-off between computational cost and accuracy is analyzed, highlighting the advantages and limitations of each approach. Furthermore, within each approach, we explore two refinements for the most computationally efficient method: (i) introducing overlapping patches with a smoothing filter and (ii) employing a two-step process with a convolutional neural network (CNN) for refinement. Our results demonstrate that patch-based PCA significantly reduces computational complexity while maintaining high accuracy, reducing end-to-end pipeline processing time by a factor of 3.7 to 4 times compared to global PCA, thefore making it a promising technique for efficient operator learning in PDE-based systems.

Florian Stadtmann, Adil Rasheed

The demand for condition-based and predictive maintenance is rising across industries, especially for remote, high-value, and high-risk assets. In this article, the diagnostic digital twin concept is introduced, discussed, and implemented for a floating offshore turbine. A diagnostic digital twin is a virtual representation of an asset that combines real-time data and models to monitor damage, detect anomalies, and diagnose failures, thereby enabling condition-based and predictive maintenance. By applying diagnostic digital twins to offshore assets, unexpected failures can be alleviated, but the implementation can prove challenging. Here, a diagnostic digital twin is implemented for an operational floating offshore wind turbine. The asset is monitored through measurements. Unsupervised learning methods are employed to build a normal operation model, detect anomalies, and provide a fault diagnosis. Warnings and diagnoses are sent through text messages, and a more detailed diagnosis can be accessed in a virtual reality interface. The diagnostic digital twin successfully detected an anomaly with high confidence hours before a failure occurred. The paper concludes by discussing diagnostic digital twins in the broader context of offshore engineering. The presented approach can be generalized to other offshore assets to improve maintenance and increase the lifetime, efficiency, and sustainability of offshore assets.

Shady E. Ahmed, Omer San, Adil Rasheed et al.

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

Prateek Gupta, Adil Rasheed, Sverre Steen

The hydrodynamic performance of a sea-going ship varies over its lifespan due to factors like marine fouling and the condition of the anti-fouling paint system. In order to accurately estimate the power demand and fuel consumption for a planned voyage, it is important to assess the hydrodynamic performance of the ship. The current work uses machine-learning (ML) methods to estimate the hydrodynamic performance of a ship using the onboard recorded in-service data. Three ML methods, NL-PCR, NL-PLSR and probabilistic ANN, are calibrated using the data from two sister ships. The calibrated models are used to extract the varying trend in ship's hydrodynamic performance over time and predict the change in performance through several propeller and hull cleaning events. The predicted change in performance is compared with the corresponding values estimated using the fouling friction coefficient ($ΔC_F$). The ML methods are found to be performing well while modelling the hydrodynamic state variables of the ships with probabilistic ANN model performing the best, but the results from NL-PCR and NL-PLSR are not far behind, indicating that it may be possible to use simple methods to solve such problems with the help of domain knowledge.

Sindre Stenen Blakseth, Adil Rasheed, Trond Kvamsdal et al.

In this work, we introduce, justify and demonstrate the Corrective Source Term Approach (CoSTA) -- a novel approach to Hybrid Analysis and Modeling (HAM). The objective of HAM is to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. CoSTA achieves this objective by augmenting the governing equation of a PBM model with a corrective source term generated using a deep neural network. In a series of numerical experiments on one-dimensional heat diffusion, CoSTA is found to outperform comparable DDM and PBM models in terms of accuracy -- often reducing predictive errors by several orders of magnitude -- while also generalizing better than pure DDM. Due to its flexible but solid theoretical foundation, CoSTA provides a modular framework for leveraging novel developments within both PBM and DDM. Its theoretical foundation also ensures that CoSTA can be used to model any system governed by (deterministic) partial differential equations. Moreover, CoSTA facilitates interpretation of the DNN-generated source term within the context of PBM, which results in improved explainability of the DNN. These factors make CoSTA a potential door-opener for data-driven techniques to enter high-stakes applications previously reserved for pure PBM.

Omer San, Adil Rasheed, Trond Kvamsdal

Most modeling approaches lie in either of the two categories: physics-based or data-driven. Recently, a third approach which is a combination of these deterministic and statistical models is emerging for scientific applications. To leverage these developments, our aim in this perspective paper is centered around exploring numerous principle concepts to address the challenges of (i) trustworthiness and generalizability in developing data-driven models to shed light on understanding the fundamental trade-offs in their accuracy and efficiency, and (ii) seamless integration of interface learning and multifidelity coupling approaches that transfer and represent information between different entities, particularly when different scales are governed by different physics, each operating on a different level of abstraction. Addressing these challenges could enable the revolution of digital twin technologies for scientific and engineering applications.

Tiril Sundby, Julia Maria Graham, Adil Rasheed et al.

Digital twins are meant to bridge the gap between real-world physical systems and virtual representations. Both stand-alone and descriptive digital twins incorporate 3D geometric models, which are the physical representations of objects in the digital replica. Digital twin applications are required to rapidly update internal parameters with the evolution of their physical counterpart. Due to an essential need for having high-quality geometric models for accurate physical representations, the storage and bandwidth requirements for storing 3D model information can quickly exceed the available storage and bandwidth capacity. In this work, we demonstrate a novel approach to geometric change detection in the context of a digital twin. We address the issue through a combined solution of Dynamic Mode Decomposition (DMD) for motion detection, YOLOv5 for object detection, and 3D machine learning for pose estimation. DMD is applied for background subtraction, enabling detection of moving foreground objects in real-time. The video frames containing detected motion are extracted and used as input to the change detection network. The object detection algorithm YOLOv5 is applied to extract the bounding boxes of detected objects in the video frames. Furthermore, the rotational pose of each object is estimated in a 3D pose estimation network. A series of convolutional neural networks conducts feature extraction from images and 3D model shapes. Then, the network outputs the estimated Euler angles of the camera orientation with respect to the object in the input image. By only storing data associated with a detected change in pose, we minimize necessary storage and bandwidth requirements while still being able to recreate the 3D scene on demand.

Suraj Pawar, Omer San, Burak Aksoylu et al.

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our approach is to augment the knowledge of the simplified theories with the underlying learning process. To emphasise on their physical importance, our architecture consists of adding certain features at intermediate layers rather than in the input layer. To demonstrate our approach, we select a canonical airfoil aerodynamic problem with the enhancement of the potential flow theory. We include features obtained by a panel method that can be computed efficiently for an unseen configuration in our training procedure. By addressing the generalizability concerns, our results suggest that the proposed feature enhancement approach can be effectively used in many scientific machine learning applications, especially for the systems where we can use a theoretical, empirical, or simplified model to guide the learning module.

Shady Ahmed, Suraj Pawar, Omer San et al.

We put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving a two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies.

Shady E. Ahmed, Omer San, Kursat Kara et al.

Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach based on memory embedding to provide physically correct boundary conditions at the interface. To enable the interface learning for hyperbolic systems by considering the domain of influence and wave structures into account, we put forth the concept of upwind learning towards a physics-informed domain decomposition. The promise of the proposed approach is shown for a set of canonical illustrative problems. We highlight that high-performance computing environments can benefit from this methodology to reduce communication costs among processing units in emerging machine learning ready heterogeneous platforms toward exascale era.

Simen Theie Havenstrøm, Adil Rasheed, Omer San

Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the physical system. However, in complex systems, such as autonomous underwater vehicles performing the dual objective of path-following and collision avoidance, decision making becomes non-trivial. We propose a solution using state-of-the-art Deep Reinforcement Learning (DRL) techniques, to develop autonomous agents capable of achieving this hybrid objective without having à priori knowledge about the goal or the environment. Our results demonstrate the viability of DRL in path-following and avoiding collisions toward achieving human-level decision making in autonomous vehicle systems within extreme obstacle configurations.

Eivind Meyer, Amalie Heiberg, Adil Rasheed et al.

Path Following and Collision Avoidance, be it for unmanned surface vessels or other autonomous vehicles, are two fundamental guidance problems in robotics. For many decades, they have been subject to academic study, leading to a vast number of proposed approaches. However, they have mostly been treated as separate problems, and have typically relied on non-linear first-principles models with parameters that can only be determined experimentally. The rise of Deep Reinforcement Learning (DRL) in recent years suggests an alternative approach: end-to-end learning of the optimal guidance policy from scratch by means of a trial-and-error based approach. In this article, we explore the potential of Proximal Policy Optimization (PPO), a DRL algorithm with demonstrated state-of-the-art performance on Continuous Control tasks, when applied to the dual-objective problem of controlling an underactuated Autonomous Surface Vehicle in a COLREGs compliant manner such that it follows an a priori known desired path while avoiding collisions with other vessels along the way. Based on high-fidelity elevation and AIS tracking data from the Trondheim Fjord, an inlet of the Norwegian sea, we evaluate the trained agent's performance in challenging, dynamic real-world scenarios where the ultimate success of the agent rests upon its ability to navigate non-uniform marine terrain while handling challenging, but realistic vessel encounters.

Herman Stavelin, Adil Rasheed, Omer San et al.

With the rise of focus on man made changes to our planet and wildlife therein, more and more emphasis is put on sustainable and responsible gathering of resources. In an effort to preserve maritime wildlife the Norwegian government has decided that it is necessary to create an overview over the presence and abundance of various species of wildlife in the Norwegian fjords and oceans. In this paper we apply and analyze an object detection scheme that detects fish in camera images. The data is sampled from a submerged data station at Fulehuk in Norway. We implement You Only Look Once (YOLO) version 3 and create a dataset consisting of 99,961 images with a mAP of $\sim 0.88$. We also investigate intermediate results within YOLO, gaining insight into how it performs object detection.

Simen Theie Havenstrøm, Camilla Sterud, Adil Rasheed et al.

Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the physical system. However, if a system is highly complex, it might be infeasible to produce a reliable mathematical model of the system. Without a model most of the theoretical tools to develop control laws break down. In these settings, machine learning controllers become attractive: Controllers that can learn and adapt to complex systems, developing control laws where the engineer cannot. This article focuses on utilizing machine learning controllers in practical applications, specifically using deep reinforcement learning in motion control systems for an autonomous underwater vehicle with six degrees-of-freedom. Two methods are considered: end-to-end learning, where the vehicle is left entirely alone to explore the solution space in its search for an optimal policy, and PID assisted learning, where the DRL controller is essentially split into three separate parts, each controlling its own actuator.

Eivind Meyer, Haakon Robinson, Adil Rasheed et al.

In this article, we explore the feasibility of applying proximal policy optimization, a state-of-the-art deep reinforcement learning algorithm for continuous control tasks, on the dual-objective problem of controlling an underactuated autonomous surface vehicle to follow an a priori known path while avoiding collisions with non-moving obstacles along the way. The artificial intelligent agent, which is equipped with multiple rangefinder sensors for obstacle detection, is trained and evaluated in a challenging, stochastically generated simulation environment based on the OpenAI gym python toolkit. Notably, the agent is provided with real-time insight into its own reward function, allowing it to dynamically adapt its guidance strategy. Depending on its strategy, which ranges from radical path-adherence to radical obstacle avoidance, the trained agent achieves an episodic success rate between 84 and 100%.

Haakon Robinson, Adil Rasheed, Omer San

In exchange for large quantities of data and processing power, deep neural networks have yielded models that provide state of the art predication capabilities in many fields. However, a lack of strong guarantees on their behaviour have raised concerns over their use in safety-critical applications. A first step to understanding these networks is to develop alternate representations that allow for further analysis. It has been shown that neural networks with piecewise affine activation functions are themselves piecewise affine, with their domains consisting of a vast number of linear regions. So far, the research on this topic has focused on counting the number of linear regions, rather than obtaining explicit piecewise affine representations. This work presents a novel algorithm that can compute the piecewise affine form of any fully connected neural network with rectified linear unit activations.