Neural operator foundational models amortize the cost of repeatedly evaluating PDEs but their opaqueness and high dimensional inner representation makes them difficult to trust and understand, especially on out of distribution tasks. For certain (linear) PDE families this opacity is avoidable in principle since each instance is generated by a closed form (frequency domain) equation with only a handful of coefficients. As such, this thesis asks whether Kolmogorov-Arnold Networks (KANs) can be the building block that closes this accuracy and intepretability gap in 2 structurally different places: a drop-in component inside a Fourier Neural Operator (FNO) and as the foundation of a purpose built symbolic operator. We introduce KANSO (Kan Symbolic Operator), a compact KAN-first spectral operator whose architecture commits to a bilinear structure of constant coefficient 2D PDEs and exposes the equation learned directly (through the inherent intepretability of KANs), although a sparseness focused training regime is necessary to maintain intepretability with small accuracy degradation. Evaluating this 4 orders of magnitude smaller model than the black-box baseline FNO, it matches or exceeds it on zero-shot transfer throughout diffusion, transport and oscillatory families of PDEs. On the other hand, simply replacing a component of an FNO (the lift layer) with a KAN is only a conditional improvement, helping on smooth operators at large amount of parameters and degrades on oscillatory problems, which establishes that KANs are potential targeted improvements and not universal MLP replacements, motivating further the design of KANSO. ... Read more

Large Vision-Language Models (LVLMs) have demonstrated impressive capabilities across a wide range of visual tasks, yet their performance often degrades in specialised domains such as Remote Sensing, where spatial reasoning in Visual Question Answering (VQA) remains particularly difficult. This limitation is primarily driven by a scarcity of high-quality training data, which comes from the rarity of complex real-world events and the labour-intensive process of annotating spatial relationships. To address this, this thesis proposes a synthetic data generation pipeline based on generative inpainting, using parked aircraft as a case study. By inserting synthetic objects into real remote sensing backgrounds, the pipeline creates complex spatial scenarios while preserving realistic context. Because the scene layout is fully controlled, it can also automatically generate grounded image-question-answer triplets together with Chain-of-Thought (CoT) reasoning traces for each answer. To measure this spatial reasoning, we construct an extensive evaluation benchmark on real overhead imagery whose questions span five question domains, from single-object properties to multi-object relational reasoning, which is necessary to properly test complex spatial reasoning in VQA. We fine-tune three open-source LVLMs from different model families on the synthetic data and evaluate them against generalist and domain-specific baselines on this benchmark. Fine-tuning on the synthetic data improves spatial reasoning across all tested domains and across all three models, raising the strongest model, Qwen3.5 9B, from 43.4\% to 71.9\% accuracy, a gain of 28.5 percentage points (pp) over its zero-shot baseline. The consistency of this improvement across architectures indicates that it comes from the data itself rather than from any single model. Adding CoT supervision raises performance further, to a best of 75.5\% (a 3.6 pp increase over standard fine-tuning, and 32.1 pp over the zero-shot baseline). The gains are not uniform: intrinsic orientation (distinguishing the front of an aircraft from its back) remains the lowest-scoring domain for every fine-tuned model, and performance declines as the number of aircraft in a scene grows. Overall, these findings show that synthetic data can serve as an effective alternative or extension to real remote sensing VQA data, helping to address the data scarcity present in this domain, and because the pipeline was built to be modular, its components hold potential beyond this case study, possibly extending to other objects and tasks. ... Read more

Inverse problems governed by partial differential equations (PDEs) are ill-posed, and responsible use of their solutions requires quantifying the uncertainty in recovered parameters. Neural operator methods for inverse problems offer fast surrogates for classical solvers, but placing posteriors over network weights is intractable at scale. This thesis extends the Inverse Generative Neural Operator (IGNO) to full Bayesian posterior sampling by adding a normalising flow prior term to the inversion objective and replacing gradient-based optimisation with the No-U-Turn Sampler (NUTS). The extension requires no retraining of any network component. We evaluate the method on four inverse problems spanning Darcy flow, electrical impedance tomography (EIT), and the viscous Burgers equation. On in-domain test instances, the posterior achieves 93% to 100% empirical coverage at the 95% nominal level across all four benchmarks and responds appropriately to changes in observation noise and sensor count. The posterior mean matches or improves on the maximum a posteriori (MAP) point estimate in every case. A Laplace approximation baseline, which fits a Gaussian posterior at the MAP estimate, fails on two of the four problems and does not consistently outperform NUTS on the two where it converges. Because the posterior formulation separates data, physics, and prior into additive terms, physical constraints can be incorporated during sampling alongside the data likelihood. Including PDE residuals as a virtual likelihood is most beneficial when observations alone leave the posterior under-determined, as demonstrated by EIT, where boundary-only measurements provide no direct information about the interior conductivity. The uncertainty estimates are unreliable for out-of-distribution coefficient fields. The learned prior pulls the posterior toward the training distribution, producing credible intervals that can be both narrow and wrong. ... Read more

Traditional computational fluid dynamics (CFD) simulations are computationally expensive and time-consuming, driving the development of cheaper machine learning-based alternatives known as surrogate models. However, a prominent gap in the literature remains the systematic comparison of generalization behaviors across distinct model types. This paper investigates the out-of-distribution (OOD) generalization behavior of data-driven, physics-informed, and hybrid models. This is evaluated on two partial differential equations (PDEs), Darcy flow and Burgers' equation. The models tested were the Fourier Neural Operator (FNO), Physics Informed Neural Operator (PINO) and the Physics-informed Fourier Neural Operator (PiFNO) also known as zero-shot PINO or data-free PINO. These models were chosen for their similarities in architecture. FNO is used as a data-driven foundation for PINO, where PINO adds a PDE residual loss in the loss function. To then train on solely the physics, PINO would exempt the data loss completely, making PiFNO. These similarities aimed to exclude any unwanted influence from a model's architecture. Each model was evaluated on different OOD cases based on the input parameters of the equations. Then, the models are compared in performance. The observed differences in L2 error between the models are small, all seem to struggle on the same test cases. PINO showed a minimal advantage on Darcy flow, mostly on the up-scaled resolution test-cases. On Burgers' equation no model shows any advantage. Overall, all models struggle extrapolating outside their training range. PINO also often includes an instance-wise finetuning upon the initial prediction using the PDE loss which was not used in these tests. This might improve the generalization behavior, which should be tested in future work. ... Read more

Numerical solvers for partial differential equations (PDEs) are accurate, but expensive when many related problem instances must be solved. Neural operators offer a faster alternative by learning mappings from input fields to solution fields. However, standard Fourier Neural Operator (FNO) training still depends on labelled simulation data, which must be generated by a solver. This study examines whether physics-informed training can improve data efficiency for neural-operator PDE surrogates. A data-driven FNO is compared with a Physics-Informed Neural Operator (PINO) using the same FNO backbone. This keeps the comparison centred on the training objective rather than the architecture. PINO adds a PDE-residual penalty to the supervised loss, encouraging predictions to satisfy the governing equation as well as match labelled data. The experiments use two PDEBench benchmarks: 2D Darcy flow and 1D Burgers' equation. Accuracy is measured with relative L₂ error, and physical consistency with PDE residual. PINO reached lower relative L₂ error than FNO on both equations at every tested fraction. It also surpassed the full-data FNO using 10% of the labels on Darcy flow and 50% on Burgers' equation. PINO reduced PDE residuals, especially for Darcy flow. However, the out-of-distribution tests showed that better in-distribution accuracy did not imply robust extrapolation. Overall, physics-informed training improved in-distribution data efficiency and physical consistency, but the gain depended on the equation, labelled-data budget, physics-loss weight and evaluation regime. ... Read more

Machine learning-based modelling of physical systems, particularly as fast surrogate models for Computational Fluid Dynamics (CFD), has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of consensus on how different neural architectures perform under physical constraints, noisy conditions, and extreme domain shifts. This paper presents a systematic comparative analysis of three popular neural surrogate models, namely a Multi-Layer Perceptron (MLP), U-Net, and Fourier Neural Operator (FNO), across time-dependent and steady-state partial differential equations, specifically the 1D Burgers' and 2D Darcy flow equations. We investigate to what extent different training strategies, including data-driven training, physics-informed regularisation, and noise augmentation, affect the accuracy, computational efficiency, and robustness of these surrogate models. Our benchmark study concludes that spatial awareness drives baseline accuracy on time-dependent flows but not uniformly across PDE types, that out-of-distribution parameter shifts reveal a universal vulnerability in complex 2D flows across all three architectures, and that physics-informed training is not a universal fix for spatially aware models. Finally, we profile computational efficiency, demonstrating that while the FNO provides predictable memory scaling, the unconstrained MLP remains unmatched for low-latency, real-time inference. ... Read more

The inverse Darcy problem aims to recover an unknown permeability field from observations of the corresponding pressure field. Recent work has proposed physics-informed neural models as a promising approach to inverse recovery, but their behavior under sparse and noisy observations remains insufficiently understood. This work investigates whether physics-informed neural operators improve inverse permeability reconstruction under such degraded observation regimes. A data-driven inverse Fourier Neural Operator is compared with a physics-informed variant on a controlled synthetic Darcy benchmark with binary permeability fields. Under noisy full-field observations, physics-informed training improves robustness relative to a clean-trained FNO baseline, although direct noise augmentation provides a stronger benefit. Under sparse observations, mask-aware training enables recovery of the dominant permeability structure from limited pressure measurements, while the additional benefit of physics-informed training is modest and difficult to isolate from the learned data prior. These results suggest that physics-informed training can improve stability in some regimes, but does not replace exposure to the observation conditions encountered at test time. Reliable reconstruction from realistic sparse and noisy measurements therefore remains an open challenge. ... Read more

Seismic denoising is essential for subsurface imaging. Deterministic methods such as Radon transforms exist but struggle to separate signal from noise. Recent solutions like vision foundation models (VFMs) offer better signal separation, but generalize poorly across geological domains. Parameter-efficient fine-tuning with LoRA and kurtosis- guided test-time adaptation (TTA) improves cross-domain generalization, yet TTA performs weight updates during inference and collapses throughput from 114.29 to 1.09 patches per second, making real-time deployment impractical. This paper inves- tigates whether group relative query optimization (GRQO), a reinforcement-learning fine-tuning method applied before deployment, can reduce reliance on TTA. A LoRA- adapted DINOv3 backbone with a U-Net decoder is fine-tuned with a GRQO objective that combines a multi-head reward, KL-divergence regularization against a frozen ref- erence, and a head-diversity penalty. On a 4,000-patch unseen synthetic data set, SFT+GRQO alone improves signal retention (MS-SSIM-R 0.638→0.604) while pre- serving a similar inference speed. GRQO does not fully replace TTA, but it lowers the optimal TTA budget for signal retention: the best configuration for MS-SSIM- R pairs GRQO with only 25 TTA epochs (MS-SSIM 0.862, MS-SSIM-R 0.452), and longer adaptation degrades performance and decreases throughput. However, GRQO alone minimally deteriorates performance when evaluated on real seismic data (LS 0.373→0.381). These results indicate that pre-deployment reinforcement learning can shorten the costly real-time adaptation and increase signal retention, but may perform worse on unseen seismic domains. ... Read more

Seismic trace denoising is a long-standing problem in geophysical data processing, and recent work has shown that vision foundation models pre-trained on natural images can be adapted to it parameter-efficiently rather than trained from scratch. Such adaptation is typically applied uniformly across all transformer layers, but it is not known where along the network the adaptation effort is actually needed --- that is, where the representation gap between natural images and seismic data is concentrated. We investigate this question for two structurally distinct families of parameter-efficient fine-tuning (PEFT): Low-Rank Adaptation (LoRA), which injects a low-rank update into the attention projections, and Pfeiffer bottleneck adapters, which insert a residual MLP module after the feed-forward sub-layer. Using a DINOv3 ViT-S/16 backbone on active-source seismic image denoising and holding the per-layer parameter budget fixed across both mechanisms, we sweep adaptation placement across restricted subsets of the twelve transformer layers within the DINOv3 architecture and measure denoising quality at each placement. We find that adaptation is strongly concentrated in the early layers: placing modules on only the first four layers recovers most of the denoising quality of full adaptation at one third of the adapter parameters, and even a single early layer is already competitive with full adaptation, while a roughly monotonic early-to-late importance ordering holds across placements. Crucially, this profile is near-identical for the two mechanisms at matched budget, indicating that the effect is a property of where adaptation is applied rather than of the particular PEFT design. These results suggest that, for this task and backbone, the natural-image-to-seismic gap is primarily a low-level, input-stage shift, and that early-layer-heavy placement is an effective and economical default for PEFT-based adaptation of vision foundation models to seismic data. ... Read more

Marine seismic surveys can contain missing or unusable receiver traces. This paper tests how well those traces can be reconstructed. It compares zero fill, linear interpolation, a U-Net trained from random initialization on BP, SwinV2 with ImageNet weights, and SFM with seismic pretraining. BP 2007 supplies complete synthetic shots, so receiver traces can be removed from the input and scored against the target. Viking Line 12 is a field line; the test removes observed field traces and scores their reconstruction after the models are trained only on BP. All learned models use inputs computed from visible traces, predict a correction to a linear interpolation estimate, copy measured traces back, and are scored only on removed traces. On BP 2007, with 75% of receiver traces removed in groups of eight, the U-Net has the lowest RMSE on removed traces, 1.170 ± 0.467. SwinV2 with LoRA is the best pretrained method on BP, 2.247 ± 0.196. On Viking Line 12, using BP-trained weights without field retraining, the U-Net has the lowest mean RMSE, 16.38 ± 22.88, but repeat variation is large. Frozen SFM is the best pretrained method on Viking by RMSE, 19.98 ± 0.62, and has the highest SSIM. ... Read more

Active seismic imaging is used to infer subsurface structure from reflected wavefields, but acquisition and ambient noise can obscure weak reflectors and reduce interpretation reliability. Seismic denoising must remove noise while keeping geological structure intact. This thesis studies a parameter-efficient method to adapt pretrained vision foundation models to this task. The method treats each seismic section as a 2D grayscale image, maps it into a format compatible with vision backbones, and applies Low-Rank Adaptation (LoRA) to limit the number of trainable parameters. It then combines the denoised outputs of multiple adapted vision models through a learned soft spatial blender. This blender merges the expert predictions at the pixel level, allowing the final model to use complementary architectural strengths such as multiscale representation and long-range dependencies. The method is evaluated against a seismic foundation model baseline, using both quantitative metrics and qualitative inspection. Across 25 seed/split repetitions, the residual joint spatial blender achieves a mean absolute error of 0.0463, a peak signal-to-noise ratio of 33.98\,dB, and a structural similarity index of 0.9727, substantially outperforming the standalone adapted experts and the frozen baseline. These results show that jointly trained spatial fusion improves seismic denoising performance while keeping training parameter-efficient. ... Read more

Seismic reflection surveys image subsurface geological structures by recording waves reflected from interfaces between rock layers, which are then processed to form 3D seismic volumes. However, the acquired signals are often contaminated by noise that degrades interpretation quality. Existing denoising approaches adapt pretrained visual foundation models to seismic data but process each slice of the 3D seismic volume independently, discarding useful spatial context. To incorporate this context while retaining the efficiency of a 2D model, three input strategies are compared: 2D-1ch, in which a single slice is repeated across the input channels; 2.5D-3ch, which uses three consecutive slices from the same volume; and 2.5D-5ch, which uses five consecutive slices. DINOv3 is adapted with low-rank adaptation (LoRA), and a lightweight decoder is trained to predict the clean central slice. On 30 synthetic Image Impeccable volumes, mean test multi-scale structural similarity improves from $0.8624$ for 2D-1ch to $0.8947$ for 2.5D-3ch and $0.9039$ for 2.5D-5ch. 2.5D gains are largest on the slices with the most noise. Additional experiments show that these improvements arise primarily from the spatial context provided by neighbouring slices. On the real-field F3 dataset, 2.5D behaviour depends on slice orientation. In the horizontal time orientation the models were trained on, 2D-1ch leaves the least structured residual, while 2.5D-3ch and 2.5D-5ch over-smooth the output. However, in the inline/crossline F3 evaluation, 2.5D reduces the over-smoothing seen in 2D-1ch and retains more structure. Cross-backbone experiments with SFM-Base and SwinV2-T show that the 2D-to-2.5D trend is not specific to DINOv3, while full fine-tuning controls show that PEFT is sufficient to achieve the observed gains. These results support 2.5D input as an effective extension on synthetic data when neighbouring slices are aligned, while highlighting its sensitivity to field-data neighbour relationships. ... Read more

Fourier Neural Operators (FNOs) have become a widely used architecture for learning solution operators of partial differential equations. Recent work has further shown that FNOs can be pretrained on mixtures of partial differential equation families and then fine-tuned on downstream tasks, suggesting a route toward scientific machine learning foundation models. At the same time, many systems governed by partial differential equations obey physical constraints that standard neural operators do not enforce by construction. This work studies whether individual physical constraint modules remain useful when inserted into a shared mixed-family FNO pretrain–fine-tune pipeline.

The empirical study uses a common mixed-domain FNO baseline across Poisson, advection–diffusion, and Helmholtz operators. This baseline provides the shared backbone, input representation, and transfer protocol against which the constraint modules are compared. The experiments therefore focus on whether adding physical structure improves downstream adaptation under matched training and evaluation conditions.

The experiments evaluate minimally invasive zero-mode constraints and residual constraints for partial differential equations. The results show that the soft partial differential equation residual penalty is the most promising tested add-on, improving transfer performance for Poisson and advection–diffusion across a broad range of downstream data budgets. In contrast, a hard zero-mode projection is generally unattractive, suggesting that exact universal projections can be too rigid in a mixed transfer setting. Helmholtz remains less conclusive, with noisier and less separable constraint effects.

Finally, experiments on PDE coefficient ranges outside the pretraining regime show that pretraining lowers error relative to scratch for Poisson and advection–diffusion, but does not remove the challenge of extrapolation. For Helmholtz, higher-frequency settings expose instability in scratch training that is less severe for the mixed pretrained model. Overall, the results support a restrained view: modular constraints can help foundation-model neural operators, but their usefulness depends strongly on enforcement type, partial differential equation family, and shift severity. ... Read more

Automated cloud classification is severely bottlenecked by the need for massive, region-specific annotated datasets. This thesis investigates few-shot learning (FSL) approaches for the classification of mesoscale cloud formations across different geographic regions under limited data conditions.

To address this problem, the influence of varying amounts of additional data on generalisation to novel cloud regimes is evaluated. The study compares representation learning strategies, including self-supervised and supervised approaches, to assess their effectiveness in structuring the latent space for distinguishing cloud types. In parallel, two learning paradigms, transfer learning and episodic meta-learning, are analysed to determine how effectively they incorporate additional data when adapting to novel classes.

The results show that self-supervised learning is most effective in the strict few-shot regime, while supervised transfer learning makes the most effective use of additional data. In particular, Barlow Twins achieves the strongest performance under minimal data by avoiding reliance on noisy labels. When additional out-of-domain data, such as ImageNet and auxiliary cloud datasets, is introduced, supervised pre-training combined with transfer learning attains performance comparable to standard supervised learning, while requiring only a small number of labelled examples. ... Read more

Accurate characterization of heliostat surface errors is essential for the efficiency of concentrating solar power (CSP) plants, yet direct measurement methods such as deflectometry remain costly and im practical at scale. This thesis investigates a physics-informed deep learning approach to reconstruct heliostat surfaces from flux density images alone—a fundamentally ill-posed problem in which many distinct surfaces can yield similar flux patterns. The proposed framework integrates simulated datasets, augmentation of real surface measurements, and a raytracing-based training loop, with additional regularization strategies to mitigate the ill-posed nature of the inverse problem. The best model achieved a median flux prediction accuracy of 84%, approaching the 92% of supervised benchmarks. For surface reconstruction, training on synthetic datasets with heliostat positions close to the receiver yielded the lowest median MeanAbsoluteError (MAE)of 2.4×10−4, comparedto 1.4×10−4 inthesupervised case. While individual surface reconstructions remained limited, the model reproduced some mean structural patterns of the training set, indicating partial learning of underlying geometric behavior. These findings demonstrate both the potential and current limitations of deep learning for heliostat surface reconstruction. With further advances in regularization, dataset design, and real-world validation, the approach may provide a scalable tool for CSP field calibration and optimization in the future. ... Read more

Arsenic contamination in groundwater is a major public health concern in the Ganges-Brahmaputra Basin, where millions rely on shallow aaquifers for drinking water. Naturally occurring arsenic is mobilised under specific sedimentological and geochemical conditions, particularly in Holocene alluvial deposits. Although extensively studied, arsenic distribution remains highly variable and difficult to predict. This study investigates how geomorphological features, specifically oxbow lakes and point bars, can be used to improve arsenic risk prediction and mapping using machine learning. The approach offers a targeted and scalable method for identifying high-risk zones, particularly in data-scarce environments. The divergence between theoretical assumptions and dataset trends illustrates the challenges of generalising risk models without high-precision, ground-validated input data. As a proof of concept, a two-stage workflow was implemented. In the first stage, a You Only Look Once object detection model was trained to locate oxbow lakes and point bars using satellite imagery. These landforms are key indicators of arsenic-prone zones due to their depositional history. The model performed well on well-isolated oxbow lakes and their associated point bars but struggled with hydrologically connected oxbow lakes and heavily vegetated areas, highlighting the need for more diverse training data and the potential value of false-colour imagery. A case study was conducted using historical arsenic well measurements to evaluate model assumptions. A supervised classification with the eXtreme Gradient Boosting algorithm confirmed the predictive value of geomorphological variables, with sand content, elevation, and soil organic carbon emerging as dominant predictors. Vegetation and precipitation data were excluded due to low relevance and poor temporal alignment. In the second stage, a Gaussian Mixture Model was applied to classify arsenic risk using the same geospatial variables. The model produced spatially coherent and interpretable risk zones, with high probability in most predictions. Areas of low probability were primarily located at transition zones between risk classes, indicating regions where higher-resolution or more precise input data may be necessary to reduce uncertainty and improve model reliability. This study provides a practical and semi-automated framework for geospatial arsenic risk assessment. While the risk classification is relative, future work should incorporate population-weighted exposure metrics to better guide mitigation. The method developed here supports more efficient fieldwork planning and decision-making in complex fluvial environments. ... Read more

Reconstructing high-resolution wind fields from sparse, low-resolution observations is a critical yet ill-posed problem in meteorological modeling. Classical approaches, such as Computational Fluid Dynamics (CFD), are often too computationally intensive to meet the demands of real- time or large-scale industrial applications. Meanwhile, conventional data-driven methods like Convolutional Neural Networks (CNNs) tend to produce overly smoothed outputs and struggle to recover fine-scale structures, especially under severe data sparsity.
This thesis explores the use of diffusion-based generative models for super-resolution in wind field reconstruction. A progressive SR3 (Super-Resolution via Repeated Refinement) frame- work is developed, combining a multi-stage architecture with stochastic denoising processes to gradually reconstruct high-resolution outputs. Extensive experiments demonstrate that the progressive SR3 consistently outperforms CNN-based baselines in terms of reconstruction accur- acy, perceptual quality, and robustness. Furthermore, a joint training strategy improves both performance and computational efficiency by enabling end-to-end optimization across stages.
The findings support the use of probabilistic diffusion models for meteorological super-resolution tasks and emphasize the effectiveness of progressive refinement in handling large upscaling factors. This approach provides a promising pathway for enhancing data-driven post-processing in atmospheric modeling. ... Read more

Accurate Wind Resource Assessment (WRA) requires the correction of systematic errors in modeled wind fields using sparse and temporally limited on-site measurements. With the emergence of microscale Large-Eddy Simulation (LES) as a high-resolution alternative to traditional mesoscale models, current correction practices, such as Measure-Correlate-Predict (MCP) for temporal extrapolation and Inverse Distance Weighting (IDW) for spatial extrapolation, need to be re-evaluated and adapted to the microscale context. This thesis investigates how data-driven methods can improve LES wind-speed error correction in both time and space, addressing three research gaps: the lack of validation of MCP on microscale data, the absence of temporal and spatial context in standard MCP-style formulations, and the limited use of flow information in spatial extrapolation.

The temporal component evaluates a set of linear and nonlinear regression models as flexible MCP-style baselines and extends them with additional contextual information. Temporal structure is incorporated through multi-step time windows, and local spatial structure is added by including neighboring LES grid cells. To represent full-field atmospheric patterns, the models are further enriched with latent encodings of the LES wind-speed field obtained through a Convolutional Autoencoder. The results show that MCP generalizes well to the microscale and that adding temporal and spatial context improves time-series accuracy across all observation locations, with combined strategies outperforming industry-standard methods.

The spatial component introduces Wind Speed-enhanced IDW (WS-IDW), which augments traditional IDW by weighting observation locations not only by geographic distance but also by similarity in LES wind speed. WS-IDW produces consistent improvements over the baseline, particularly when more observation locations are available. Analysis of the correction maps reveals that WS-IDW partially smooths misplaced fine-scale streaks in the LES wind field, supporting the hypothesis that LES is prone to slight spatial misalignment of coherent structures. The proposed method generalizes reasonably across sites and across different numbers of source masts.

Together, the temporal and spatial results demonstrate that incorporating LES-derived spatial and temporal information yields systematic improvements in microscale correction performance. The thesis provides a refined understanding of how LES behavior interacts with data-driven correction methods and offers a foundation for developing more robust microscale WRA correction frameworks in future work. ... Read more

Self-Adaptive Physics-Informed Neural Networks (SA-PINNs) are a variation of traditional Physics-Informed Neural Networks (PINNs) designed to solve the challenges of solving ”stiff” partial differential equations (PDEs). By using adaptive weighting, SA-PINNs are able to focus their attention on areas of the domain with higher errors, therefore improving accuracy. This work investigates the roles of individual loss components, namely residuals, boundary conditions, and initial conditions, in the performance of SA-PINNs. ... Read more