Library · Signals, sensing & imaging

What Fourier & Spectral Transformation got wrong, from 73 theses

Summary written by a model from the records below: The records document practical failures, baseline defeats, and design rejections when using Fourier and spectral transformations across scientific and machine learning applications. Researchers consistently encountered difficulties with non-stationary signals, high computational costs, representation rigidity, and numerical errors. These records come from graduate theses, 2021 to 2026, each labeled with its degree where the repository states it, and each links to its thesis. They were extracted by language models reading the full text, so treat each as a lead to read, not a verdict.

73
theses
22
institutions
76
failure records
8
failure modes

Plus 9 problems the authors left open, listed at the end.

Failure modes, by theses reporting them

Select a mode to jump to its records.

Standard Fourier methods lose temporal localization when applied to non-stationary or transient signals
13
13 theses · 12 institutions · 14 records
Fourier basis expansions and feature encodings struggle with asymmetric, complex, or non-periodic structures
13
13 theses · 8 institutions · 13 records
Truncation, boundary mismatches, and noise introduce spectral leakage and numerical artifacts
10
10 theses · 9 institutions · 10 records
Spectral graph convolutions and embeddings suffer from oversmoothing, blur, and loss of local semantics
10
10 theses · 8 institutions · 10 records
Spectral deconvolution and unmixing fail under peak overlap, limited components, and uncalibrated transfer functions
8
8 theses · 7 institutions · 10 records
Fourier neural operators and spectral networks encounter optimization difficulties and baseline losses
8
8 theses · 5 institutions · 8 records
Spectral clustering exhibits runtime bottlenecks and inflexible cluster count constraints
5
5 theses · 3 institutions · 5 records
Dense matrix operations and full spectrum evaluations create computational and scaling bottlenecks
6
6 theses · 6 institutions · 6 records

Standard Fourier methods lose temporal localization when applied to non-stationary or transient signals

13 theses · 12 institutions

Global basis functions and fixed window durations fail to track abrupt shifts and local non-linearities in time-varying data. These constraints cause spectral leakage, phase loss, and degraded resolution compared to adaptive time-frequency or wavelet representations.

Considered and rejected

Considered and rejected: Rejected Fourier transform for rs-fMRI frequency decomposition due to global basis functions failing to handle local non-linearities without significant frequency leakage.

NEW APPROACHES FOR ASSESSING TIME-VARYING FUNCTIONAL BRAIN CONNECTIVITY USING FMRI DATA · Johns Hopkins · PhD

Tried and failed

1D discrete wavelet transform on raw time-series applied to electromagnetic side-channel signal classification. Outcome: worse than baseline. Reason: Failed to capture complex spectral-temporal variation compared to 2D time-frequency spectrogram analysis

Machine Learning Methodologies For Low-Level Hardware-Based Malware Detection · Georgia Tech · PhD

Tried and failed

Hilbert transform and classic spectrogram applied to instantaneous frequency estimation from sensor signals. Outcome: unstable. Reason: Edge effect artifacts and spectral leakage occurred without strict bandpass filtering

Investigation of the interaction between left ventricular assist devices and the native heart under normal and abnormal conditions · Imperial · PhD

Considered and rejected

Considered and rejected: Rejected Fourier and Short-Time Fourier Transforms for signal processing due to loss of time localization and fixed windowing on non-stationary MZI signals.

A fibre optic and machine learning based health monitoring system for superconducting power applications in modern supergrids · EPFL · PhD

Considered and rejected

Considered and rejected: Rejected pure Fourier Transform (FT) due to lack of time-domain localization for transient/non-stationary disturbances.

Power Quality Disturbance Classification in IEEE 9-Bus System using STFT and Deep Learning · Texas Tech · Master's

Considered and rejected

Considered and rejected: Rejected discrete Fourier transform / standard Fourier transform for time-varying seismic signal analysis due to complete lack of temporal localisation

Seismic characterisation based on time-frequency spectral analysis · Imperial · PhD

Considered and rejected

Considered and rejected: Rejected fixed-window short-time Fourier transform (STFT) due to the rigid trade-off between temporal and spectral resolution and spectral leakage from window side lobes

Seismic characterisation based on time-frequency spectral analysis · Imperial · PhD

Considered and rejected

Considered and rejected: Rejected Discrete Fourier Transform (DFT) for ramp-rate power reference filtering because it loses time localization of frequency components.

Energy storage for complementary services in grid-tied PV systems · Nottingham · PhD

Considered and rejected

Considered and rejected: Rejected standard FFT spectrogram analysis due to poor resolution for abrupt frequency/time shifts, adopting 3D Time Fast Fourier Transform (TFFT) instead.

A comparative study of the creative processes in selected works of Roxy Music’s Phil Manzanera and Andy Mackay · De Montfort University · PhD

Considered and rejected

Considered and rejected: Rejected Fourier transform in favor of continuous wavelet transform due to its inability to assess time-varying, non-stationary periodicities in noisy hydrological datasets.

Nao control on multi-annual periodicities in water resources and their utility for managing water resource extremes. · Cranfield · PhD

Considered and rejected

Considered and rejected: Rejected standard discrete Fourier transforms and piece-wise segmentation for mutating materials because breaking time-translation invariance causes systematic over- and under-prediction errors.

Novel Rheometric Techniques and Constitutive Models for Linear and Nonlinear Rheology: Applications to Polymeric Solutions and Colloidal Gels · MIT · PhD

Tried and failed

Short-time Fourier transform spectral feature extraction applied to non-stationary operational vibration signals. Outcome: did not generalise. Reason: Spectral features degraded under non-stationary ambient operating conditions compared to impulse excitation

Data-Driven Structural Health Monitoring of Wind Turbine Blades under Operational and Environmental Variability · University College Dublin · PhD

Considered and rejected

Considered and rejected: Rejected standard Fourier and wavelet transforms for decomposing ionospheric EM field signals due to their inability to properly handle non-stationary geophysical signals.

Electromagnetic Characterization of the Ionosphere in the Framework of the Magnetosphere-Ionosphere-Lithosphere Coupling · University of Trento · PhD

Considered and rejected

Considered and rejected: Fourier transform / Windowed Fourier transform was rejected due to lack of variable time-frequency scaling window resolution.

Application of Wavelet-based Denoising to Improve the Accuracy of Nanopore Sequencing Data · Saskatchewan · Master's

Fourier basis expansions and feature encodings struggle with asymmetric, complex, or non-periodic structures

13 theses · 8 institutions

Predefined Fourier series and frequency encodings cannot easily capture asymmetric profiles or fine spatial details, yielding higher truncation errors than learned or domain-specific bases. In addition, corrupting or clustering Fourier coefficients often degrades downstream neural predictions and destroys essential semantic shapes.

Tried and failed

Fourier basis functions instead of polynomial basis applied to Koopman operator linear dynamic models. Outcome: worse than baseline. Reason: Fourier basis did not yield significantly better linearization results than polynomial basis

On the Application of Machine Learning and Physical Modeling Theory to Causal Lifting Linearizations of Nonlinear Dynamical Systems with Exogenous Input and Control · MIT · PhD

Tried and failed

non-learned Fourier series basis functions applied to dynamic motion representation. Outcome: worse than baseline. Reason: insufficiently expressive and lacked smoothness compared to learned neural network representations

4D VISION: REPRESENT, RECONSTRUCT AND GENERATE THE DYNAMIC 3D WORLD · Penn · PhD

Tried and failed

Fourier transform input encoding for bound propagation applied to neural network robustness verification. Outcome: worse than baseline. Reason: offered limited benefit over pixel-space verification while adding unnecessary complexity for high-frequency perturbations

Expressive specifications for neural network verification and certified training · Imperial · PhD

Tried and failed

Fourier series expansion for spatial profile representation applied to radial non-uniform flow profile reconstruction. Outcome: worse than baseline. Reason: yielded higher truncation error than domain-specific orthonormal basis functions without significant improvement at higher orders

Incorporation of High-Fidelity Flow Field Information into Preliminary Design of Multi-Stage Axial Compressors · MIT · PhD

Tried and failed

Fourier basis expansion for weight function parameterization applied to functional Gaussian process regression. Outcome: did not generalise. Reason: Fourier expansion cannot capture asymmetric profiles, restricting model expressivity across diverse true underlying shapes

Automatic relevance determination for Gaussian process regression with functional inputs · Iowa State · PhD

Tried and failed

alternative positional encodings for 3D coordinates applied to spatiotemporal electrode neural decoding. Outcome: worse than baseline. Reason: sinusoidal and Fourier encodings degraded performance compared to standard RBF spatial encoding

From thoughts to actions: cracking the neural code across scales and modalities · Penn · PhD

Tried and failed

frequency-domain clustering prior to sequence prediction applied to multivariate time series prediction. Outcome: worse than baseline. Reason: clustering via Fourier features failed to provide useful grouping for subsequent neural network prediction

Runway safety improvements through a data driven approach for risk flight prediction and simulation · Georgia Tech · PhD

Tried and failed

adding spectral loss to temporal regression objective applied to 1D temporal waveform reconstruction. Reason: increased FFT loss weight did not improve morphology recovery over mean squared error alone

A Temporal Encoder-Decoder Approach to Extracting Blood Volume Pulse Signal Morphology from Face Videos · Virginia Tech · Master's

Tried and failed

Omitting corrupted samples prior to discrete Fourier transform applied to Fourier phase estimation from image data. Outcome: worse than baseline. Reason: Excluding bad pixels reduced measurement sensitivity compared to spatial domain interpolation

Kernel-phase interferometry for detection of close in companions : binary demographics of brown dwarfs from birth to maturity · UT Austin · PhD

Tried and failed

perturbing low-frequency Fourier components during data augmentation applied to image semantic segmentation models. Outcome: worse than baseline. Reason: corrupting low-frequency information destroys essential visual structure and semantics needed for generalization

Harnessing Synthetic Data for Robust and Reliable Vision · Georgia Tech · PhD

Considered and rejected

Considered and rejected: Rejected Fourier series approaches for correcting asteroid rotational light curve noise because they do not account for the variation in the rotation curve form as a function of phase angle.

Small Bodies and Large Surveys: What Modern Dynamics can teach us about the Solar System · Harvard · PhD

Considered and rejected

Considered and rejected: Rejected Discrete Fourier Transform (DFT) / Short-Time Fourier Transform fingerprints because they require thousands of averaged captures and fail to match FM/square-wave harmonic structures.

On Optimizing The Radio Side-Channel For Application Modeling · Penn · PhD

Considered and rejected

Considered and rejected: Rejected standard thresholded Fourier Transform on binary images due to binarization distortion; adopted Fourier Transform over continuous exponential level-set functions instead.

Algorithmic design of photonic structures with deep learning · Georgia Tech · PhD

Truncation, boundary mismatches, and noise introduce spectral leakage and numerical artifacts

10 theses · 9 institutions

Transforming finite, truncated, or irregularly bounded data produces numerical aliasing, spurious high-frequency noise, and severe Gibbs phenomenon. Furthermore, missing observations and high stochastic noise disrupt frequency smoothing and cause accumulated numerical errors relative to direct quadrature or exact baselines.

Tried and failed

Fast Fourier transform deconvolution applied to solving Volterra integral equations. Outcome: worse than baseline. Reason: accumulated numerical errors and instability at long times compared to direct numerical quadrature

Memory and fluctuations in chemical dynamics · MIT · PhD

Tried and failed

standard fast Fourier transform applied to noisy time-series vibration signals. Reason: severe spectral data leakage and high stochastic noise corrupted the power spectral estimates

Structure-Borne Vehicle Interior Noise Estimation Using Accelerometer Based Intelligent Tires in Passenger Vehicles · Virginia Tech · Master's

Tried and failed

spectral domain transformation for fast inference applied to spatiotemporal state-space models with missing data. Reason: Fourier transformation breaks down when data contains missing values, preventing complexity reduction

Statistical spatio-temporal models with applications to natural processes · Georgia Tech · PhD

Tried and failed

FFT low-pass filtering for seasonal decomposition applied to SAR backscatter time-series. Outcome: no signal. Reason: High-frequency fluctuations disrupted Fourier transform smoothing, preventing phase identification

Earth Observation for Sustainable Sugarcane Production · Cranfield · PhD

Lost to a baseline

Fourier-acoustics angular spectrum method produces numerical aliasing artifacts compared to direct 1D numerical integration of the exact Bessel-beam modal decomposition integral for circular pistons.

Scattering and diffraction of acoustic waves in three problems with broken symmetry · UT Austin · PhD

Lost to a baseline

Spectral truncation loses to Tikhonov regularisation when filter functions align with higher-frequency/tail eigenfunctions (shape A).

Sparsely Observed Functional Time Series: Theory and Applications · EPFL · PhD

Considered and rejected

Considered and rejected: Rejected sliding discrete Fourier transform (SDFT) with partial substitution for separating coherent low-frequency modes because it produced spurious high-frequency noise and failed to converge harmonics unless sub-harmonics were used.

A fluid-solid coupled heat transfer methodology as applied to rotating cavities · Oxford · PhD

Considered and rejected

Considered and rejected: Rejected simple Fourier frequency-domain integration of Psi_4 due to spectral leakage and Gibbs phenomenon from the finite length and junk-radiation truncation of waveforms.

Dynamics of Mixed Binary Mergers using Numerical Relativity Simulations · Georgia Tech · PhD

Tried and failed

truncating spatial boundaries before Fourier transform applied to spatial dispersion extraction in small lattices. Outcome: worse than baseline. Reason: truncating limited spatial data points reduced frequency resolution more than removing boundary artifacts helped

Dynamic Behavior Of Periodic Media And Elastic Metamaterials · Penn · PhD

Considered and rejected

Considered and rejected: Rejected standard Fourier Transform (FFT) for spatial mode identification due to its strict requirement for spatial periodicity

Data-driven reduced-order modelling of the plasma systems dynamics · Imperial · Doctorate

Spectral graph convolutions and embeddings suffer from oversmoothing, blur, and loss of local semantics

10 theses · 8 institutions

Spectral graph filters rely on low-pass assumptions and Laplacian eigenvectors that break spatial locality and smooth out sharp localized transitions. These projections induce isotropic blur and can degrade representation capacity compared to spatial convolutions or phase-variant models.

Lost to a baseline

Basic (phase-variant) convolution model outperformed spectral convolution models across total unbanded neural variance (EVR ~0.40 vs ~0.25 at rank 10).

Spectral transformations of facial behavior, associated neural activity patterns, and novel tools for the longitudinal tracking of neurons · Harvard · PhD

Tried and failed

graph convolutional network on patch-induced graphs applied to spectrally diverse graph patches. Outcome: worse than baseline. Reason: fixed low-pass filtering assumptions conflicted with spectrally diverse graph patches

Towards Open World Graph Learning and Applications · Virginia Tech · Doctorate

Tried and failed

all-layer spectral normalisation applied to deep reinforcement learning value networks. Outcome: worse than baseline. Reason: over-constraining network to be 1-Lipschitz degrades model capacity and harms performance

Understanding learning from non-stationary data · Imperial · PhD

Tried and failed

Chebyshev graph convolutional neural networks applied to fault localization in power grids. Outcome: did not generalise. Reason: polynomial spectral interpolation smooths out sharp localized transitions between attacks and topology changes

Achieving Security and Reliability of Industrial Control Systems Using Data-Driven Models Informed by Physical Domain Knowledge · Georgia Tech · PhD

Lost to a baseline

LSGC+LSTM (MAE 3.16 mph) performed worse than vanilla LSTM (MAE 2.70 mph) on the LOOP dataset due to insufficient parameters in 1-layer localized spectral convolution.

Deep Learning for Short-term Network-wide Road Traffic Forecasting · University of Washington · PhD

Considered and rejected

Considered and rejected: Rejected spectral domain convolutions (projecting feature maps and kernels into spectral domain) because they lose semantic information

Motion and Activity Understanding in 360° Videos: An Egocentric Perspective · Texas State University · PhD

Considered and rejected

Considered and rejected: Standard spectral graph convolutions via full eigendecomposition rejected due to O(N^2) complexity, replaced by Chebyshev polynomial approximations

Network time series forecasting in photovoltaics power production · EPFL · PhD

Considered and rejected

Considered and rejected: Decided against spectral graph convolutions in favor of spatial spiral convolutions to avoid isotropic blur and better capture fine surface details.

Advancing 3D hand reconstruction and modelling with geometric deep learning · Imperial · PhD

Considered and rejected

Considered and rejected: Rejected spectral graph neural networks relying on graph Laplacian eigendecomposition because eigenvectors break locality and are unstable across varying graph topologies

Learning Representations For Matching · Penn · PhD

Tried and failed

single-stage hyperplane partitioning in spectral embedding applied to graph clustering. Reason: asymmetric perturbations cause multiple candidate hyperplanes to overlap heavily on a single cluster

Sublinear Algorithms for Spectral Graph Clustering · EPFL · PhD

Spectral deconvolution and unmixing fail under peak overlap, limited components, and uncalibrated transfer functions

8 theses · 7 institutions

Linear and low-component spectral deconvolution cannot distinguish mixed physical phases that share overlapping peak positions or vary purely in amplitude. Applying uncalibrated literature models or poorly configured loss functions also introduces large systematic estimation errors and non-physical peak artifacts.

Tried and failed

support vector regression for spectral super-resolution applied to hyperspectral image reconstruction. Outcome: did not generalise. Reason: introduced high-frequency noise and failed to generalize from synthetic shifts to real-world optical measurements

Computational approaches for sub-meter ocean color remote sensing · MIT · PhD

Tried and failed

multiphase spectral deconvolution applied to infrared vibrational absorption bands. Outcome: no signal. Reason: the spectral feature varied predominantly in amplitude rather than shape or position across phases

Infrared Spectroscopy at Three and Six Microns of Water Ices Mixtures of Astrochemical Interest · Georgia Tech · PhD

Tried and failed

spectral information similarity loss function applied to infrared spectra prediction. Reason: internal Gaussian convolution produced non-physical, infinitely sharp peak artifacts

Investigations into Message Passing Neural Networks and Polymer Fouling · MIT · PhD

Tried and failed

multicomponent linear spectral deconvolution fitting applied to infrared spectra with overlapping phase peaks. Reason: linear fitting cannot distinguish phases with nearly identical peak positions, causing misclassification

Infrared Spectroscopy at Three and Six Microns of Water Ices Mixtures of Astrochemical Interest · Georgia Tech · PhD

Tried and failed

Precomputed radiative transfer model grid fitting applied to Multiwavelength photometric spectral energy distributions. Outcome: did not generalise. Reason: Standard grid models systematically overestimated far-infrared flux by an order of magnitude without custom wavelength reweighting

The Effects of Molecular Cloud Structure on its CO Emission and Star Formation · Harvard · PhD

Tried and failed

applying uncalibrated literature transfer functions applied to spectroscopic density and volume estimation. Outcome: did not generalise. Reason: instrument-specific non-linearities and simplified dimensional assumptions induced large systematic errors

MAGMATIC DRIVERS OF EXPLOSIVE VOLCANISM: INSIGHT FROM MAGMA MIXING, MELT INCLUSIONS AND RAMAN SPECTROSCOPY · Cornell · PhD

Tried and failed

custom free-standing infrared spectrometer prototype applied to tissue optical spectroscopy. Reason: Non-uniform illumination, low detector sensitivity, and poor signal-to-noise ratio caused irreproducible spectral measurements.

Digistain Prognostic Score Development: Infrared Spectroscopy to Guide Chemotherapy Decisions · Imperial · PhD

Tried and failed

two-component spectral deconvolution modeling applied to mixed-phase infrared absorption spectra. Outcome: worse than baseline. Reason: two components lacked sufficient degrees of freedom to capture the observed multi-phase spectral variations

Infrared Spectroscopy at Three and Six Microns of Water Ices Mixtures of Astrochemical Interest · Georgia Tech · PhD

Lost to a baseline

Uniform and random wavelength selection with SSE segregation resulted in lower spectral unmixing accuracy than conventional unmixing when tested with more than four wavelengths

Multiparametric prostate ultrasound imaging · Johns Hopkins · PhD

Considered and rejected

Considered and rejected: Rejected analyzing the offset amplitude and CLS offset constants in monoexponential fits of 2D IR spectra due to distortion from partial spectral overlap with neighboring peaks

Lighting up the stage : ultrafast dynamics of the reverse micelle interface · UT Austin · PhD

Fourier neural operators and spectral networks encounter optimization difficulties and baseline losses

8 theses · 5 institutions

Fourier neural operators and spectral networks often lose to standard convolutional baselines like UNet or struggle to enforce physical constraints on unseen test data. Moreover, models with single Fourier features or higher-frequency Cartesian mask representations face spectral bias, vanishing gradients, and contour oscillations.

Tried and failed

Fourier neural operators applied to PDE gradient and Hessian operator learning. Outcome: worse than baseline. Reason: Standard UNet outperformed Fourier Neural Operator in both accuracy and GPU inference speed

Generative models for seismic imaging and inversion · UT Austin · PhD

Tried and failed

non-autoregressive Fourier neural operator for transient dynamics applied to time-dependent PDE inverse problems. Outcome: worse than baseline. Reason: lack of autoregressive modeling across sequential time channels caused elevated errors at early time steps

Physics Informed Deep Learning Application In High-Dimensional Groundwater Inverse Modeling Of Hydraulic Tomography · Georgia Tech · PhD

Tried and failed

physics-informed Fourier neural operator with soft regularization applied to current density continuity in heterogeneous media. Outcome: did not generalise. Reason: Soft penalty loss failed to strictly enforce flux conservation and zero-divergence constraints on unseen test data

Integration of machine learning for enhanced digital rock physics workflows · UT Austin · PhD

Tried and failed

fully-connected physics-informed neural networks with single Fourier features applied to multi-scale high-frequency differential equations. Outcome: did not converge. Reason: spectral bias prevents capturing multi-scale and high-frequency dynamics

PHYSICS-INFORMED MACHINE LEARNING: THEORY, ALGORITHMS AND APPLICATIONS · Penn · PhD

Tried and failed

Min-max normalization to [-1, 1] applied to Fourier neural operator input features. Outcome: overfit. Reason: Min-max scaling led to overfitting compared to standard z-score normalization during training

Direct pore-scale modeling of foam transport in porous media and related machine learning · UT Austin · PhD

Lost to a baseline

Spectral neural network had higher energy period RMSE (0.43 s) than the median transfer function benchmark (0.37 s)

Measuring waves in difficult places: New approaches to observing waves in hurricanes and sea ice · University of Washington · PhD

Left open

Investigate why higher frequency coefficients in Cartesian Fourier mask representations suffer from low gradients and cause oscillating contours. Blocker: None

Instance Segmentation and 3D Multi-Object Tracking for Autonomous Driving · Tübingen · PhD

Left open

Investigate why higher-frequency Fourier coefficients exhibit low gradients and oscillations when trained with Cartesian Chamfer loss in instance segmentation models. Blocker: None

Representations in Object Detection and Instance Segmentation · Tübingen · PhD

Spectral clustering exhibits runtime bottlenecks and inflexible cluster count constraints

5 theses · 3 institutions

Static spectral clustering scales poorly to dynamic snapshots and large frame sets due to heavy computational overhead. In addition, relying on spectral clustering requires specifying cluster counts in advance and can violate discrete matching constraints.

Considered and rejected

Considered and rejected: Rejected treating dynamic graph snapshots independently via static spectral clustering at each step because it is computationally time-consuming and lacks convergence guarantees under noise.

Statistical learning and change detection for dynamic networks · Georgia Tech · PhD

Considered and rejected

Considered and rejected: Rejected discrete mode clustering via DBSCAN, k-medoids, spectral clustering, and hierarchical clustering in favor of k-means for simplicity and explicit cluster count control.

Modeling and Control of Networked Systems: Applications to Air Transportation · MIT · PhD

Considered and rejected

Considered and rejected: Rejected classical clustering methods (such as Spectral Clustering and K-means) for recall initiator extraction because they require specifying cluster numbers in advance, which is impractical for hundreds or thousands of unstructured records.

Blockchain, Recommender System, and Artificial Intelligence: Leveraging advanced digital technology for disruption risk mitigation in the medical device closed-loop supply chain · University College Dublin · PhD

Considered and rejected

Considered and rejected: Rejected k-means rounding on spectral graph embeddings for multiway matching because k-means violates the distinctness constraint.

Data Association Algorithms and Representations for Robust Geometric Perception · MIT · PhD

Considered and rejected

Considered and rejected: Rejected K-means++ and spectral clustering for channel pruning due to combinatorial search spaces over layer-wise cluster counts.

Robust Efficient Edge AI: New Principles and Frameworks for Empowering Artificial Intelligence on Edge Devices · Georgia Tech · PhD

Dense matrix operations and full spectrum evaluations create computational and scaling bottlenecks

6 theses · 6 institutions

Direct Fourier transforms of non-uniform points and Galerkin-collocation spectral methods scale poorly because of dense matrix inverses and an inability to use standard fast transforms. Similarly, computing full Fourier representations when only a few coefficients are needed runs significantly slower than specialized non-uniform algorithms.

Lost to a baseline

Galerkin-collocation spectral methods were significantly slower than finite-difference methods due to dense matrix operations and inverses, without improving stability

Simulating Semiclassical Black Holes · Nottingham · PhD

Lost to a baseline

Spectral-Galerkin eigenvalue accuracy drops significantly faster than spectral-collocation for higher eigenmodes.

Spectral Stability of Plasma Flow in Magnetic Nozzle · Saskatchewan · Master's

Considered and rejected

Considered and rejected: Fast Fourier Transform (FFT) for frequency extraction was rejected in favor of time-varying Extended Kalman Filter due to FFT's limitations with irregular sampling, phase/amplitude shifts, and embedded real-time processing.

Psychological Monitoring: Detecting Real-Time Emotional Changes Real-Time Emotional Monitoring: A Constant Dimension Approach · Virginia Tech · Master's

Tried and failed

direct Fourier transform of discrete point distributions applied to particle spatial spectral estimation. Outcome: too slow. Reason: direct summation of non-uniform delta functions scales poorly and cannot exploit FFT algorithms

Computational study of particle clustering and dispersion in turbulence · Imperial · PhD

Tried and failed

Fast Fourier Transform for few coefficients applied to evaluating numerical complex contour integrals. Outcome: too slow. Reason: computes all N Fourier coefficients when only two low-order coefficients are needed

An exact solution to Lambert’s problem · Iowa State · Master's

Lost to a baseline

fourier_toolkit spreading and interpolation was '2-10 times slower' than FINUFFT v2.2.0 for identical kernel widths.

Computational Imaging: a Multi-Facet Perspective · EPFL · PhD

Left open by the authors

Problems the authors named and did not get to.

Left open

Implement Fourier Neural Operator architectures within equation-based optimization frameworks like OMLT for NLP solver compatibility. Blocker: None

Merging First-Principles with Machine Learning for the Optimization of Process and Energy Systems · Georgia Tech · PhD

Left open

Train Fourier Neural Operators as surrogate models for physics-based gradient evaluations to accelerate multi-fiducial ASPIRE. Blocker: None

Generative Models for Uncertainty of Medical and Seismic Imaging · Georgia Tech · PhD

Left open

Integrate Fourier Neural Operator surrogates with generative models like VAEs or GANs for inverse modeling in complex non-Gaussian random fields. Blocker: None

Physics Informed Deep Learning Application In High-Dimensional Groundwater Inverse Modeling Of Hydraulic Tomography · Georgia Tech · PhD

Left open

Replace finite-difference forward solvers with Fourier Neural Operators or PINNs in physics-guided seismic inversion, and evaluate GANs or Vision Transformers as encoders. Blocker: None

Regularizing seismic inverse problems : transdimensional and machine learning based strategies · UT Austin · PhD

Left open

Integrate neural operator surrogates, such as Fourier Neural Operators, to accelerate PDE evaluations during variational transport map training. Blocker: None

Gradient-based dimension reduction for Bayesian inverse problems and simulation-based inference · MIT · PhD

Left open

Develop a multi-fidelity Fourier Neural Operator combining coarse and refined temporal discretizations to forecast longer time horizons under GPU memory constraints. Blocker: None

Direct pore-scale modeling of foam transport in porous media and related machine learning · UT Austin · PhD

Left open

Extend randomized prior ensemble uncertainty quantification to Fourier Neural Operators and attention-based operator architectures using dimension reduction techniques. Blocker: None

Deep Learning And Uncertainty Quantification: Methodologies And Applications · Penn · PhD

Left open

Implement and evaluate algebraic multigrid techniques and Kron reduction for graph coarsening in spectral graph convolutional networks. Blocker: None

Leveraging topology, geometry, and symmetries for efficient Machine Learning · EPFL · PhD

Left open

Modify the ANN loss function to penalize underestimation errors more heavily to mitigate spectral saturation at high soil moisture levels. Blocker: Requires the private multi-modal UAV and GPR field datasets paired with in-situ soil moisture measurements collected in the thesis

Advancing Soil Moisture Mapping with Multi-Modal Drone Sensing and AI: Integrating GPR, Hyperspectral, and Thermal Imaging for Precision Agriculture · Virginia Tech · Doctorate

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