Chapter Four · failure evidence
What Gaussian Processes got wrong, from 68 dissertations
The records document practical challenges and empirical limitations encountered when deploying Gaussian process models across various engineering and scientific domains. Practitioners frequently observed that Gaussian processes struggle with computational scaling, extrapolation beyond training bounds, miscalibrated uncertainties, and competition from simpler or specialized baselines. These records come from PhD theses at 14 institutions, 2021 to 2026. 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.
Cubic computational complexity and memory scaling prevent application to large datasets or real-time tasks
Exact Gaussian process regression requires cubic matrix inversion scaling and heavy memory usage that quickly becomes intractable on large datasets or in online settings exceeding several hundred samples. Because of these computational bottlenecks, practitioners routinely reject exact formulations in favor of sparse inducing-point approximations, state-space representations, or alternative surrogate models.
Considered and rejected
Considered and rejected: Rejected exact O(N^3) Gaussian process regression in dynamic pairwise models in favor of linear-time state-space models via Kalman/RTS smoothers
Considered and rejected
Considered and rejected: Rejected covariance/uncertainty prediction during structural optimization in Gaussian Process buckling surrogates due to requirement of per-prediction linear solves; used only precomputed mean dot products.
Data-Driven and GPU-Accelerated Computational Methods for High-Fidelity Aerostructural Design · Georgia Tech
Considered and rejected
Considered and rejected: Rejected Gaussian Process Bayesian Optimization due to O(n^3) matrix inversion scaling, adopting neural network heteroscedastic surrogate models instead.
Surrogate Modeling for Semiconductor Packaging and Systems Using Machine Learning · Georgia Tech
Considered and rejected
Considered and rejected: Gaussian Process Regression (GPR) achieved the best RMSE in initial MATLAB tests but was rejected for full block-model estimation because it was computationally intractable for predicting ~6 million block centroids.
A Comparative Study of Machine Learning and Traditional Techniques for Grade Prediction and Grade-Tonnage Evaluation in a Small VMS Deposit · Virginia Tech
Tried and failed
Gaussian process implicit surfaces with derivative observations applied to 3D surface reconstruction. Outcome: infeasible cost. Reason: Surface normal observations added high computational cost without significant reconstruction accuracy improvement over off-surface points
Tried and failed
standard full Gaussian process regression applied to large dataset surrogate modeling. Outcome: infeasible cost. Reason: cubic computational complexity and memory limits on large flight loads dataset
Robust optimisation of wing aerostructural response · Cranfield
Tried and failed
pointwise Gaussian process regression applied to point cloud segmentation. Outcome: too slow. Reason: computational cost was too high for real-time processing and struggled with occlusion
Online vehicle trajectory extraction based on LiDAR data · Texas Tech
Tried and failed
Gaussian process regression applied to online adaptive control. Outcome: too slow. Reason: computational complexity became intractable with more than 500 data points
Safe Robot Planning and Control Using Uncertainty-Aware Deep Learning · Georgia Tech
Tried and failed
two-phase Gaussian process adaptive sampling applied to high-dimensional benchmark function optimization. Outcome: infeasible cost. Reason: prohibitive computational time and memory scaling at n=1500 in 12 dimensions
Active Learning Methods for Emulation and Inverse Design · Georgia Tech
Tried and failed
centered Gaussian process parameterization in Stan applied to transmission flow rate estimation. Outcome: infeasible cost. Reason: computationally intractable inversion of large covariance matrices
Bayesian methods for source attribution using HIV deep sequence data · Imperial
Considered and rejected
Considered and rejected: Decided against Gaussian Process Regression (GPR) for large output dimensions (fullerene/graphene) due to the computational expense of matrix inversion in high-dimensional spaces.
Transferable Coarse-Grained Models: From Hydrocarbons to Polymers, and Backmapped by Machine Learning · Virginia Tech
Considered and rejected
Considered and rejected: Rejected fully nonparametric Gaussian Process feedback kernels in favor of semiparametric delayed-exponential kernels due to massive computational integration costs and numerical instability during forecasting.
Considered and rejected
Considered and rejected: Multi-output Gaussian Process regression: rejected in favor of three independent scalar GPs due to computational intensity and complex model selection
Data-Driven, Non-Parametric Model Reference Adaptive Control Methods for Autonomous Underwater Vehicles · Virginia Tech
Considered and rejected
Considered and rejected: Rejected continuous spatio-temporal Gaussian Process learning without gridding due to prohibitive computational costs in sizeable urban areas.
Urban air pollution modelling with machine learning using fixed and mobile sensors · Imperial
Considered and rejected
Considered and rejected: Rejected treating collision as an independent coupled constraint via a parallel Gaussian process model during Bayesian optimization due to increased computational cost and convergence difficulty.
Origami based deployable surfaces: an optimization approach · Imperial
Considered and rejected
Considered and rejected: Rejected Gaussian Process integral-based traversability evaluation across continuous paths due to high computational cost, opting for upper confidence bound slope sampling inside an ellipse.
Safe Bipedal Locomotion and Navigation in Uncertain Environments · Georgia Tech
Considered and rejected
Considered and rejected: Rejected full exact Gaussian Process Bayesian inference (O(N^3) scaling) in favor of sparse variational Gaussian processes with M=500 inducing points (O(NM^2) scaling) for computational feasibility.
Computational Modeling of Multi-Agent, Continuous Decision Making in Competitive Contexts · DukeSpace
Gaussian process models underperform simpler baselines or alternative machine learning algorithms
In numerous regression and Bayesian optimization benchmarks, Gaussian process models delivered higher prediction errors than linear regressions, polynomial models, neural networks, or decision forests. These underperformances were especially noticeable in higher dimensional settings, discrete search spaces, and asymmetric or heavy-tailed target distributions.
Tried and failed
Gaussian process regression for multimodal signal fusion applied to locomotion sensor and oscillator fusion. Outcome: worse than baseline. Reason: Yielded no significant performance benefit over simple linear regression
A multi-sensor, hybrid model- and signal-based control system for powered lower limb prostheses · Imperial
Tried and failed
Gaussian process as surrogate forward model applied to offline model-based optimization. Outcome: worse than baseline. Reason: underperformed compared to neural network surrogate models on top-1 evaluation tasks
Distributionally Robust Machine Intelligence for Medicine and Scientific Discovery · Penn
Tried and failed
Gaussian process regression applied to spatial productivity regression. Outcome: worse than baseline. Reason: Severe cross-validation performance with negative R² values compared to random forests
Lost to a baseline
Binding score method slightly outperformed Gaussian process regression in RMSE in the least complex linear simulation model (Model 1) under high running variable correlations.
Measurement in K-12 Policy Analysis · Harvard
Lost to a baseline
Radial basis function (RBF) surrogate outperformed Gaussian process regression on the 6-dimensional OTL circuit benchmark function
RETROSPECTIVE AND EXPLORATORY ANALYSES FOR ENHANCING THE SAFETY OF ROTORCRAFT OPERATIONS · Georgia Tech
Lost to a baseline
Binding score method slightly outperformed Gaussian process regression in precision and RMSE in the least complex linear simulation model (Model 1) under very high running variable correlations.
Measurement in K-12 Policy Analysis · Harvard
Lost to a baseline
Gaussian Process regression was outperformed by Neural Network architectures in higher dimensions (e.g., 20D MMT dataset) in terms of estimated uncertainty.
Lost to a baseline
3rd-order polynomial regression beat Gaussian process regression for port transmission variance prediction with LOOCV MSE 1.71e-3 vs 0.0214 across the spectrum.
Statistical Modeling of the Effects of Process Variations on Silicon Photonics · MIT
Lost to a baseline
Model-based sensor placement methods (conditional Entropy and Mutual Information criteria based on Gaussian Processes) were outperformed by data-driven placement methods (Greedy SVR and PCA with QR-Pivoting) for contact localization accuracy.
Machine-Learning-Driven Haptic Sensor Design · Publikationssystem UB Tuebingen
Considered and rejected
Considered and rejected: Rejected standard Bayesian optimization (BaO) for parameter space exploration because BaO is constrained to Gaussian process regression, which was outperformed by linear ridge regression in modeling brain responses.
An active learning framework for quantifying the effect of neuromodulation · Georgia Tech
Lost to a baseline
Gaussian Process surrogate underperformed GradientBoosting during Bayesian optimization, dipping below p=0.05 around iteration 50.
Data-Driven Design of Recycling-Friendly Aluminium Alloys · MIT
Considered and rejected
Considered and rejected: Rejected standard Gaussian process regression for Bayesian optimization exploration in HOLMES due to poor scaling in high-dimensional binary search spaces, adopting Genetic Algorithm recombination/mutation instead
Robust Representation Learning and Real-Time Serving of Deep Models for Health Time Series · Georgia Tech
Lost to a baseline
Integrated MBO (Bayesian Optimization with standard Gaussian Process targeting mean performance) performed worse than decoupled MNN and MTree methods on asymmetric, heavy-tailed performance distributions.
Machine Learning for Efficient and Robust Datacenter Performance Management · DukeSpace
Hyperparameter optimization and prior misspecification lead to biased or miscalibrated uncertainty estimates
Practitioners found that gradient-based tuning and improper priors frequently produced severe overconfidence or excessively wide predictive standard deviations. The models also exhibited severe sensitivity to leverage points and outliers, while oversmoothing priors caused frequentist credible interval coverage to collapse.
Tried and failed
Gaussian process regression applied to nonlinear sinusoidal degradation signals. Outcome: worse than baseline. Reason: Deviated more from expected range under Bayesian likelihood estimation compared to neural network alternatives
Uncertainty Management in the Prediction of the Remaining Useful Life of Ball Bearings and Li-ion Batteries · Texas Tech
Tried and failed
gradient-based hyperparameter optimization for sparse Gaussian processes applied to robotic manipulation dynamic modeling. Outcome: overfit. Reason: optimizers consistently overestimated signal variance, treating true functional features as noise
Decision-Making Architectures for Control of Uncertain Systems · Georgia Tech
Tried and failed
standard Gaussian process regression applied to data with leverage points and outliers. Outcome: did not generalise. Reason: mean hyperparameter optimization via weighted least squares causes severe bias from vertical outliers and bad leverage points
Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models · Virginia Tech
Tried and failed
Gaussian process regression with polynomial trend term applied to astronomical radial velocity time series. Outcome: no signal. Reason: Did not improve Bayesian log-evidence compared to simpler model
Detection and Characterization of Hot Super-Earth Exoplanets · MIT
Tried and failed
Gaussian process regression using flat priors applied to multidimensional surrogate function modelling. Outcome: worse than baseline. Reason: Linear bias from flat priors caused model overconfidence, degrading predictive likelihood as sample size increased.
Uncertainty quantification and management in multidisciplinary design optimisation. · Cranfield
Tried and failed
Gaussian process with fully Bayesian hyperparameter integration applied to aeroelastic gust response surrogate modeling. Reason: Hyperparameter posterior integration yielded overly diffuse predictive distributions with excessive variance
Uncertainty quantification and management in multidisciplinary design optimisation. · Cranfield
Tried and failed
Gaussian process regression with polynomial kernel applied to uncertainty quantification and predictive modeling. Outcome: did not generalise. Reason: Severely overestimated predictive standard deviation, producing overly wide and uninformative confidence intervals
Engineering-driven Machine Learning Methods for System Intelligence · Virginia Tech
Tried and failed
Gaussian process regression with oversmoothing prior applied to nonparametric regression uncertainty quantification. Reason: Prior smoothness exceeding true function regularity causes asymptotic frequentist credible interval coverage to collapse to zero
Theoretical and methodological advances in Bayesian semiparametrics with variational inference · Imperial
Considered and rejected
Considered and rejected: Rejected factor analysis directions in Gaussian process covariance due to severe over-fitting on validation sets.
A methodology for evaluating the performance of tow-steered composite technology over a range of planform configurations · Georgia Tech
Standard Gaussian process kernels fail to extrapolate beyond training bounds and struggle with nonlinear dynamics
Stationary kernels caused predictions to revert rapidly to the prior mean when extrapolating outside the training domain or across large unobserved regions. They also failed to capture complex nonlinear physical couplings, leading to underpredicted peak amplitudes and massive extrapolation errors.
Tried and failed
Gaussian process regression applied to equipment health degradation modeling. Outcome: did not generalise. Reason: Multivariate normal distributional assumptions do not match operational engineering data
Tried and failed
Gaussian process regression applied to solving nonlinear partial differential equations. Outcome: worse than baseline. Reason: forced linear approximations limited performance on non-linear operators
Merging First-Principles with Machine Learning for the Optimization of Process and Energy Systems · Georgia Tech
Tried and failed
Gaussian process regression for adsorption property prediction applied to flexible porous material gas loading. Outcome: did not generalise. Reason: linear and kernel regression could not capture complex nonlinear coupling and extrapolate loading ratios accurately
Efficient and Accurate Incorporation of Flexibility and Defects Into the Modeling of Adsorption in Metal-Organic Frameworks · Georgia Tech
Tried and failed
precision-weighted aggregation of local gaussian processes applied to spatial satellite temperature prediction. Outcome: did not generalise. Reason: aggregation degraded predictions across large unobserved spatial extrapolation regions
Precision Aggregated Local Models · Virginia Tech
Tried and failed
tree-based Gaussian process regression applied to extrapolation of performance distributions. Outcome: did not generalise. Reason: generated massive prediction errors during extrapolation beyond the training domain
Statistical Methods for Variability Management in High-Performance Computing · Virginia Tech
Tried and failed
proper orthogonal decomposition with Gaussian process regression applied to spatiotemporal thermal fluid fluctuations. Outcome: did not generalise. Reason: failed to capture prominent peak frequencies and underpredicted signal amplitudes
Tried and failed
Gaussian processes with RBF kernels applied to extrapolating oscillatory frequency spectra. Outcome: did not generalise. Reason: Rapid correlation decay causes predictions to quickly revert to the prior outside the training range.
Rapid Assessment and Uncertainty Quantification for Electrical Responses Using Machine Learning Based Predictions and Extrapolations · Georgia Tech
Considered and rejected
Considered and rejected: Rejected using Gaussian Processes directly to map feedstock characteristics to BMP biogas production curves because GP lacks extrapolation capability outside training data bounds.
Deep and multi-output Gaussian process extensions suffer from inference instability and inaccurate approximations
Multi-output and deep Gaussian process architectures suffered from estimation errors in task covariances and suboptimal posterior parameter sampling. Furthermore, variational approximations of deep Gaussian process posteriors yielded inaccurate variance estimates that disrupted downstream acquisition functions.
Tried and failed
multi-task Gaussian processes applied to low-noise multi-output regression. Outcome: worse than baseline. Reason: estimation error in the task covariance matrix when sampling variation is small
Distribution-free statistical process control and Bayesian feasibility determination · Georgia Tech
Tried and failed
multi-output Gaussian process with auxiliary information applied to Bayesian optimization. Outcome: worse than baseline. Reason: performed barely better than random sampling while being computationally prohibitive
Lost to a baseline
Single-fidelity Gaussian process regression (GPR) baseline for crystallization tendency (RMSE 17.04%) was outperformed by multi-fidelity co-kriging models (RMSE 12.58% and 13.06%)
Machine Learning based Models for the Design of Solid Polymer Electrolytes · Georgia Tech
Tried and failed
Gaussian approximation of deep Gaussian process posteriors applied to Bayesian optimization uncertainty estimation. Reason: yielded poor uncertainty quantification and inaccurate variance estimates for acquisition functions
Physics-informed Machine Learning for Digital Twins of Metal Additive Manufacturing · Virginia Tech
Lost to a baseline
Deep Gaussian Process (DGP) achieved lower coverage than the simpler shallow GP in leave-one-out cross-validation for Florida TC error fields.
Bayesian Uncertainty Quantification while Leveraging Multiple Computer Model Runs · Virginia Tech
Lost to a baseline
On the Langley Glide-Back Booster experiment, both 2- and 3-layer DGPs were unable to match the out-of-sample RMSE of treed Gaussian processes (TGP).
Deep Gaussian Process Surrogates for Computer Experiments · Virginia Tech
Tried and failed
deep Gaussian process active learning applied to aerodynamic dynamics emulation. Outcome: worse than baseline. Reason: suboptimal Bayesian MCMC parameter inference hindered performance compared to standard kriging
Active Learning Methods for Emulation and Inverse Design · Georgia Tech
Considered and rejected
Considered and rejected: Rejected standard Gaussian approximation of DGP posteriors via DSVI because variance estimates were inaccurate for BO acquisition.
Physics-informed Machine Learning for Digital Twins of Metal Additive Manufacturing · Virginia Tech
Homoscedasticity and standard kernel assumptions fail on heteroscedastic, discrete, or complex data
Assuming uniform noise variance failed to accommodate spatially and temporally varying measurement uncertainty across physical observation channels. In addition, standard continuous formulations proved unsuited for modeling sparse discrete count distributions and required cumbersome kernel modifications.
Tried and failed
linear and rational-quadratic Gaussian process kernels applied to anatomical motion regression. Outcome: worse than baseline. Reason: linear and rational-quadratic kernels underperformed compared to standard radial basis function kernels
Considered and rejected
Considered and rejected: Rejected non-zero Gaussian Process mean functions (m != 0) in Bayesian optimization due to lack of prior knowledge and computational simplicity.
Understanding and mitigating universal adversarial perturbations for computer vision neural networks · Imperial
Considered and rejected
Considered and rejected: Learning heteroscedastic noise via a second Gaussian process, rejected in favor of directly supplying empirical bin velocity uncertainties
A Gaussian Process Model for the Local Galactic Velocity Field · Queens University Institutional Repository
Tried and failed
homoscedastic Gaussian process regression applied to noisy measurement interpolation. Outcome: worse than baseline. Reason: Arbitrary constant noise assumption failed to capture spatially varying observational uncertainty.
Considered and rejected
Considered and rejected: Homoscedastic Gaussian process regression with globally constant noise variance; rejected because it failed to capture spatially and temporally varying intrinsic scatter in edge plasma measurements.
Tried and failed
Gaussian process regression applied to sparse discrete spatial count data. Outcome: worse than baseline. Reason: failed to model spatial distribution of sparse discrete counts effectively
Adaptive Robotic Search and Sampling of Sparse Natural Phenomena · MIT
Tried and failed
Gaussian process active learning applied to high-dimensional state-action correlation modeling. Outcome: worse than baseline. Reason: failed to capture complex multi-dimensional correlations across the task space
Learning and optimization of anticipatory feedback controllers for robot manipulation · EPFL
Left open by the authors
Problems the authors named and did not get to.
Left open
Learn robot motion model uncertainty from data using Gaussian processes as priors within the state estimation factor graph. Blocker: None
Methods for Vision-Based State Estimation and Online Motion Model Adaptation Using Multi-Modal Measurements and Motion Constraints · Publikationssystem UB Tuebingen
Left open
Implement online Gaussian Process Regression hyperparameter retraining at runtime and measure allocation delay and robot distribution in simulation. Blocker: None
MACROSCOPIC ENSEMBLE METHODS FOR MULTI ROBOT TASK ASSIGNMENT IN DYNAMIC ENVIRONMENTS · Penn
Left open
Implement Gaussian Process Regression instead of uniform RBF grid placement to model non-linear surface force corrections in dynamical system modulation. Blocker: None
Left open
Implement online Gaussian Process regression to learn environmental disturbances concurrently during multi-robot task allocation and RCBF-based control execution. Blocker: None
A Data-Driven Approach to Long-Duration Autonomy for Heterogenous Robot Teams · Georgia Tech
Left open
Extend static sensor allocation, reward functions, and motion planning to continuous space using Gaussian process regression and interpolation. Blocker: None
Hybrid Sensor Networks for Active Monitoring: Collaboration, Optimization, And Resilience · Georgia Tech
Left open
Replace the nonstationary Gaussian process regression component with a deep Gaussian process regression model for RUL prediction and uncertainty quantification. Blocker: None
Left open
Benchmark and compare different Gaussian process regression kernels and models for modeling stellar activity in radial velocity data of young stars. Blocker: None
The epoch of giant planet migration : searching for young planets within the stellar noise · UT Austin
Left open
Implement and compare Gaussian process regression and Bayesian calibration for uncertainty quantification in the Wire Arc DED PINN framework. Blocker: None
Improving Part Quality in Wire Arc DED through Machining-Based Hybrid Manufacturing and Scientific Machine Learning · Georgia Tech
Left open
Replace Gaussian mixture modeling of potential outcome residuals with non-parametric clustering algorithms to estimate complier average treatment effects under measurement error. Blocker: None
Left open
Implement online local approximate Gaussian processes using mean-square prediction error design criteria instead of k-nearest neighbors for neighborhood selection. Blocker: None
Multi-Stage Modeling with Gaussian Processes · Virginia Tech
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