Comprehensive evaluation and systematic comparison of Gaussian process (GP) modelling applications in peptide quantitative structure-activity relationship

Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of inverse modeling. First, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Second, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Finally, we present an Automatic Gaussian Process Emulator (AGAPE) that approximates the forward physical model via interpolation, reducing the number of necessary nodes. Empirical evidence of the performance of these models will be presented through illustrative examples of vegetation monitoring and atmospheric modeling.

The Gaussian process regression (GPR) model, which is a powerful machine learning tool for probabilistic prediction, is introduced into slope displacement prediction. Using this model, the displacements of the slope of the permanent ship lock of the Three Gorges Project, the Wolongsi slope, and the high slope of Longtan hydropower station were predicted. In addition, the predictive uncertainty index (PUI) for describing the uncertainty of the predicted results was proposed, and the corresponding classification of the PUI was established. The study results demonstrate that the GPR model can self-adaptively acquire model parameter values and has satisfactory adaptability for predicting nonlinear time series of slope displacement. The proposed PUI and its classification based on the GPR model enable quantitative uncertainty analysis and, in turn, reliability evaluation of the predicted results. The GPR model provides a new approach to displacement prediction and safety management in slope engineering.

This paper describes a real-time data collection framework and an adaptive machining learning method for constructing a real-time energy prediction model for a machine tool. To effectively establish the energy consumption pattern of a machine tool over time, the energy prediction model is continuously updated with new measurement data to account for time-varying effects of the machine tool, such as tool wear and machine tool deterioration. In this work, a real-time data collection and processing framework is developed to retrieve raw data from a milling machine tool and its sensors and convert them into relevant input features. The extracted input features are then used to construct the energy prediction model using Gaussian Process (GP) regression. To update the GP regression model with real-time streaming data, we investigate the use of sparse representation of the covariance matrix to reduce the computational and storage demands of the GP regression. We compare computational efficiency of sparse GP to that of full GP regression model and show the effectiveness of the sparse GP regression model for tracking the variation in the energy consumption pattern of the target machine.

Gaussian process regression with skewed errors

Understanding the interaction between polymers and proteins is of interest for researchers in medicine, biology, food science, and water treatment, among other fields. The goal may be to create strong interactions with enzymes to improve their catalytic stability, while in nanomedicine and biomedical engineering, the focus is often on reducing protein adsorption on polymer surfaces. Researchers have developed libraries of polymers with various monomer combinations and tested their binding to different proteins to better understand these interactions. In this work, we aimed to identify the polymer with the highest or lowest binding affinity to all proteins, respectively, using Gaussian Process Regression (GPR). However, incorporating categorical features such as the type of monomer has not been widely applied in GPR. Here we compare a range of process models, which were coined Multiplicative kernel, Additive kernel, Easy to interpret Gaussian Process model (EzGP), Latent Variable Gaussian Processes (LVGP), and the Latent Map Gaussian Processes (LMGP) by their developers. The LVGP model was found to perform best on the polymer-protein data set, where the output for binding strength was given by Förster resonance energy transfer (FRET), which can be used to help generate large data sets for machine learning (ML). The polymer that had the highest affinity to glucose oxidase (GOx), uricase (Uri), casein (Cas), trypsin (Trp), carbonic anhydrase (CAn) and bovine serum albumin (BSA) carried positive charges as well as hydrophobic benzyl groups. Negatively charged monomers dominated the polymer that rejected the most proteins intermixed with some cationic units, reminiscent of zwitterionic polymers.

Machine learning (ML) force fields are revolutionizing molecular dynamics (MD) simulations as they bypass the computational cost associated with ab initio methods but do not sacrifice accuracy in the process. In this work, the GPyTorch library is used to create Gaussian process regression (GPR) models that are interfaced with the next-generation ML force field FFLUX. These models predict atomic properties of different molecular configurations that appear in a progressing MD simulation. An improved kernel function is utilized to correctly capture the periodicity of the input descriptors. The first FFLUX molecular simulations of ammonia, methanol, and malondialdehyde with the updated kernel are performed. Geometry optimizations with the GPR models result in highly accurate final structures with a maximum root-mean-squared deviation of 0.064 Å and sub-kJ mol-1 total energy predictions. Additionally, the models are tested in 298 K MD simulations with FFLUX to benchmark for robustness. The resulting energy and force predictions throughout the simulation are in excellent agreement with ab initio data for ammonia and methanol but decrease in quality for malondialdehyde due to the increased system complexity. GPR model improvements are discussed, which will ensure the future scalability to larger systems.

Over the last decade, innovations in satellite remote sensing (RS) and data science have widened the scope and relevance of agricultural monitoring and management applications at farm and territorial scales. Recently launched and upcoming hyperspectral satellite missions (e.g., ASI-PRISMA, DLR-ENMAP, Planet-Tanager, ESA-CHIME, Kuva-Hyperfield) provide high spectral resolution (< 10 nm) across the 400-2500 nm range, opening new frontiers for assessing biophysical and biochemical functional traits of agroecosystems, while advancements in machine learning (ML) and artificial intelligence (AI) allow the efficient exploitation of the information content of high-dimensionality spectral datasets. Here we summarize the results and lessons learned from three experiments in different European agricultural systems (croplands and grasslands), analysing how the synergy between hyperspectral imaging spectroscopy (field and satellite), ML, and foundation models could support adaptive agroecosystem management through the retrieval of vegetation and soil properties related to the nutrient cycle. The three case studies are:(1) Assessment of biomass and nutritional quality of Alpine pastures: Gaussian Process Regression (GPR) models were calibrated on 250 vegetation samples and field spectra collected in 2024 and 2025 from semi-natural pastures in Valtournanche (Aosta, Italy) and Val Camonica (Brescia, Italy). PRISMA-derived maps for biomass and leaf-level protein, and fiber content showed good accuracy against in-situ data (LAI [-] R2 = 0.71, RMSE = 0.89; Biomass [g · m-2] R2 = 0.67, RMSE = 178.71; DM [%] R2 = 0.65, RMSE = 2.70; CP [%] R2 = 0.58, RMSE = 0.52; ADF [%] R2 = 0.45, RMSE = 2.42; NDF [%] R2 = 0.50, RMSE = 0.61), allowing mapping of pasture metabolizable energy in support of grazing management.(2) Monitoring of nutritional status of paddy fields: GPR models were developed on 200 vegetation samples and field spectra collected in 2024 and 2025 in several fields located in the Ferrara region (Italy). These models, demonstrated on PRISMA and EnMAP time-series, effectively monitored crop development across a temporally and spatially independent test set (LAI [-] R2 = 0.83, RMSE = 0.30; Fresh Biomass [g · m-2] R2 = 0.72, RMSE = 627.67; LCC [μg · cm-2] R2 = 0.58, RMSE = 3.40; LNC [μg · cm-2] R2 = 0.34, RMSE = 22.51; CNC [g · m-2] R2 = 0.56, RMSE = 0.77).(3) Retrieval of Soil Organic Carbon (SOC) and soil Nitrogen (N) on arable lands: A transformer-based, sensor-agnostic deep learning architecture was fine-tuned on open global spectral libraries. When applied to EMIT and Tanager-1 imagery over the Po Plain (Italy) and Northern Netherlands regions, the model yielded high accuracy (SOC [%] R2 = 0.61, MAE = 0.37; N [%] R2 = 0.68, MAE = 0.12) against 289 independent field observations.Our findings demonstrate that satellite hyperspectral spectroscopy can complement operational multi-spectral missions, adding key information about agroecosystems nutritional status. Furthermore, we show that the use of pre-trained ML and AI models on global spectral libraries and field reflectance data allows accurate retrieval even in the absence of ground truth acquisition synchronous to the satellite overpass, offering a potential scalable solution for agroecosystems management and monitoring at landscape scale.

Elevated temperatures limit the peak performance of systems because of frequent interventions by thermal throttling. Non-uniform thermal states across system nodes also cause performance variation within seemingly equivalent nodes leading to significant degradation of overall performance. In this paper we present a framework for creating a lightweight thermal prediction system suitable for run-time management decisions. We pursue two avenues to explore optimized lightweight thermal predictors. First, we use feature selection algorithms to improve the performance of previously designed machine learning methods. Second, we develop alternative methods using neural network and linear regression-based methods to perform a comprehensive comparative study of prediction methods. We show that our optimized models achieve improved performance with better prediction accuracy and lower overhead as compared with the Gaussian process model proposed previously. Specifically we present a reduced version of the Gaussian process model, a neural network–based model, and a linear regression–based model. Using the optimization methods, we are able to reduce the average prediction errors in the Gaussian process from $4.2^\circ$ C to $2.9^\circ$ C. We also show that the newly developed models using neural network and Lasso linear regression have average prediction errors of $2.9^\circ$ C and $3.8^\circ$ C respectively. The prediction overheads are 0.22, 0.097, and 0.026 ms per prediction for reduced Gaussian process, neural network, and Lasso linear regression models, respectively, compared with 0.57 ms per prediction for the previous Gaussian process model. We have implemented our proposed thermal prediction models on a two-node system configuration to help identify the optimal task placement. The task placement identified by the models reduces the average system temperature by up to $11.9^\circ$ C without any performance degradation. Furthermore, these models respectively achieve 75, 82.5, and 74.17 percent success rates in correctly pointing to those task placements with better thermal response, compared with 72.5 percent success for the original model in achieving the same objective. Finally, we extended our analysis to a 16-node system and we were able to train models and execute them in real time to guide task migration and achieve on average 17 percent reduction in the overall system cooling power.

The control of underactuated balance robots is aimed at performing both the external (actuated) subsystem trajectory tracking and internal (unactuated) subsystem balancing tasks. In this article, we propose a learning-based control design for underactuated balance robots. The key idea integrates a model predictive control method to design the desired internal subsystem trajectory and perform the external subsystem tracking task, while an inverse dynamics controller is used to stabilize the internal subsystem to its desired trajectory. The control design is based on Gaussian process (GP) regression models that are learned from experiments without requiring <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge about the robot dynamics or the demonstration of successful stabilization. GP regression models also provide estimates of modeling uncertainties of the robotic systems, and these estimations are used to enhance control robustness to modeling errors. The learning-based control design is analyzed with guaranteed stability and performance. The proposed design is demonstrated by experiments on a Furuta pendulum and an autonomous bikebot.

Carbon use efficiency (CUE) is a key indicator in coupled biological-abiotic systems that accounts for their capacity of effectively retain carbon, offering insights of ecosystem functioning and the dynamics of carbon cycle. Generally, CUE assessments have been limited to an autotrophic perspective, quantifying plant efficiency while neglecting carbon losses from heterotrophic respiration. This provides an incomplete view of ecosystem carbon retention. To address this critical gap, we offer a global quantification of a more holistic ecosystem-level CUE, that incorporates all respiratory fluxes. This paper proposes a methodology for mapping ecosystem CUE at global scale from in situ data, remote sensing observations and machine learning. This data-driven approach exploits a Gaussian Processes Regression (GPR) model trained with CUE from eddy-covariance towers and concomitant observations from the Moderate resolution Imaging Spectroradiometer (MODIS). The performance of the model shows high correspondence (R2 = 0.84) and low error and bias (RMSE = 0.1, ME = 0.01) regarding in situ data. The execution of the GPR model upscaled CUE and associated uncertainty from tower level to global scale and provided multitemporal global CUE estimates from 2001 to 2023. The GPR model reports a mean global CUE of 0.43 ± 0.08 for this period. A preliminary analysis carried out for different climatic zones and biomes illustrates the increase of mean CUE from tropical (0.36 ± 0.08) to cold (0.55 ± 0.08) zones. The lowest mean CUE is found over evergreen broadleaved forests (0.37 ± 0.04), whereas the largest mean CUE is found over open shrublands (0.53 ± 0.12). Finally, a global trend of (-1.2 ± 0.3) × 10-3 yr- 1 is reported for mean global CUE from 2001 to 2023. The results of this work highlight the dependence of CUE on both climate and biome type, as well as the decreasing carbon sequestration power of vegetation at global scale, which is key to better understand the effects of climate change.

Predicting binary solution phase behavior of polymers has remained a challenge since the early theory of Flory-Huggins, hindering the processing, synthesis, and design of polymeric materials. Herein, we take a complementary data-driven approach by building a machine learning framework to make fast and accurate predictions of polymer solution cloud point temperatures. Using polystyrene, both upper and lower critical solution temperatures are predicted within experimental uncertainty (1-2 °C) with a deep neural network, Gaussian process regression (GPR) model, and a combination of polymer, solvent, and state features. The GPR model also enables intelligent exploration of solution phase space, where as little as 25 cloud points are required to make predictions within 2 °C for polystyrene of arbitrary molecular weight in cyclohexane. This study demonstrates the effectiveness of machine learning for the prediction of liquid-liquid equilibrium of polymer solutions and establishes a framework to incorporate other polymers and complex macromolecular architectures.

Quantitative prediction of subjective pain intensity from whole-brain fMRI data using Gaussian processes

Simulating root length density dynamics of sunflower in saline soils based on machine learning

Recently, machine learning (ML) models are increasingly being used in process analytical technology (PAT) frameworks for pharmaceutical manufacturing. Yet, the applications of ML-integrated PAT frameworks are limited by big data requirements. This work introduces a computational framework to develop data-efficient ML models to guide drug particle synthesis in an automated continuous flow precipitation platform. The framework incorporates classification algorithms to identify feasible (fouling-free) operating regions of the precipitation platform, a multiple-output Gaussian process (GP) regression model to relate key process parameters to the drug particle size, and active learning to optimally generate new data for training and validation of the GP model. The usefulness of the proposed framework is demonstrated on the synthesis of ibuprofen microparticles in an automated flow precipitation platform. We envision that properly trained GP models developed using the proposed framework can be employed to fine tune the drug particle size, targeting desired particle bioavailability and processability.

Active learning sensitivity analysis of γ'(L12) precipitate morphology of ternary co-based superalloys