Publications | Jim Boelrijk

Papers & preprints

2026

Shape-Aware Gaussian Process Kernels for Closed-Loop Bayesian Optimization of Gradients in Automated LC Method Development

Boelrijk, Jim, Detlefsen, Sebastian, Dürholt, Johannes P., and Haas, Christian P.

ChemRxiv preprint 2026

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Bayesian optimization (BO) is a promising strategy for accelerating gradient-elution liquid chromatography (LC) method development, but its practical success depends on several tightly coupled components. Here we report two main advances. First, for the Gaussian process (GP) surrogate models used within BO, we introduce a shape-aware gradient representation that compares gradient profiles directly through a Wasserstein-distance kernel, rather than through the pump-timetable coordinates used by standard representations. Second, we establish a robust automated acquisition and analysis workflow based on a trap phase that isolates gradient-driven elution and makes reliable closed-loop measurement possible. These are supported by three refinements: a flexible gradient domain with variable method duration and user-defined composition bounds, a window-relative sampler for monotonic gradient programs, and an adaptive reference point for multi-objective optimization. Across in silico and experimental datasets, Wasserstein-based representations generally predict separation quality more accurately than timetable-based approaches, especially when only a few training samples are available. This improved accuracy translates into more data-efficient single- and multi-objective optimization campaigns. Finally, we demonstrate the closed-loop framework in experimental case studies, where both single- and multi-objective campaigns improve upon a custom baseline method for a polymer-additive sample. Together, these results show that shape-aware gradient representations improve both GP predictive accuracy and BO sample efficiency, and that a flexible gradient domain, robust automated acquisition and analysis, and compatible sampling and optimization strategies enable effective closed-loop LC method development.

2025

Comparison of optimization algorithms for automated method development of gradient profiles

van Henten, Gerben B., Boelrijk, Jim, Kattenberg, Céline, Bos, Tijmen S., Ensing, Bernd, Forré, Patrick, and Pirok, Bob W.J.

Journal of Chromatography A 2025

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Optimization algorithms play an important role in method development workflows for gradient elution liquid chromatography. Their effectiveness has not been evaluated for chromatographic method development using standardized comparisons across factors such as sample complexity, chromatographic response functions (CRFs), gradient complexity, and application type. This study compares six optimization algorithms - Bayesian optimization (BO), differential evolution (DE), a genetic algorithm (GA), covariance-matrix adaptation evolution strategy (CMA-ES), random search, and grid search - for the development of gradient elution LC methods. Utilizing a multi-linear retention modeling framework, these algorithms were assessed across diverse samples, CRFs, and gradient segments, considering two observation modes: dry (in silico, deconvoluted), and wet (search-based, requiring peak detection). The optimization algorithms were evaluated based on their data (i.e. number of iterations) and time efficiency. Of the algorithms compared in this study, DE proved to be a highly competitive method for dry optimization purposes in terms of both data and time efficiency. BO outperformed all other algorithms in terms of data efficiency and was found to be most effective for search-based optimization, which requires a low number of iterations (<200). However, BO was found to be impractical for dry optimization requiring a large iteration budget due to its unfavorable computational scaling. It was observed that both the CRF and the sample have a strong influence on the efficiency of the algorithms, emphasizing the need for better benchmark samples and highlighting the importance of assessing CRF-induced complexity in the optimization landscape.

2024

Enhancing LC×LC separations through multi-task Bayesian optimization

Boelrijk, Jim, Molenaar, Stef R.A., Bos, Tijmen S., Dahlseid, Tina A., Ensing, Bernd, Stoll, Dwight R., Forré, Patrick, and Pirok, Bob W.J.

Journal of Chromatography A 2024

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Method development in comprehensive two-dimensional liquid chromatography (LC×LC) is a challenging process. The interdependencies between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, make trial-and-error method development time-consuming and highly dependent on user experience. Retention modeling and Bayesian optimization (BO) have been proposed as solutions to mitigate these issues. However, both approaches have their strengths and weaknesses. On the one hand, retention modeling, which approximates true retention behavior, depends on effective peak tracking and accurate retention time and width predictions, which are increasingly challenging for complex samples and advanced gradient assemblies. On the other hand, Bayesian optimization may require many experiments when dealing with many adjustable parameters, as in LC×LC. Therefore, in this work, we investigate the use of multi-task Bayesian optimization (MTBO), a method that can combine information from both retention modeling and experimental measurements. The algorithm was first tested and compared with BO using a synthetic retention modeling test case, where it was shown that MTBO finds better optima with fewer method-development iterations than conventional BO. Next, the algorithm was tested on the optimization of a method for a pesticide sample and we found that the algorithm was able to improve upon the initial scanning experiments. Multi-task Bayesian optimization is a promising technique in situations where modeling retention is challenging, and the high number of adjustable parameters and/or limited optimization budget makes traditional Bayesian optimization impractical.

2023

Multi-objective optimization via equivariant deep hypervolume approximation

Boelrijk, Jim, Ensing, Bernd, and Forré, Patrick

ICLR 2023

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Optimizing multiple competing objectives is a common problem across science and industry. The inherent inextricable trade-off between those objectives leads one to the task of exploring their Pareto front. A meaningful quantity for the purpose of the latter is the hypervolume indicator, which is used in Bayesian Optimization (BO) and Evolutionary Algorithms (EAs). However, the computational complexity for the calculation of the hypervolume scales unfavorably with increasing number of objectives and data points, which restricts its use in those common multi-objective optimization frameworks. To overcome these restrictions we propose to approximate the hypervolume function with a deep neural network, which we call DeepHV. For better sample efficiency and generalization, we exploit the fact that the hypervolume is scale-equivariant in each of the objectives as well as permutation invariant w.r.t. both the objectives and the samples, by using a deep neural network that is equivariant w.r.t. the combined group of scalings and permutations. We evaluate our method against exact, and approximate hypervolume methods in terms of accuracy, computation time, and generalization. We also apply and compare our methods to state-of-the-art multi-objective BO methods and EAs on a range of synthetic benchmark test cases. The results show that our methods are promising for such multi-objective optimization tasks.
Closed-loop automatic gradient design for liquid chromatography using Bayesian optimization

Boelrijk, Jim, Ensing, Bernd, Forré, Patrick, and Pirok, Bob

Analytica Chimica Acta 2023

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Contemporary complex samples require sophisticated methods for full analysis. This work describes the development of a Bayesian optimization algorithm for the automated and unsupervised development of gradient programs. The algorithm was tailored to LC using a Gaussian process model with a novel covariance kernel. To facilitate unsupervised learning, the algorithm was designed to interface directly with the chromatographic system. Single-objective and multi-objective Bayesian optimization strategies were investigated for the separation of a complex (n>80) dye mixture. The multi-objective strategy was found to be very powerful and flexible in terms of exploring the Pareto front. The single-objective strategy was found to be slightly faster in finding a satisfactory optimum. One additional advantage of the multi-objective approach was that it allows a trade-off to be made between multiple objectives. In general, the Bayesian optimization strategy was found to be particularly suitable, but not limited to, cases where retention modelling is not possible, although its scalability might be limited in terms of the number of parameters that can be simultaneously optimized.
Predicting RP-LC retention indices of structurally unknown chemicals from mass spectrometry data

Boelrijk, Jim, van Herwerden, Denice, Ensing, Bernd, Forré, Patrick, and Samanipour, Saer

Journal of Cheminformatics 2023

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Non-target analysis combined with high resolution mass spectrometry is considered one of the most comprehensive strategies for the detection and identification of known and unknown chemicals in complex samples. However, many compounds remain unidentified due to data complexity and limited structures in chemical databases. In this work, we have developed and validated a novel machine learning algorithm to predict the retention index (r_i) values for structurally (un)known chemicals based on their measured fragmentation pattern. The developed model, for the first time, enabled the predication of r_i values without the need for the exact structure of the chemicals, with an R^2 of 0.91 and 0.77 and root mean squared error (RMSE) of 47 and 67 r_i units for the Norman and amide test set, respectively. This fragment based model showed comparable accuracy in r_i prediction compared to conventional descriptor-based models that rely on known chemical structure, which obtained a R^2 of 0.85 with and RMSE of 67.
Computer-driven optimization of complex gradients in comprehensive two-dimensional liquid chromatography

Molenaar, Stef R.A., Bos, Tijmen S., Boelrijk, Jim, Dahlseid, Tina A., Stoll, Dwight R., and Pirok, Bob W.J.

Journal of Chromatography A 2023

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Method development in comprehensive two-dimensional liquid chromatography (LC × LC) is a complicated endeavor. The dependency between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, renders method development by "trial-and-error" time-consuming and highly dependent on user experience. In this work, an open-source algorithm for the automated and interpretive method development of complex gradients in LC × LC-mass spectrometry (MS) was developed. A workflow was designed to operate within a closed-loop that allowed direct interaction between the LC × LC-MS system and a data-processing computer which ran in an unsupervised and automated fashion. Obtaining accurate retention models in LC × LC is difficult due to the challenges associated with the exact determination of retention times, curve fitting because of the use of gradient elution, and gradient deformation. Thus, retention models were compared in terms of repeatability of determination. Additionally, the design of shifting gradients in the second dimension and the prediction of peak widths were investigated. The algorithm was tested on separations of a tryptic digest of a monoclonal antibody using an objective function that included the sum of resolutions and analysis time as quality descriptors. The algorithm was able to improve the separation relative to a generic starting method using these complex gradient profiles after only four method-development iterations (i.e., sets of chromatographic conditions). Further iterations improved retention time and peak width predictions and thus the accuracy in the separations predicted by the algorithm.

2022

Chemometric Strategies for Fully Automated Interpretive Method Development in Liquid Chromatography

Bos, Tijmen, Boelrijk, Jim, Molenaar, Stef, van’t Veer, Brian, Niezen, Leon, van Herwerden, Denice, Samanipour, Saer, Stoll, Dwight, Forré, Patrick, Ensing, Bernd, Somsen, Govert, and Pirok, Bob

Analytical Chemistry 2022

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The great potential gains in separation power and analysis time that can result from rigorously optimizing LC-MS and 2D-LC-MS methods for routine measurements has prompted many scientists to develop computer-aided method-development tools. The applicability of these has been proven in numerous applications, but their proliferation is still limited. Arguably, the majority of LC methods are still developed in a conventional manner, i.e. by analysts who rely on their knowledge and experience. In this work, a novel, open-source algorithm was developed for automated and interpretive method development of LC separations. A closed-loop workflow was constructed that interacted directly with the LC and ran unsupervised in an automated fashion. The algorithm was tested using two newly designed strategies. The first utilized retention modeling, whereas the second used the Bayesian-optimization machine-learning approach. In both cases, the algorithm could arrive within ten iterations at an optimum of the objective function, which included resolution and measurement time. The design of the algorithm was modular, so as to facilitate compatibility with previous works in literature and its performance thus hinged on each module (e.g., signal processing, choice of retention model, objective function). Key focus areas for further improvement were identified. Bayesian optimization did not require any peak tracking or retention modeling. Accurate prediction of elution profiles was found to be indispensable for the strategy using retention modeling. This is the first interpretive algorithm demonstrated with complex samples. Peak tracking was conducted using UV-Vis absorbance detection, but use of MS detection is expected to significantly broaden the applicability of the workflow.

2021

Bayesian optimization of comprehensive two-dimensional liquid chromatography separations

Boelrijk, Jim, Pirok, Bob, Ensing, Bernd, and Forré, Patrick

Journal of Chromatography A 2021

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Comprehensive two-dimensional liquid chromatography (LCxLC), is a powerful, emerging separation technique in analytical chemistry. However, as many instrumental parameters need to be tuned, the technique is troubled by lengthy method development. To speed up this process, we applied a Bayesian optimization algorithm. The algorithm can optimize LCxLC method parameters by maximizing a novel chromatographic response function based on the concept of connected components of a graph. The algorithm was benchmarked against a grid search (11,664 experiments) and a random search algorithm on the optimization of eight gradient parameters for four different samples of 50 compounds. The worst-case performance of the algorithm was investigated by repeating the optimization loop for 100 experiments with random starting experiments and seeds. Given an optimization budget of 100 experiments, the Bayesian optimization algorithm generally outperformed the random search and often improved upon the grid search. Moreover, the Bayesian optimization algorithm offered a considerably more sample-efficient alternative to grid searches, as it found similar optima to the grid search in far fewer experiments (a factor of 16–100 times less). This could likely be further improved by a more informed choice of the initialization experiments, which could be provided by the analyst’s experience or smarter selection procedures. The algorithm allows for expansion to other method parameters (e.g., temperature, flow rate, etc.) and unlocks closed-loop automated method development.

Theses

Bayesian optimization for liquid chromatography separations

Boelrijk, Jim

PhD thesis, University of Amsterdam 2024

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The increasing complexity of newly developed drugs requires increasingly sophisticated analytical tools. Compared to the synthesis and analysis of a small molecule drug such as paracetamol, the pharmaceutical industry today synthesizes highly specific drugs ranging from simple peptides to complete monoclonal antibodies. It is essential to qualify and quantify minor impurities in the synthesis. Meanwhile, liquid chromatography (LC), a powerful separation technique and the workhorse for this type of analysis, is being expanded with new variations, hyphenations, and settings to respond to these needs. While successful, this inevitably leads to more adjustable parameters, requiring considerable time, resources, and expertise to optimize effectively, hindering the breakthrough of powerful techniques such as two-dimensional LC (2D-LC). In this thesis, we investigate and develop sample efficient optimization techniques, which find optima in as few experiments as possible, that can automatically optimize LC methods and can make advanced techniques more accessible. In Part 1, we focus on the techniques of retention modeling and Bayesian optimization to optimize separations in LC and 2D-LC. We first study these techniques in separate use cases. We will see that both techniques are powerful on their own but have their strengths and weaknesses. Therefore, we focus on combining the strengths of both methods in the last chapter Part 1. Part 2 focusses on scaling up multi-objective optimization to a larger number of objectives by approximating the hypervolume indicator, a common objective for assessing the quality of a Pareto front, with equivariant deep learning. Lastly, we focus on the task of predicting retention indices (that is, normalized retention times) directly from mass spectrometry data using machine learning, potentially aiding in tracking chemicals of emerging concern.
Incorporating maximally localized Wannier functions into neural network potentials

Boelrijk, Jim

Master's thesis, University of Amsterdam 2019

Supervised by Ambuj Tiwari

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A efficient and accurate description of the inter-atomic potential energy surface (PES) is immensely important for molecular modelling, which is a fundamental tool for chemistry, computational biology and material science. While electronic structure methods are accurate, they are computationally expensive. Approximation methods typically are more computationally efficient, yet this comes with a reduction in accuracy. In recent years, the development of atomistic potentials using machine learning (ML) techniques have offered a solution to the accuracy versus efficiency problem. A type of ML, deep neural networks, can "learn" the topology of the PES by adjusting a number of parameters with the aim to reproduce a set of reference ab initio data as accurately as possible. These neural network potentials (NNPs) have been used to describe chemical systems, ranging from small organic molecules to complex alloys with high accuracy compared to the underlying electronic structure method, at a fraction of the computational cost. In addition, NNPs allow for linear scaling with system size, making them both accurate and efficient for the study of larger system. Their flexible construction also allows for the making and breaking of bonds, which enables reactivity studies. However, current NNP methods are purely atomistic, and although trained on electronic structure methods, do not incorporate electronic information directly, which limits their application to the computation of non-electronic properties. This thesis, investigated the incorporation of electronic information, in the form of maximally localised Wannier functions (MLWFs), within existing NNP frameworks in order to improve accuracy and transferability, while also allowing for the analysis of electronic information. Two scenarios where implemented in the DeepPot-SE method. In the first scenario, the Wannier function centers (WFCs) were considered as classical particles and incorporated in the NNP structure as well as in the local input. In scenario 2, the WFCs were only incorporated in the local input. Although scenario 1 resulted in high-accuracy predictions of the data set, it was not usable for molecular dynamics simulations. It was not evident what mass the WFCs should be given for proper propagation. In addition, a more complete data set must be used in order to cover the state-space of the WFCs, necessary for this scenario. Scenario 2 did not improve prediction accuracy over the conventional methods and a incorporation of the spreads of the WFCs might be necessary to improve this.